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97 results on '"Équipe Méthodes et Algorithmes en Commande (LAAS-MAC)"'

1. Solving Nonlinear Algebraic Loops Arising in Input-Saturated Feedbacks

Author

Franco Blanchini, Giulia Giordano, Francesco Riz, Luca Zaccarian, Dipartimento di Ingegneria Industriale [Trento], University of Trento [Trento], Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), and ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018)

Subjects
[SPI]Engineering Sciences [physics], Iterative methods, Control and Systems Engineering, Linear matrix inequalities, Heuristic algorithms, Software packages, Approximation algorithms, Simulation, Tuning, Electrical and Electronic Engineering, Computer Science Applications
Abstract

We propose a dynamic augmentation scheme for the asymptotic solution of the nonlinear algebraic loops arising in well-known input saturated feedbacks typically designed by solving linear matrix inequalities (LMIs). We prove that the existing approach based on dynamic augmentation, which replaces the static loop by a dynamic one through the introduction of a sufficiently small time constant, works under some restrictive sufficient well-posedness conditions, requiring the existence of a diagonal Lyapunov matrix. However it can fail in general, even when the algebraic loop is well-posed. Then, we propose a novel approach whose effectiveness is guaranteed whenever wellposedness holds. We also show how this augmentation allows preserving the guaranteed region of attraction with Lyapunovbased designs, as long as a gain parameter is sufficiently large. We finally propose an adaptive version of the scheme where this parameter is adjusted online. Simulation results show the effectiveness of the proposed solutions.

Published
2023

2. Hybrid Control of Self-Oscillating Resonant Converters

Author

Nicola Zaupa, Luis Martínez-Salamero, Carlos Olalla, Luca Zaccarian, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Université Toulouse III - Paul Sabatier (UT3), Universitat Rovira i Virgili, Dipartimento di Ingegneria Industriale [Trento], University of Trento [Trento], Spanish Ministry of Science and Innovation (Grant Number: PID2019-111443RB-100), International Exchange Program of the University of Trento, Italy, ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018), ZAUPA, Nicola, and Systèmes Dynamiques Hybrides et en Réseau - - HANDY2018 - ANR-18-CE40-0010 - AAPG2018 - VALID

Subjects
[SPI.AUTO] Engineering Sciences [physics]/Automatic, Control and Systems Engineering, Power electronics, [SPI.NRJ]Engineering Sciences [physics]/Electric power, Electrical and Electronic Engineering, Stability of hybrid systems, Resonant converters, Power conversion, Lyapunov methods, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; We describe parallel and series resonant converters via a unified set of input-dependent coordinates whose dynamics is intrinsically hybrid. We then propose a hybrid feedback showing a self-oscillating behavior whose amplitude and frequency can be adjusted by a reference input ranging from zero to π. For any reference value in that range we give a Lyapunov function certifying the existence of a unique nontrivial hybrid limit cycle whose basin of attraction is global except for the origin. Our results are confirmed by experimental results on a series resonant converter prototype.

Published
2023

3. SONC optimization and exact nonnegativity certificates via second-order cone programming

Author

Magron, Victor, Wang, Jie, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), ANR-18-ERC2-0004,COPS,Optimisation garantie pour la vérification des systèmes cyber-physiques(2018), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), European Project: 813211,H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (Main Programme), H2020-EU.1.3.1. - Fostering new skills by means of excellent initial training of researchers ,10.3030/813211,POEMA(2019), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, and European Project: 813211,H2020,POEMA(2019)

Subjects
FOS: Computer and information sciences, Computer Science - Symbolic Computation, Algebra and Number Theory, MathematicsofComputing_NUMERICALANALYSIS, Symbolic Computation (cs.SC), sum of binomial squares, exact nonnegativity certificate, Mathematics - Algebraic Geometry, Computational Mathematics, rounding-projection algorithm, Optimization and Control (math.OC), sum of nonnegative circuit polynomials, second-order cone programming, polynomial optimization, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, FOS: Mathematics, second-order conerepresentation, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Algebraic Geometry (math.AG), Mathematics - Optimization and Control
Abstract

The second-order cone (SOC) is a class of simple convex cones and optimizing over them can be done more efficiently than with semidefinite programming. It is interesting both in theory and in practice to investigate which convex cones admit a representation using SOCs, given that they have a strong expressive ability. In this paper, we prove constructively that the cone of sums of nonnegative circuits (SONC) admits a SOC representation. Based on this, we give a new algorithm for unconstrained polynomial optimization via SOC programming. We also provide a hybrid numeric-symbolic scheme which combines the numerical procedure with a rounding-projection algorithm to obtain exact nonnegativity certificates. Numerical experiments demonstrate the efficiency of our algorithm for polynomials with fairly large degree and number of variables., 29 pages, 7 tables, 6 figures, extended version of the article published in the proceedings of ISSAC 2020. arXiv admin note: text overlap with arXiv:1906.06179

Published
2023

4. Data-driven stabilization of input-saturated systems

Author

Valentina Breschi, Luca Zaccarian, Simone Formentin, Control Systems, Eindhoven University of Technology [Eindhoven] (TU/e), Dipartimento di Ingegneria Industriale [Trento], University of Trento [Trento], Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Dipartimento di Electtronica, Informazione e Bioingegneria [Politecnico Milano] (POLIMI), Politecnico di Milano [Milan] (POLIMI), and ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018)

Subjects
[SPI]Engineering Sciences [physics], Control and Optimization, Data-driven control, Control and Systems Engineering, input saturation, Linear systems, State feedback, Lyapunov methods
Abstract

International audience; We provide a data-driven stabilization approach for input-saturated systems with formal Lyapunov guarantees. Through a generalized sector condition, we propose a convex design algorithm based on linear matrix inequalities for obtaining a regionally stabilizing datadriven static state-feedback gain. Regional, rather than global, properties allow us to address non-exponentially stable plants, thereby making our design broad in terms of applicability. Moreover, we discuss consistency issues and introduce practical tools to deal with measurement noise. Numerical simulations show the effectiveness of our approach and its sensitivity to the features of the dataset.

Published
2023

5. Existence and Completeness of Solutions to Extended Projected Dynamical Systems and Sector-Bounded Projection-Based Controllers

Author

W. P. M. H. Heemels, Aneel Tanwani, Eindhoven University of Technology [Eindhoven] (TU/e), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
Nonsmooth dynamics, Control and Optimization, Control and Systems Engineering, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Projection based control
Abstract

Projection-based control (PBC) systems have significant engineering impact and receive considerable scientific attention. To properly describe closed-loop PBC systems, extensions of classical projected dynamical systems are needed, because partial projection operators and irregular constraint sets (sectors) are crucial in PBC. These two features obstruct the application of existing results on existence and completeness of solutions. To establish a rigorous foundation for the analysis and design of PBC, we provide essential existence and completeness properties for this new class of discontinuous systems.

Published
2023

6. Stabilization using shifted equilibria for saturated discrete-time linear systems⋆

Author

Braun, Philipp, Jungers, Marc, Zaccarian, Luca, Jungers, Marc, Australian National University (ANU), Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), and ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018)

Subjects
[SPI.AUTO] Engineering Sciences [physics]/Automatic, Systems with saturation, Asymptotic stabilization, Control and Systems Engineering, discrete-time systems, semidefinite programming, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Lyapunov methods
Abstract

International audience; We discuss controller designs for asymmetric saturated discrete-time linear systems. Under the assumption that a locally stabilizing controller of the origin is known, we augment the original controller with an additional term that vanishes in a neighborhood of the origin. The augmented controller outperforms the original controller in terms of the estimate of the region of attraction. The paper translates the results discussed in Braun et al. (2022a,b), from the continuous-time setting to the discrete-time setting, and numerically verifies that the results derived for continuous-time systems are recovered if the discrete-time system is obtained through an Euler discretization of a continuous-time system with a sufficiently small sampling rate.

Published
2023

7. Robust Global Asymptotic Stabilization of Linear Cascaded Systems With Hysteretic Interconnection

Author

Alessandro Bosso, Luca Zaccarian, Andrea Tilli, Matteo Barbieri, Department of electrical, electronic and information engineering 'GUGLIELMO MARCONI' [Bologna] (DEI), Alma Mater Studiorum Università di Bologna [Bologna] (UNIBO), Dipartimento di Ingegneria Industriale [Trento], University of Trento [Trento], Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Bosso A., Zaccarian L., Tilli A., and Barbieri M.

Subjects
Lyapunov method, Control and Optimization, Control and Systems Engineering, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Hysteresi, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], switched systems, Prandtl-Ishlinskii operator
Abstract

International audience; We address the problem of setpoint regulation for cascaded minimum-phase linear systems interconnected through a scalar hysteresis, modeled as a Prandtl-Ishlinskii operator. Employing well-posed constrained differential inclusions to represent the hysteretic dynamics, we formulate the control problem in terms of stabilization of a compact set of equilibria depending on the hysteresis states. For our design, we firstly consider a proportional-integral controller for linear systems with hysteretic input, and provide model-free sufficient conditions based on high-gain arguments for closed-loop stability. Then, the controller is dynamically extended to obtain an inversion-free stabilizer of the overall cascade. For the presented schemes, we prove robust global asymptotic stability of a compact set that ensures setpoint regulation, regardless of the hysteresis states.

Published
2023

8. Distributed Hybrid Observer With Prescribed Convergence Rate for a Linear Plant Using Multi-Hop Decomposition

Author

Riccardo Bertollo, Pablo Millan, Luis Orihuela, Alexandre Seuret, Luca Zaccarian, Università degli Studi di Trento (UNITN), Universidad Loyola Andalucía = Loyola University Andalucía, Universidad de Sevilla / University of Sevilla, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), and ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018)

Subjects
Hybrid observer, Control and Optimization, Input-to-State Stability, Sensor network, Control and Systems Engineering, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], FOS: Mathematics, Distributed estimation, Linear systems, Dynamical Systems (math.DS), Mathematics - Dynamical Systems
Abstract

With a continuous-time formulation of the multihop decomposition, we propose a distributed hybrid observer for a sensor network where the plant and local observers run in continuous time and the information exchange among the sensing nodes is sampled-data. Process disturbances, measurement noise and communication noise are considered, and we prove that under some necessary detectability assumptions the observer gains can be tuned to guarantee exponential ISS with a prescribeda convergence rate. Simulations illustrate the performance of the proposed observer.

Published
2023

9. A note on the wave equation controlled with a dynamic saturating boundary control

Author

Gauvrit, Mario, Prieur, Christophe, Tarbouriech, Sophie, Ecole Normale Supérieure Paris-Saclay (ENS Paris Saclay), GIPSA - Infinite Dimensional Dynamics (GIPSA-INFINITY), GIPSA Pôle Automatique et Diagnostic (GIPSA-PAD), Grenoble Images Parole Signal Automatique (GIPSA-lab), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Grenoble Alpes (UGA), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Jochen Trumpf, Robert Mahony, and ANR-19-P3IA-0003,MIAI,MIAI @ Grenoble Alpes(2019)

Subjects
well-posedness, Control and Systems Engineering, saturation, Infinite-dimensional systems, stability, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; This paper studies the nonlinear systems obtained by considering a wave equation in closed loop with a nonlinear dynamical boundary controller. The controller is subject to a magnitude limitation and modeled by a linear ordinary differential equation with a saturation map in the input. The well-posedness of the obtained infinite-dimensional system is first studied and then two stability results are given. These two stability results apply for two cascade cases and give sufficient conditions for the asymptotic stability of the equilibrium. The well-posedness is proven by using nonlinear semigroups techniques, whereas the global asymptotic stability results are obtained by Lyapunov-based arguments in infinite-dimensional state space.

Published
2023

10. Hybrid Control of Self-Oscillating Resonant Converters With Three-Level Input

Author

Nicola Zaupa, Carlos Olalla, Isabelle Queinnec, Luis Martinez-Salamero, Luca Zaccarian, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Université Toulouse III - Paul Sabatier (UT3), Universitat Rovira i Virgili, Dipartimento di Ingegneria Industriale [Trento], University of Trento [Trento], Spanish Ministry of Science and Innovation (Grant Number: PID2019-111443RB-100 and PID2020-120151RB-I00), MUR through PRIN Grant DOCEAT (Grant Number: 2020RTWES4), and ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018)

Subjects
Control and Optimization, Control and Systems Engineering, Power electronics, [SPI.NRJ]Engineering Sciences [physics]/Electric power, Stability of hybrid systems, Lyapunov methods, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; We propose a hybrid feedback law inducing self-oscillating behavior in second-order resonant converters. With our controller, the converter switches at the resonant frequency of its tank, without the need of external oscillators. In addition, the output amplitude can be adjusted by a reference signal ranging from zero to π /2. The amplitude modulation is then performed while maintaining an approximately constant switching frequency. Theoretical results show uniqueness and almost global asymptotic stability of a nontrivial hybrid limit cycle. Experimental results show that a circuit implementing the new controller successfully matches the desirable simulated behavior.

Published
2023

11. Exploiting Constant Trace Property in Large-scale Polynomial Optimization

Author

Ngoc Hoang Anh Mai, J. B. Lasserre, Victor Magron, Jie Wang, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Equipe Polynomial OPtimization (LAAS-POP), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), ANR-18-ERC2-0004,COPS,Optimisation garantie pour la vérification des systèmes cyber-physiques(2018), European Project: 813211,H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (Main Programme), H2020-EU.1.3.1. - Fostering new skills by means of excellent initial training of researchers ,10.3030/813211,POEMA(2019), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), and European Project: 813211,H2020,POEMA(2019)

Subjects
Optimization and Control (math.OC), Applied Mathematics, FOS: Mathematics, MathematicsofComputing_NUMERICALANALYSIS, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Optimization and Control, Software
Abstract

We prove that every semidefinite moment relaxation of a polynomial optimization problem (POP) with a ball constraint can be reformulated as a semidefinite program involving a matrix with constant trace property (CTP). As a result such moment relaxations can be solved efficiently by first-order methods that exploit CTP, e.g., the conditional gradient-based augmented Lagrangian method. We also extend this CTP-exploiting framework to large-scale POPs with different sparsity structures. The efficiency and scalability of our framework are illustrated on second-order moment relaxations for various randomly generated quadratically constrained quadratic programs., 43 pages, 6 algorithms, 23 tables

Published
2022

12. Graph-based conditions for feedback stabilization of switched and LPV systems

Author

Della Rossa, Matteo, Lima, Thiago Alves, Jungers, Marc, Jungers, Raphaël M., Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institute of Information and Communication Technologies, Electronics and Applied Mathematics (ICTEAM), Université Catholique de Louvain = Catholic University of Louvain (UCL), Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018), and European Project: 864017,L2C

Subjects
Piecewise-Defined Functions, Feedback Stabilization, Optimization and Control (math.OC), Graph Theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Switched Systems, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, Systems and Control (eess.SY), [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Optimization and Control, Electrical Engineering and Systems Science - Systems and Control, Linear matrix inequalities
Abstract

This paper presents novel stabilizability conditions for switched linear systems with arbitrary and uncontrollable underlying switching signals. We distinguish and study two particular settings: i) the \emph{robust} case, in which the active mode is completely unknown and unobservable, and ii) the \emph{mode-dependent} case, in which the controller depends on the current active switching mode. The technical developments are based on graph-theory tools, relying in particular on the path-complete Lyapunov functions framework. The main idea is to use directed and labeled graphs to encode Lyapunov inequalities to design robust and mode-dependent piecewise linear state-feedback controllers. This results in novel and flexible conditions, with the particular feature of being in the form of linear matrix inequalities (LMIs). Our technique thus provides a first controller-design strategy allowing piecewise linear feedback maps and piecewise quadratic (control) Lyapunov functions by means of semidefinite programming. Numerical examples illustrate the application of the proposed techniques, the relations between the graph order, the robustness, and the performance of the closed loop.

Published
2023

13. Feedback Interconnections of Passive Linear Cone Complementarity Systems

Author

Brogliato, Bernard, Tanwani, Aneel, Modélisation, simulation et commande des systèmes dynamiques non lisses (TRIPOP), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
[SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

This paper is largely concerned with generic interconnections of a class of passive nonsmooth nonlinear dynamical systems, namely linear cone complementarity systems (LCCS). Criteria which guarantee the passivity of the interconnection are given. Asymptotic stability is studied in a particular case. Examples from nonsmooth circuits and switching DAEs (Differential Algebraic Equations) illustrate the theory.

Published
2023

14. On the Viability and Invariance of Proper Sets under Continuity Inclusions in Wasserstein Spaces

Author

Bonnet-Weill, Benoît, Frankowska, Hélène, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), and Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)

Subjects
Mathematics - Analysis of PDEs, Viability, Optimization and Control (math.OC), Continuity Inclusions, Dynamics with Time Discontinuities, Optimal Transport, Invariance, FOS: Mathematics, 28B20, 34G25, 46N20, 49Q22, [MATH]Mathematics [math], Mathematics - Optimization and Control, Wasserstein Geometry, Analysis of PDEs (math.AP)
Abstract

In this article, we derive necessary and sufficient conditions for the existence of solutions to state-constrained continuity inclusions in Wasserstein spaces whose right-hand sides may be discontinuous in time. These latter are based on fine investigations of the infinitesimal behaviour of the underlying reachable sets, through which we show that up to a negligible set of times, every admissible velocity of the inclusion can be approximately realised as the metric derivative of a solution of the dynamics, and vice versa. Building on these results, we are able to establish necessary and sufficient geometric conditions for the viability and invariance of stationary and time-dependent constraints, which involve a suitable notion of contingent cones in Wasserstein spaces, presented in ascending order of generality. We then close the article by exhibiting two prototypical examples of constraints sets appearing in applications for which one can compute relevant subfamilies of contingent directions., Comment: 43 pages

Published
2023

15. A singular perturbation approach for the control of electromagnetic actuators

Author

Ariba, Yassine, Gouaisbaut, Frédéric, Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
Lyapunov method, Electromagnetic actuator, Electromagnetic actuator nonlinear control application Lyapunov method singular perturbation method, singular perturbation method, nonlinear control application, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

Pre-print paper, submitted version for the IFAC World Congress 2023; The paper is devoted to the control of electromagnetic actuators. Compared to most results in the literature, the design explicitly takes into account the nonlinearities and the magnetic saturation. An approach based on singularly perturbed systems is proposed to take advantage of the different time scales of the model and provide a minimal complexity control law. Associated with an integral action, this control law ensures accuracy and robustness w.r.t some disturbances and some unknown parameters of the actuator. The use of the singular perturbation method allows also to limit the implementation complexity compared to classical methods such as backstepping control. The synthesis of the control law is then tested through simulations that illustrate the efficiency of the method.

Published
2023

16. Anti-windup coordination strategy around a fair equilibrium in resource sharing networks

Author

Agner, Felix, Kergus, Pauline, Rantzer, Anders, Tarbouriech, Sophie, Zaccarian, Luca, Lund University [Lund], COmmande et DIAgnostic des Systèmes Electriques (LAPLACE-CODIASE), LAboratoire PLasma et Conversion d'Energie (LAPLACE), Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and University of Trento [Trento]

Subjects
[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Electrical Engineering and Systems Science - Systems and Control
Abstract

International audience; This paper aims at coordinating interconnected agents where the control input of each agent is limited by the control input of others. In that sense, the systems have to share a limited resource over a network. Such problems can arise in different areas and it is here motivated by a simplified district heating example. When the shared resource is insufficient for the combined need of all systems, the resource will have to be shared in an optimal fashion. In this scenario, we want the systems to automatically converge to an optimal equilibrium. The contribution of this paper is the proposal of a control architecture where each separate system is controlled by a local PI controller. The controllers are then coordinated through a global rank-one anti-windup signal. It is shown that the equilibrium of the proposed closed-loop system minimizes the infinity-norm of stationary state deviations. Convergence is investigated via a randomized numerical study, and a district heating-inspired example illustrates the utility of the proposed method.

Published
2023

17. Procédé de commande d’un actionneur éléctromagnétique d’un détendeur, et actionneur et détendeur configuré pour mettre en œuvre ledit procédé

Author

Deschaux, Flavien, Ariba, Yassine, de Seze, Damien, Gouaisbaut, Frédéric, Dugué, François, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), Centre National d'Etudes Spatiales - Direction Des Lanceurs. (CNES), Conception de systèmes et technologie mécanique (CSTM) (CSTM), and CNES / CSTM / CNRS / ICAM site de Toulouse

Subjects
Classification CIB : F16K 17/20, F16K 1/04, F16K 31/02, G05B 15/00, G05D 7/06Classification CPC : G05D 16/2013, Y02B 30/70, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

Famille de brevets : FR3121193A1 ; WO2022200710A1; National audience; La présente invention concerne le domaine des actionneurs électromagnétiques,configurés en particulier pour actionner un détendeur à commande électronique, plusparticulièrement un tel détendeur adapté pour réguler la pression d’un fluide en aval dudétendeur.

Published
2023

18. Carleman estimates for the wave equation in heterogeneous media with non-convex interface

Author

Lucie Baudouin, Pamela Godoy, Alberto Mercado, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Universidad Tecnica Federico Santa Maria [Valparaiso] (UTFSM), ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), and Université Fédérale Toulouse Midi-Pyrénées

Subjects
Transmission system, Applied Mathematics, 010102 general mathematics, Wave equation, 02 engineering and technology, [MATH]Mathematics [math], 0101 mathematics, Carleman estimates, 021001 nanoscience & nanotechnology, 0210 nano-technology, 01 natural sciences, Analysis
Abstract

International audience; A wave equation whose main coefficient is discontinuous models the evolution of waves amplitude in a media composed of at least two different materials, in which the propagation speed is different. In our mathematical setting, the spatial domain where the partial differential equation evolves is an open bounded subset of R^2 and the wave speed is assumed to be constant in each one of two sub-domains, separated by a smooth and possibly non-convex interface. This article is concerned with the construction of Carleman weights for this wave operator, allowing generalizations of previous results to the case of an interface that is not necessarily the boundary of a convex set. Indeed, using the orthogonal projection onto this interface, we define convex functions satisfying the transmission conditions imposed by the equation, such that, under usual hypothesis on the sign of the jump of the wave speed, can be used as Carleman weights.

Published
2022

19. Co-design of an event-triggered dynamic output feedback controller for discrete-time LPV systems with constraints

Author

Valter J. S. Leite, Carla de Souza, Sophie Tarbouriech, Eugênio B. Castelan, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Centro Federal de Educação Tecnológica de Minas Gerais (CEFET-MG), and Universidade Federal de Santa Catarina = Federal University of Santa Catarina [Florianópolis] (UFSC)

Subjects
Regional stability, Co-design, Output feedback, Lyapunov stability, 0209 industrial biotechnology, Computer Networks and Communications, Computer science, Applied Mathematics, Control (management), 02 engineering and technology, Saturation, Optimal control, Dynamic controller, Linear parameter-varying systems, [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, Discrete time and continuous time, Exponential stability, Control and Systems Engineering, Control theory, Signal Processing, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Event-triggered control
Abstract

International audience; This paper investigates an event-triggered control design approach for discrete-time linear parametervarying (LPV) systems under control constraints. The proposed conditions can simultaneously design a parameter-dependent dynamic output feedback controller and an event generator, ensuring the closedloop system's regional asymptotic stability. Based on the Lyapunov stability theory, these conditions are given in terms of linear matrix inequalities (LMIs). Moreover, using some proposed optimization procedures, it is possible to minimize the number of sensor transmissions, maximize the estimation of the region of attraction of the origin, and incorporate optimal control criteria into the formulation. Through numerical examples, some comparisons with other approaches in the literature evidence the proposed technique's efficacy.

Published
2022

20. Joint Coefficient and Solution Estimation for the 1D Wave Equation: An Observer-Based Solution to Inverse Problems

Author

Constantinos Kitsos, Mathieu Bajodek, Lucie Baudouin, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), and Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1)

Subjects
inverse problems, Control and Systems Engineering, coefficient identification/estimation in the wave equation, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Electrical and Electronic Engineering, observers for PDEs, Computer Science Applications
Abstract

International audience; The estimation of an unknown source coefficient and of the solution to a 1-dimensional (1D) wave equation via exponentially convergent state observers is the problem under consideration in this work. The coefficient is assumed to depend on the space variable only and to be polynomial. The main observation information for this inverse problem is the value of the solution to the wave equation in a subinterval of the domain, including also some of its higher-order spatial derivatives. In order to estimate the source coefficient, we turn it into a new state as in finite-dimensional parameter identification approaches. However in this infinite-dimensional setting, this requires the introduction of a novel indirect approach involving an infinite-dimensional state transformation. Sufficient conditions allow the design of a composite observer consisting of an internal observer, which estimates in higher regularity spatial norms both the source term and the solution on a subinterval, and a boundary observer, in order to eventually provide the estimation of the solution everywhere. The observer convergence is proven by means of Lyapunov analysis. An extension of this approach to the case of the identification of a potential in the wave equation is finally considered, which is a nonlinear inverse problem since here, in the equation, the unknown coefficient multiplies the solution.

Published
2022

21. Anti-windup-like Compensator Synthesis for Discrete-Time Quantized Control Systems

Author

Alsamadi, S., Ferrante, F., Tarbouriech, S., IMT École nationale supérieure des Mines d'Albi-Carmaux (IMT Mines Albi), Institut Mines-Télécom [Paris] (IMT), Centre Génie Industriel (CGI), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Università degli Studi di Perugia = University of Perugia (UNIPG), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), and Masaaki Kanno

Subjects
LMIs, [SPI]Engineering Sciences [physics], Quantized control, Optimization and Control (math.OC), Control and Systems Engineering, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, anti-windup like compensator design, Systems and Control (eess.SY), stability, Mathematics - Optimization and Control, Electrical Engineering and Systems Science - Systems and Control
Abstract

This paper addresses the problem of designing an anti-windup like compensator for discrete-time linear control systems with quantized input. The proposed compensator provides a correction signal proportional to the quantization error that fed to the controller. The compensator is designed to ensure that solutions to the closed-loop systems converge in finite time into a compact set containing the origin that can be tuned by the designer. A numerically tractable algorithm with feasibility guarantees is provided for the design of the compensator. The proposed results are illustrated on an academic example and an open-loop unstable aircraft system., Comment: Extended version of the conference paper. V1 is submitted for presentation at the 10th IFAC Symposium on Robust Control Design ROCOND 2022. V2 and V3, and V4 fix some minor oversights

Published
2022

22. Dynamic event-triggered stabilization for the Schrödinger equation

Author

Koudohode, Florent, Baudouin, Lucie, Tarbouriech, Sophie, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, and Tarbouriech, Sophie

Subjects
[PHYS]Physics [physics], Observability inequality, [SPI.AUTO] Engineering Sciences [physics]/Automatic, Control and Systems Engineering, [INFO]Computer Science [cs], Schrödinger equation, Dynamic event-triggering mechanism, [MATH]Mathematics [math], Exponential stability, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; The paper presents a dynamic event-triggering mechanism for the constant and the localized damped linear Schrödinger equation. The following results are tackled: the existence of solution to the closed-loop event-triggered control system; the avoidance of the Zeno behavior due to the absence of any accumulation point of the sequence of time instants and the exponential stability based on energy estimate through the observability inequality. A simulation example based on the one-dimensional Schrödinger equation is presented to validate the theoretical results.

Published
2022

23. Open wind tunnel experiments of the DarkO tail-sitter longitudinal stabilization with constant wind

Author

Sansou, Florian, Demourant, Fabrice, Hattenberger, Gautier, Loquen, Thomas, Zaccarian, Luca, ENAC - Equipe Optim (OPTIM), Ecole Nationale de l'Aviation Civile (ENAC), ONERA / DTIS, Université de Toulouse [Toulouse], ONERA-PRES Université de Toulouse, Dipartimento di Ingegneria Industriale [Trento], University of Trento [Trento], Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
Control and Systems Engineering, Hovering, Linear robust control, UAVs, Tail-sitter, UAVs Tail-sitter Hovering Linear robust control, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; We describe an experimental platform for testing the DarkO tail-sitter drone in an open wind tunnel experiment. The DarkO convertible UAV is developed and 3D printed at the Ecole Nationale de l'Aviation Civile (ENAC), in Toulouse (France). The objective of the experimental platform is to allow testing control laws in a realistic and secure context. We propose a test bench with a single degree of freedom corresponding to the drone pitch axis. We design a linear proportional/integral feedback hovering stabilizer in the presence of constant wind, and we illustrate its effectiveness in stabilizing a hovering position through experimental results.

Published
2022

24. Stability and Performance Verification of Dynamical Systems Controlled by Neural Networks: Algorithms and Complexity

Author

Milan Korda, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
Control and Optimization, Optimization and Control (math.OC), Control and Systems Engineering, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, FOS: Mathematics, Dynamical Systems (math.DS), Mathematics - Dynamical Systems, [MATH]Mathematics [math], Mathematics - Optimization and Control
Abstract

International audience; This note makes several observations on stability and performance verification of nonlinear dynamical systems controlled by neural networks. First, we show that the stability and performance of a polynomial dynamical system controlled by a neural network with semialgebraically representable activation functions (e.g., ReLU) can be certified by convex semidefinite programming. The result is based on the fact that the semialgebraic representation of the activation functions and polynomial dynamics allows one to search for a Lyapunov function using polynomial sum-of-squares methods; the approach can be viewed as a special case of the general framework of [3]. Second, we remark that even in the case of a linear system controlled by a neural network with ReLU activation functions, the problem of verifying asymptotic stability is undecidable. Finally, under additional assumptions, we establish a converse result on the existence of a polynomial Lyapunov function for this class of systems. Numerical results on academic examples of dimension up to 50 and neural networks with several hundred neurons demonstrate the method.

Published
2022

25. Event-Triggered Neural Network Control for LTI Systems

Author

C. de Souza, S. Tarbouriech, A. Girard, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Laboratoire des signaux et systèmes (L2S), and CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)

Subjects
[SPI]Engineering Sciences [physics], Control and Optimization, Quadratic constraints, Neural network control, Lyapunov theory, Control and Systems Engineering, Event-triggered control, Linear Matrix inequalities, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; This paper addresses the problem of eventtriggered control (ETC) of discrete-time linear time-invariant (LTI) systems stabilized by neural network controllers. The event-triggering mechanisms (ETMs) is proposed to update only a portion of the layers required to maintain stability and satisfactory performance of the feedback system, thus reducing the computational cost associated with the evaluation of the neural network. Sufficient convex conditions in the form of linear matrix inequalities (LMIs) are provided to compute the triggering parameters and characterize an estimate of the domain of attraction for the feedback system. The formulation is based on the use of Lyapunov theory and a set of generalized sector constraints that deal with the nonlinear activation functions, represented in this case by the saturation function. Optimization procedures are also formulated to effectively reduce the amount of computation in the neural network. An example borrowed from the literature is used to illustrate the effectiveness of the proposal.

Published
2023

26. Tour d’horizon sur les systèmes dynamiques hybrides

Author

Queinnec, Isabelle, Tarbouriech, Sophie, Zaccarian, Luca, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Dipartimento di Ingegneria Industriale [Trento], and University of Trento [Trento]

Subjects
Stabilité analyse, Systèmes dynamiques hybrides, Systèmes dynamiques hybrides Stabilité Attracteur Systèmes à réinitialisation Hybrid dynamical systems Stability Attractor Reset systems, Systèmes à réinitialisation Hybrid dynamical systems, [SPI]Engineering Sciences [physics], Stabilité Lyapunov, Reset systems, Attractor, Attracteur, [MATH]Mathematics [math], Stabilité, Stability
Abstract

National audience; This paper provides an overview of hybrid dynamical systems, namely systems that comprise continuous and discrete dynamics. After presenting a mathematical framework that allows describing this class of systems, the key ideas behind the solution and stability concepts are presented mathematically and illustrated by examples. Some sufficient conditions for proving global uniform asymptotic stability are then proposed, by relying on Lyapunov functions, possibly associated with the LaSalle invariance principle.; Cet article propose un tour d’horizon sur les systèmes dynamiques hybrides, c’est-à-dire les systèmes combinant des dynamiques continues et des dynamiques discrète. Après avoir présenté le formalisme hybride qui permet de traiter cette classe de systèmes, les concepts clés de solutions et de stabilité sont abordés via des définitions mathématiques et illustrés par des exemples. Des conditions suffisantes pour prouver la stabilité asymptotique uniforme globale pour un système dynamique hybride sont alors proposées via l’utilisation d’une fonction de Lyapunov, associée dans certains cas au principe d’invariance de LaSalle.

Published
2023

27. Finite-time stability properties of Lur'e systems with piecewise continuous nonlinearities

Author

Mariano, Simone, Postoyan, Romain, Zaccarian, Luca, Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Dipartimento di Ingegneria Industriale [Trento], University of Trento [Trento], Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), and ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018)

Subjects
[SPI]Engineering Sciences [physics], FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Systems and Control (eess.SY), Dynamical Systems (math.DS), Mathematics - Dynamical Systems, Electrical Engineering and Systems Science - Systems and Control, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

We analyze the stability properties of Lur'e systems with piecewise continuous nonlinearities by exploiting the notion of set-valued Lie derivative for Lur'e-Postnikov Lyapunov functions. We first extend an existing result of the literature to establish the global asymptotic stability of the origin under a more general sector condition. We then present the main results of this work, namely additional conditions under which output and state finite-time stability properties also hold for the considered class of systems. We highlight the relevance of these results by certifying the stability properties of two engineering systems of known interest: mechanical systems affected by friction and cellular neural networks.

Published
2023
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28. Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients

Author

Victor Magron, Mohab Safey El Din, Trung-Hieu Vu, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Equipe Polynomial OPtimization (LAAS-POP), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Polynomial Systems (PolSys), LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), DesCartes funded by the CREATE Programme on AI-based Decision making in Critical Urban Systems, FastQI funded by the institute Quantum technologies in Occitanie, EPICS funded by the Gaspard Monge Program for Optimization and operationnal research, Fondation Jacques Hadamard, ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), ANR-18-ERC2-0004,COPS,Optimisation garantie pour la vérification des systèmes cyber-physiques(2018), European Project: 813211,H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (Main Programme), H2020-EU.1.3.1. - Fostering new skills by means of excellent initial training of researchers ,10.3030/813211,POEMA(2019), Magron, Victor, Artificial and Natural Intelligence Toulouse Institute - - ANITI2019 - ANR-19-P3IA-0004 - P3IA - VALID, TREMPLIN-ERC - Optimisation garantie pour la vérification des systèmes cyber-physiques - - COPS2018 - ANR-18-ERC2-0004 - TERC - VALID, Polynomial Optimization, Efficiency through Moments and Algebra - POEMA - - H20202019-01-01 - 2022-12-31 - 813211 - VALID, Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, and European Project: 813211,H2020,POEMA(2019)

Subjects
Computer Science - Symbolic Computation, FOS: Computer and information sciences, Optimization and Control (math.OC), Applied Mathematics, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, FOS: Mathematics, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Symbolic Computation (cs.SC), Mathematics - Optimization and Control, Software, Theoretical Computer Science
Abstract

Assessing non-negativity of multivariate polynomials over the reals, through the computation of {\em certificates of non-negativity}, is a topical issue in polynomial optimization. This is usually tackled through the computation of {\em sums-of-squares decompositions} which rely on efficient numerical solvers for semi-definite programming. This method faces two difficulties. The first one is that the certificates obtained this way are {\em approximate} and then non-exact. The second one is due to the fact that not all non-negative polynomials are sums-of-squares. In this paper, we build on previous works by Parrilo, Nie, Demmel and Sturmfels who introduced certificates of non-negativity modulo {\em gradient ideals}. We prove that, actually, such certificates can be obtained {\em exactly}, over the rationals if the polynomial under consideration has rational coefficients and we provide {\em exact} algorithms to compute them. We analyze the bit complexity of these algorithms and deduce bit size bounds of such certificates., Comment: 24 pages, 2 tables

Published
2023

29. Event-triggered boundary damping of a linear wave equation

Author

Baudouin, Lucie, Marx, Swann, Tarbouriech, Sophie, Valein, Julie, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Laboratoire des Sciences du Numérique de Nantes (LS2N), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ), Institut Élie Cartan de Lorraine (IECL), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
practical stability, Zeno behavior free, Optimization and Control (math.OC), [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, FOS: Mathematics, Wave equation, Wave equation event-triggered boundary control Lyapunov functionals practical stability Zeno behavior free, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Lyapunov functionals, 34H15, 93B52, 93C20, 35L05, Mathematics - Optimization and Control, event-triggered boundary control
Abstract

This article presents an analysis of the stabilization of a multidimensional partial differential wave equation under a well designed event-triggering mechanism that samples the boundary control input. The wave equation is set in a bounded domain and the control is performed through a boundary classical damping term, where the Neumann boundary condition is made proportional to the velocity. First of all, existence and regularity of the solution to the closed- loop system under the event-triggering mechanism of the control are proven. Then, sufficient conditions based on the use of a specific Lyapunov functional are proposed in order to ensure that the solutions converge into a compact set containing the origin, that can be tuned by the designer. Furthermore, as expected, any Zeno behavior of the closed-loop system is avoided.

Published
2023
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30. Symmetry reduction and recovery of trajectories of optimal control problems via measure relaxations

Author

Augier, Nicolas, Henrion, Didier, Korda, Milan, Magron, Victor, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Equipe Polynomial OPtimization (LAAS-POP), Czech Technical University in Prague (CTU), This work was supported by the FastQI grant funded by the Institut Quantique Occitan, the PHC Proteus grant 46195TA as well as by the National Research Foundation, Prime Minister’s Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme., ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), European Project: 813211,H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (Main Programme), and H2020-EU.1.3.1. - Fostering new skills by means of excellent initial training of researchers ,10.3030/813211,POEMA(2019)

Subjects
49M20, 90C22, 93C10, 28A99, Optimization and Control (math.OC), FOS: Mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Optimization and Control
Abstract

We address the problem of symmetry reduction of optimal control problems under the action of a finite group from a measure relaxation viewpoint. We propose a method based on the moment-SOS aka Lasserre hierarchy which allows one to significantly reduce the computation time and memory requirements compared to the case without symmetry reduction. We show that the recovery of optimal trajectories boils down to solving a symmetric parametric polynomial system. Then we illustrate our method on the symmetric integrator and the time-optimal inversion of qubits., Comment: 38 pages, 23 figures

Published
2023
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31. Event-triggered Neural Network Control using Quadratic Constraints for Perturbed Systems

Author

de Souza, Carla, Girard, Antoine, Tarbouriech, Sophie, Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT), Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018)

Subjects
Event-triggering mechanisms, [SPI]Engineering Sciences [physics], Quadratic constraints, Neural network control, Emulation
Abstract

International audience; This paper investigates the event-triggered control problem for perturbed systems under neural network controllers. We propose a novel event-triggering mechanism, based on local sector conditions related to the activation functions, to reduce the computational cost associated with the neural network evaluation. It avoids redundant computations by updating only a portion of the layers instead of evaluating periodically the whole neural network. Sufficient conditions in terms of matrix inequalities are established to design the parameters of the event-triggering mechanism and compute an inner-approximation of the region of attraction for the perturbed feedback system. The theoretical conditions are obtained by using a quadratic Lyapunov function and an abstraction of the activation functions via quadratic constraints to decide whether the outputs of the layers should be transmitted through the network or not. Such conditions allow us to reduce the computational activity on the neural network while preserving the stability and performance level of the perturbed feedback system. To illustrate the efficacy of our approach, we consider the nonlinear inverted pendulum system stabilized by a trained neural network.

Published
2023

32. Soft-Reset Control with Max-of-Quadratics Lyapunov Certificates

Author

R. Bertollo, A.R. Teel, L. Zaccarian, Dipartimento di Ingegneria Industriale [Trento], University of Trento [Trento], Center for Control, Dynamical-Systems, and Computation [Santa Barbara] (CCDC), University of California [Santa Barbara] (UC Santa Barbara), University of California (UC)-University of California (UC), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), and ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018)

Subjects
stability of hybrid systems, Reset control, computational methods, Control and Systems Engineering, computer-aided control design, Electrical and Electronic Engineering, hybrid systems, Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; We further develop a novel control paradigm encoding the core behavior of a reset control system within a continuoustime feedback, described by a differential inclusion. A tuning knob allows adjusting how close the continuous-time feedback resembles the behavior of the underlying reset controller. The Lyapunov conditions that we derive naturally lead to a sum-of-squares formulation allowing for the design of max-of-quadratics Lyapunov certificates certified by polynomial multipliers. A few application examples confirm the practical effectiveness of the proposed solutions.

Published
2023

33. LMI conditions for contraction, integral action, and output feedback stabilization for a class of nonlinear systems

Author

Giaccagli, Mattia, Andrieu, Vincent, Tarbouriech, Sophie, Astolfi, Daniele, Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique (LAGEPP), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-École Supérieure de Chimie Physique Électronique de Lyon (CPE)-Centre National de la Recherche Scientifique (CNRS), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018), and ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011)

Subjects
LMIs, Contraction, observers, monotonic, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], nonlinear systems, sector bound, integral action, incremental stability, separation principle
Abstract

International audience; This article focuses on the class of linear systems coupled with a nonlinearity satisfying a sector bound or a monotonic condition. First, we present a set of sufficient conditions based on Linear Matrix Inequalities (LMIs) to establish if such a system defines a contraction. Then, we propose a contractive state-feedback control law designed via the use of LMIs which may include nonlinear terms. Furthermore, the design is extended to the case in which an integral action is included in order to achieve constant output regulation. Following a similar approach, the design of contractive observers for the aforementioned class of systems is also considered. Finally, based on previous conditions, we establish a new nonlinear separation principle in which the feedback and the observer gains may be designed independently. Throughout the paper, we illustrate our results by means of practical examples.

Published
2023

34. Anti-Windup Design for a Reaction-Diffusion Equation

Author

Shreim, Suha, Ferrante, Francesco, Prieur, Christophe, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Università degli Studi di Perugia = University of Perugia (UNIPG), GIPSA - Infinite Dimensional Dynamics (GIPSA-INFINITY), GIPSA Pôle Automatique et Diagnostic (GIPSA-PAD), Grenoble Images Parole Signal Automatique (GIPSA-lab), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Grenoble Images Parole Signal Automatique (GIPSA-lab), and Université Grenoble Alpes (UGA)

Subjects
[SPI]Engineering Sciences [physics], [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], [INFO]Computer Science [cs], Partial differential equations, linear matrix inequalities, saturated control, Lyapunov methods
Abstract

International audience; This paper focuses on the anti-windup design for saturated one-dimensional linear reaction-diffusion equation. The considered open-loop system admits a finite number of unstable poles. We consider a scenario in which the system is controlled via a dynamic, finite-dimensional output feedback controller ensuring closed-loop exponential stability. Within this setting, a method is proposed to design a dynamic, finitedimensional anti-windup compensator to maximize the region of attraction and minimize the effect of external perturbations. More precisely, the sufficient conditions for the local exponential stability of the closed-loop system are derived and expressed in terms of a set of matrix inequalities. Using generalized sector conditions and proper change of variables, the conditions are then recast as an optimization problem solving linear matrix inequalities. A numerical example is provided to showcase the proposed method and highlight its effectiveness on the system performance.

Published
2023

35. Long term dynamics of the subgradient method for Lipschitz path differentiable functions

Author

Bolte, Jerome, Pauwels, Edouard, Rios-Zertuche, Rodolfo, Toulouse School of Economics (TSE-R), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Argumentation, Décision, Raisonnement, Incertitude et Apprentissage (IRIT-ADRIA), Institut de recherche en informatique de Toulouse (IRIT), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), ANR-19-CE23-0017,MaSDOL,Mathématiques de l'optimisation déterministe et stochastique liées à l'apprentissage profond(2019), and ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011)

Subjects
I.2.6, G.1.6, Applied Mathematics, General Mathematics, [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO], Numerical Analysis (math.NA), Dynamical Systems (math.DS), Optimization and Control (math.OC), FOS: Mathematics, Mathematics - Numerical Analysis, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Dynamical Systems, Mathematics - Optimization and Control, 65K10 (Primary), 37A50, 37B35, 62M45 (Secondary)
Abstract

We consider the long-term dynamics of the vanishing stepsize subgradient method in the case when the objective function is neither smooth nor convex. We assume that this function is locally Lipschitz and path differentiable, i.e., admits a chain rule. Our study departs from other works in the sense that we focus on the behavoir of the oscillations, and to do this we use closed measures. We recover known convergence results, establish new ones, and show a local principle of oscillation compensation for the velocities. Roughly speaking, the time average of gradients around one limit point vanishes. This allows us to further analyze the structure of oscillations, and establish their perpendicularity to the general drift., Comment: 28 pages, 2 figures

Published
2022

36. Order of Legendre-LMI conditions to assess stability of time-delay systems

Author

Mathieu Bajodek, Alexandre Seuret, Frédéric Gouaisbaut, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Universidad de Sevilla, Bajodek, Mathieu, Universidad de Sevilla. Departamento de Ingeniería de Sistemas y Automática, Universidad de Sevilla. TEP102: Ingeniería Automática y Robótica, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), and Universidad de Sevilla / University of Sevilla

Subjects
Time-delay systems, [SPI.AUTO] Engineering Sciences [physics]/Automatic, Control and Systems Engineering, Computer Science::Systems and Control, Polynomial approximation, Stability conditions, LMI, Converse Lyapunov theorem, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; This paper investigates the stability analysis of time-delay systems through Lyapunov arguments. Using the existence of a complete Lyapunov-Krasovskii functional and relying on the polynomial approximation theory, our main goal is to approximate the complete Lyapunov functional and to take profit of the supergeometric convergence rate of the truncated error part. Necessary and sufficient conditions in the linear matrix inequality (LMI) framework for sufficiently large approximated orders are consequently proposed. Moreover, an estimation of the necessary order is provided analytically with respect to system parameters.

Published
2022

37. Infinite gain margin, contraction and optimality: an LMI-based design

Author

Mattia Giaccagli, Vincent Andrieu, Sophie Tarbouriech, Daniele Astolfi, Laboratoire d'automatique, de génie des procédés et de génie pharmaceutique (LAGEPP), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-École Supérieure de Chimie Physique Électronique de Lyon (CPE)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
General Engineering, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY]
Abstract

International audience; In this paper we focus on nonlinear systems composed by a linear term plus a nonlinearity satisfying a monotonic or a sector bound condition. We present sufficient conditions based on LMIs for the design of a feedback control law possessing an infinite gain margin property that makes the closed-loop system to define a contraction. Then, we analyze the connection between infinite gain margin contractive feedbacks and optimization problems by showing how such an infinite gain control design minimizes a given cost function. A practical case of study is given to illustrate our results.

Published
2022

38. Suboptimal Filtering over Sensor Networks with Random Communication

Author

Aneel Tanwani, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Centre National de la Recherche Scientifique (CNRS), ANR-20-JSTM-0001,CyphAI,Méthodes formelles pour l'analysis et le développement de systèmes cyber-physiques intégrant l'intelligence artificielle(2020), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse 1 Capitole (UT1)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), and Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1)

Subjects
020301 aerospace & aeronautics, 0209 industrial biotechnology, Matrix differential equation, Covariance matrix, Computer science, Node (networking), [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], MathematicsofComputing_NUMERICALANALYSIS, 02 engineering and technology, Covariance, Computer Science Applications, Matrix (mathematics), Filter design, 020901 industrial engineering & automation, 0203 mechanical engineering, Control and Systems Engineering, Sensor node, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Electrical and Electronic Engineering, Algorithm, Wireless sensor network
Abstract

International audience; The problem of filter design is considered for linear stochastic systems using distributed sensors. Each sensor unit, represented by a node in an an undirected and connected graph, collects some information about the state and communicates its own estimate with the neighbors. It is stipulated that this communication between sensor nodes is time-sampled randomly and the sampling process is assumed to be a Poisson counter. Our proposed filtering algorithm for each sensor node is a stochastic hybrid system: It comprises a continuous-time differential equation, and at random time instants when communication takes place, each sensor node updates its state estimate based on the information received by its neighbors. In this setting, we compute the expectation of the error covariance matrix for each unit which is governed by a matrix differential equation. To study the asymptotic behavior of these covariance matrices, we show that if the gain matrices are appropriately chosen and the mean sampling rate is large enough, then the error covariances practically converge to a constant matrix.

Published
2022

39. Global robust attitude tracking with torque disturbance rejection via dynamic hybrid feedback

Author

Invernizzi, Davide, Lovera, Marco, Zaccarian, Luca, Politecnico di Milano [Milan] (POLIMI), Dipartimento di Ingegneria Industriale [Trento], University of Trento [Trento], Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), and ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018)

Subjects
Control and Systems Engineering, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Electrical and Electronic Engineering
Abstract

International audience; In this paper an approach to the design of robust global attitude tracking controllers for fully actuated rigid bodies is proposed. The challenge of simultaneously dealing with topological obstructions to global attitude tracking and with disturbances affecting the attitude dynamics is tackled by means of a hybrid hierarchical design that exploits the cascade structure of the underlying mathematical model. The proposed hierarchical strategy is based on an inner-outer loop paradigm comprising a dynamic control law for angular velocity tracking (inner loop) and a hybrid control law for attitude tracking (outer loop). By leveraging recent tools for the stability analysis of hybrid systems, we prove a robust global tracking property by assuming mild properties on the dynamics of the velocity feedback. We also discuss a few relevant examples satisfying these properties, encompassing harmonic disturbance compensators and conditional integrators, capable of rejecting unknown constant disturbances with an intrinsic anti-windup action.

Published
2022

40. Viability and Exponentially Stable Trajectories for Differential Inclusions in Wasserstein Spaces

Author

Bonnet, Benoît, Frankowska, Hélène, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG (UMR_7586)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), and Bonnet-Weill, Benoît

Subjects
Optimization and Control (math.OC), [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, FOS: Mathematics, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [INFO.INFO-AU] Computer Science [cs]/Automatic Control Engineering, Mathematics - Optimization and Control
Abstract

In this article, we prove a general viability theorem for continuity inclusions in Wasserstein spaces, and provide an application thereof to the existence of exponentially stable trajectories obtained via the second method of Lyapunov.

Published
2022

41. Sliding Mode Control of DFIG for a Variable Speed Wind Turbine

Author

Fatnassi, Bechir, Torchani, Borhen, Sellami, Anis, Garcia, Germain, Ecole Supérieure des Ingénieurs de Medjez El Bab (ESIM), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
[SPI]Engineering Sciences [physics]
Abstract

International audience; This paper presents the study of a variable speed wind turbine. The power conversion system is based on a double-fed induction generator (DFIG). The parameters involved in this study are the active and reactive powers exchanged between the DFIG stator and the grid. For this purpose, sliding mode control will be adopted to ensure the control of these powers and obtain the appropriate voltages and currents. The validity of the sliding mode control will be verified with simulations performed on Matlab/Simulink software. In fact, the results obtained verify the performance of such a control to ensure a good quality of energy that will be injected into the electrical network.

Published
2022

42. L 2+ Induced Norm Analysis of Continuous-Time LTI Systems Using Positive Filters and Copositive Programming

Author

Yoshio Ebihara, Hayato Motooka, Hayato Waki, Noboru Sebe, Victor Magron, Dimitri Peaucelle, Sophie Tarbouriech, Kyushu University, Kyushu Institute of Technology (Kyutech), Equipe Polynomial OPtimization (LAAS-POP), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), This research is part of the programme DesCartes and is supported by the National Research Foundation, Prime Minister’s Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) programme., ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011), European Project: 813211,H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (Main Programme), and H2020-EU.1.3.1. - Fostering new skills by means of excellent initial training of researchers ,10.3030/813211,POEMA(2019)

Subjects
nonnegative signal, positive filter, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, copositive programming, L2+ induced norm
Abstract

International audience; This paper is concerned with the analysis of the L2 induced norm of continuous-time LTI systems where the input signals are restricted to be nonnegative. This induced norm is referred to as the L2+ induced norm in this paper. It has been shown very recently that the L2+ induced norm is particularly useful for the stability analysis of nonlinear feedback systems constructed from linear systems and static nonlinearities where the nonlinear elements only provide nonnegative signals. For the upper bound computation of the L2+ induced norm, an approach with copositive programming has also been proposed. It is nonetheless true that this approach becomes effective only for multi-input systems, and for single-input systems this approach does not bring any improvement over the trivial upper bound, the standard L2 norm. To overcome this difficulty, we newly introduce positive filters to increase the number of positive signals. This enables us to enlarge the size of the copositive multipliers so that we can obtain better (smaller) upper bounds with copositive programming.

Published
2022

43. On local-global hysteresis-based hovering stabilization of the DarkO convertible UAV

Author

Sansou, Florian, Zaccarian, Luca, ENAC - Programme transverse Drones (DRONES), Ecole Nationale de l'Aviation Civile (ENAC), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), University of Trento [Trento], and ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018)

Subjects
[SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; We characterize an input-affine model of the UAV DarkO: a convertible drone designed and developed at the Ecole Nationale de L'Aviation Civile (ENAC) in Toulouse (France). Starting from a nonlinear model available in the literature, we present an approximate input-affine nonlinear model, whose dynamics simplifies the control design task. For this simplified model, we characterize the hovering equilibria in the absence of wind, and we derive the corresponding linearized dynamics. Then present a hysteresis-based switching mechanism combining a nonlinear feedback (providing a large basin of attraction) with a linearized feedback (providing improved performance but a smaller basin of attraction). Simulation results, using the original nonlinear model, confirm the effectiveness of the proposed feedback design.

Published
2022

44. Event-based control of a damped linear Schrödinger equation

Author

Koudohode, Florent, Baudouin, Lucie, Tarbouriech, Sophie, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)

Subjects
Observability inequality, Global exponential stability, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Schrödinger equation, Event-triggering mechanism
Abstract

International audience; This paper presents the design of an eventtriggering mechanism for the damped linear Schrödinger equation. Indomain Constant and localized damping are considered. The absence of any accumulation points of the time updates sequence is proven, ensuring the avoidance of Zeno behavior. The global exponential stability is ensured through some energy estimates exploiting observability inequality. An illustrative example based on the one dimensional Schrödinger equation demonstrates the efficiency of the results.

Published
2022

45. Stability analysis of linear ODE-PDE interconnected systems

Author

Bajodek, Mathieu, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, Université Toulouse III - Paul Sabatier (UT3), CDSN, Université de Toulouse 3 Paul Sabatier, Alexandre Seuret, Frédéric Gouaisbaut, Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Université Paul Sabatier - Toulouse III, and STAR, ABES

Subjects
Approximation polynomiale, Inégalités matricielles linéaires LMI, Polynomial approximation, [INFO.INFO-DS]Computer Science [cs]/Data Structures and Algorithms [cs.DS], Infinite dimensional systems, Linear matrix inequalities, Infinite-dimensional systems, [INFO.INFO-DS] Computer Science [cs]/Data Structures and Algorithms [cs.DS], ODE-PDE coupling, Inégalité matricielles linéaires, Lyapunov stabiliyty, Polynomial, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Couplage EDO-EDP, Systèmes de dimension infinie, Lyapunov stability, Linear matrix inequalities - LMI, Stabilité de Lyapunov
Abstract

Infinite dimensional systems allow to model a large panel of physical phenomena for which the state variables evolve both temporally and spatially. This manuscript deals with the evaluation of the stability of their equilibrium point. Two case studies are treated in particular: the stability analysis of ODE-transport, and ODE-reaction-diffusion interconnected systems. Theoretical tools exist for the stability analysis of these infinite-dimensional linear systems and are based on an operator algebra rather than a matrix algebra. However, these existence results raise a problem of numerical constructibility. During implementation, an approximation is performed and the results are conservative. The design of numerical tools leading to stability guarantees for which the degree of conservatism is evaluated and controlled is then a major issue. How can we develop reliable numerical criteria to rule on the stability or instability of infinite-dimensional linear systems? In order to answer this question, one proposes here a new generic method, which is decomposed in two steps. First, from the perspective of Legendre polynomials approximation, augmented models are built and split the original system into two blocks: on the one hand, a finite-dimensional approximated system is isolated, on the other hand, the infinite-dimensional truncation error is preserved and modeled. Then, frequency and time tools of finite dimension are deployed in order to propose stability criteria that have high or low numerical load depending on the approximated order. In frequencies, with the aid of the small gain theorem, sufficient stability conditions are obtained. In temporal, with the aid of the Lyapunov theorem, an under estimate of the stability regions is proposed as a linear matrix inequality and an over estimate as a positivity test. Our two case studies have been treated with this general methodology. The main result concerns the case of ODE-transport interconnected systems, for which the approximation and stability analysis using Legendre polynomials leads to exponentially fast converging estimates of stability regions. The method developed in this manuscript can be adapted to other types of approximations and exported to other infinite-dimensional linear systems. Thus, this work opens the way to obtain necessary and sufficient finite-dimensional conditions of stability for infinite-dimensional systems., Les systèmes de dimension infinie permettent de modéliser un large spectre de phénomènes physiques pour lesquels les variables d'états évoluent temporellement et spatialement. Ce manuscrit s'intéresse à l'évaluation de la stabilité de leur point d'équilibre. Deux études de cas seront en particulier traitées : l'analyse de stabilité des systèmes interconnectés à une équation de transport, et à une équation de réaction-diffusion. Des outils théoriques existent pour l'analyse de stabilité de ces systèmes linéaires de dimension infinie et s'appuient sur une algèbre d'opérateurs plutôt que matricielle. Cependant, ces résultats d'existence soulèvent un problème de constructibilité numérique. Lors de l'implémentation, une approximation est réalisée et les résultats sont conservatifs. La conception d'outils numériques menant à des garanties de stabilité pour lesquelles le degré de conservatisme est évalué et maîtrisé est alors un enjeu majeur. Comment développer des critères numériques fiables permettant de statuer sur la stabilité ou l'instabilité des systèmes linéaires de dimension infinie ? Afin de répondre à cette question, nous proposons ici une nouvelle méthode générique qui se décompose en deux temps. D'abord, sous l'angle de l'approximation sur les polynômes de Legendre, des modèles augmentés sont construits et découpent le système original en deux blocs : d'une part, un système de dimension finie approximant est isolé, d'autre part, l'erreur de troncature de dimension infinie est conservée et modélisée. Ensuite, des outils fréquentiels et temporels de dimension finie sont déployés afin de proposer des critères de stabilité plus ou moins coûteux numériquement en fonction de l'ordre d'approximation choisi. En fréquentiel, à l'aide du théorème du petit gain, des conditions suffisantes de stabilité sont obtenues. En temporel, à l'aide du théorème de Lyapunov, une sous-estimation des régions de stabilité est proposée sous forme d'inégalité matricielle linéaire et une sur-estimation sous forme de test de positivité. Nos deux études de cas ont ainsi été traitées à l'aide de cette méthodologie générale. Le principal résultat obtenu concerne le cas des systèmes EDO-transport interconnectés, pour lequel l'approximation et l'analyse de stabilité à l'aide des polynômes de Legendre mène à des estimations des régions de stabilité qui convergent exponentiellement vite. La méthode développée dans ce manuscrit peut être adaptée à d'autres types d'approximations et exportée à d'autres systèmes linéaires de dimension infinie. Ce travail ouvre ainsi la voie à l'obtention de conditions nécessaires et suffisantes de stabilité de dimension finie pour les systèmes de dimension infinie.

Published
2022

46. Exact SOHS Decompositions of Trigonometric Univariate Polynomials with Gaussian Coefficients

Author

Magron, Victor, Din, Mohab Safey El, Schweighofer, Markus, Vu, Trung Hieu, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Sorbonne Université (SU), Polynomial Systems (PolSys), LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Fachbereich Mathematik und Statistik, University of Konstanz, ANR-18-ERC2-0004,COPS,Optimisation garantie pour la vérification des systèmes cyber-physiques(2018), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), ANR-11-LABX-0040,CIMI,Centre International de Mathématiques et d'Informatique (de Toulouse)(2011), European Project: 813211,H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (Main Programme), H2020-EU.1.3.1. - Fostering new skills by means of excellent initial training of researchers ,10.3030/813211,POEMA(2019), Magron, Victor, TREMPLIN-ERC - Optimisation garantie pour la vérification des systèmes cyber-physiques - - COPS2018 - ANR-18-ERC2-0004 - TERC - VALID, Artificial and Natural Intelligence Toulouse Institute - - ANITI2019 - ANR-19-P3IA-0004 - P3IA - VALID, Centre International de Mathématiques et d'Informatique (de Toulouse) - - CIMI2011 - ANR-11-LABX-0040 - LABX - VALID, and Polynomial Optimization, Efficiency through Moments and Algebra - POEMA - - H20202019-01-01 - 2022-12-31 - 813211 - VALID

Subjects
FOS: Computer and information sciences, Computer Science - Symbolic Computation, Optimization and Control (math.OC), ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, FOS: Mathematics, MathematicsofComputing_NUMERICALANALYSIS, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Symbolic Computation (cs.SC), Mathematics - Optimization and Control
Abstract

Certifying the positivity of trigonometric polynomials is of first importance for design problems in discrete-time signal processing. It is well known from the Riesz-Fej\'ez spectral factorization theorem that any trigonometric univariate polynomial positive on the unit circle can be decomposed as a Hermitian square with complex coefficients. Here we focus on the case of polynomials with Gaussian integer coefficients, i.e., with real and imaginary parts being integers. We design, analyze and compare, theoretically and practically,three hybrid numeric-symbolic algorithms computing weighted sums of Hermitian squares decompositions for trigonometric univariate polynomials positive on the unit circle with Gaussian coefficients. The numerical steps the first and second algorithm rely on are complex root isolation and semidefinite programming, respectively. An exact sum of Hermitian squares decomposition is obtained thanks to compensation techniques. The third algorithm, also based on complex semidefinite programming, is an adaptation of the rounding and projection algorithm by Peyrl and Parrilo. For all three algorithms, we prove bit complexity and output size estimates that are polynomial in the degree of the input and linear in the maximum bitsize of its coefficients. We compare their performance on randomly chosen benchmarks, and further design a certified finite impulse filter., Comment: 8 pages, 1 table

Published
2022

47. Globally Optimal Solution to Inverse Kinematics of 7DOF Serial Manipulator

Author

Pavel Trutman, Mohab Safey El Din, Didier Henrion, Tomas Pajdla, Czech Institute of Informatics, Robotics and Cybernetics [Prague] (CIIRC), Czech Technical University in Prague (CTU), Polynomial Systems (PolSys), LIP6, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), P. Trutman was supported by the EU Structural and Investment Funds, Operational Programe Research, Development and Education under the project IMPACT (reg. no. CZ.02.1.01/0.0/0.0/15_003/0000468) and Grant Agency of the CTU Prague project SGS19/173/OHK3/3T/13. T. Pajdla was supported by EU Structural and Investment Funds, Operational Programe Research, Development and Education under the project The Robotics for Industry 4.0 project (reg. no. CZ.02.1.01/0.0/0.0/15_003/0000470, the EUH2020 ARtwin No. 856994, and EU H2020 SPRING No. 871245 Projects.Didier Henrion and Mohab Safey El Din are supported by the European Union’s Horizon2020 research and innovation programme under the MarieSkłodowska-Curie grant agreement N°813211 (POEMA). Mohab Safey ElDin is supported by the ANR grants ANR-18-CE33-0011 Sesame, ANR-19-CE40-0018 De Rerum Natura, ANR-19-CE48-0015 ECARP and the CAMiSAdo PGMO project, ANR-18-CE33-0011,SESAME,Singularités Et Stabilité des AsservisseMEnts référencés capteurs(2018), ANR-19-CE40-0018,DeRerumNatura,Décider l'irrationalité et la transcendance(2019), ANR-19-CE48-0015,ECARP,Algorithmes efficaces et exacts pour la planification de trajectoire en robotique(2019), European Project: 813211,H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (Main Programme), H2020-EU.1.3.1. - Fostering new skills by means of excellent initial training of researchers ,10.3030/813211,POEMA(2019), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées, European Project: 813211,H2020,POEMA(2019), Faculty of Electrical Engineering [Prague] (FEL CTU), Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Institut National Polytechnique (Toulouse) (Toulouse INP), and Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)

Subjects
FOS: Computer and information sciences, Computer Science - Symbolic Computation, [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], Control and Optimization, Mechanical Engineering, Biomedical Engineering, Symbolic Computation (cs.SC), Computer Science Applications, Human-Computer Interaction, Computer Science::Robotics, Computer Science - Robotics, Optimization and Control (math.OC), Artificial Intelligence, Control and Systems Engineering, FOS: Mathematics, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], Computer Vision and Pattern Recognition, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Robotics (cs.RO), Mathematics - Optimization and Control
Abstract

International audience; The Inverse Kinematics (IK) problem is concerned with finding robot control parameters to bring the robot into a desired position under the kinematics and collision constraints. We present a global solution to the optimal IK problem for a general serial 7DOF manipulator with revolute joints and a quadratic polynomial objective function. We show that the kinematic constraints due to rotations can be all generated by the second-degree polynomials. This is an important result since it significantly simplifies the further step where we find the optimal solution by Lasserre relaxations of nonconvex polynomial systems. We demonstrate that the second relaxation is sufficient to solve a general 7DOF IK problem. Our approach is certifiably globally optimal. We demonstrate the method on the 7DOF KUKA LBR IIWA manipulator and show that we are in practice able to compute the optimal IK or certify infeasibility in 99.9 % tested poses. We also demonstrate that by the same approach, we are able to solve the IK problem for a random generic manipulator with seven revolute joints.

Published
2022

48. Design of Saturating State-Feedback with Sign-Indefinite Quadratic Forms

Author

Sophie Tarbouriech, Luca Zaccarian, Isabelle Queinnec, Giorgio Valmorbida, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Dynamical Interconnected Systems in COmplex Environments (DISCO), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire des signaux et systèmes (L2S), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), University of Trento [Trento], ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018), Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), and Université Fédérale Toulouse Midi-Pyrénées

Subjects
Lyapunov function, 0209 industrial biotechnology, Linear system, Degrees of freedom (statistics), 02 engineering and technology, Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, Nonlinear system, 020901 industrial engineering & automation, Control and Systems Engineering, Convex optimization, symbols, Piecewise, Applied mathematics, Electrical and Electronic Engineering, Constant (mathematics), Mathematics, Sign (mathematics)
Abstract

International audience; We propose a novel class of piecewise smooth Lyapunov functions leading to LMI-based stability/performance analysis and control design for linear systems with saturating inputs. We provide conditions for global properties, and also conditions for local properties and guaranteed estimates of the basin of attraction. The backbone of our result consists in using quadratic forms with constant matrices that are not necessarily sign definite, thereby providing additional degrees of freedom. Using generalized sector conditions involving the dead-zone nonlinearity and its derivative, we formulate convex optimization conditions to verify their positivity in the region of interest. Several numerical examples with connections to existing results, illustrate the potential behind our novel construction.

Published
2022

49. Stability of Linear Systems under Extended Weakly-Hard Constraints

Author

Victor Magron, Nils Vreman, Jie Wang, Paolo Pazzaglia, Martina Maggio, Automatic Control Group [Lund], Lund University [Lund], Saarland University [Saarbrücken], Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Equipe Polynomial OPtimization (LAAS-POP), ANR-18-ERC2-0004,COPS,Optimisation garantie pour la vérification des systèmes cyber-physiques(2018), ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), European Project: 813211,H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions (Main Programme), H2020-EU.1.3.1. - Fostering new skills by means of excellent initial training of researchers ,10.3030/813211,POEMA(2019), Magron, Victor, TREMPLIN-ERC - Optimisation garantie pour la vérification des systèmes cyber-physiques - - COPS2018 - ANR-18-ERC2-0004 - TERC - VALID, Artificial and Natural Intelligence Toulouse Institute - - ANITI2019 - ANR-19-P3IA-0004 - P3IA - VALID, and Polynomial Optimization, Efficiency through Moments and Algebra - POEMA - - H20202019-01-01 - 2022-12-31 - 813211 - VALID

Subjects
Control and Optimization, Optimization and Control (math.OC), Control and Systems Engineering, FOS: Mathematics, [MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics - Optimization and Control
Abstract

Control systems can show robustness to many events, like disturbances and model inaccuracies. It is natural to speculate that they are also robust to sporadic deadline misses when implemented as digital tasks on an embedded platform. This paper proposes a comprehensive stability analysis for control systems subject to deadline misses, leveraging a new formulation to describe the patterns experienced by the control task under different handling strategies. Such analysis brings the assessment of control systems robustness to computational problems one step closer to the controller implementation., 6 pages, 1 table, published in IEEE Control Systems Letters and in the proceedings of the Control and Decision Conference 2022

Published
2022

50. Static Linear Anti-Windup Design With Sign-Indefinite Quadratic Forms

Author

Alberto Priuli, Sophie Tarbouriech, Luca Zaccarian, University of Trento [Trento], Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Laboratoire d'analyse et d'architecture des systèmes (LAAS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), and ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018)

Subjects
Control and Optimization, Control and Systems Engineering, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; We design static anti-windup gains to mitigate the effect of input saturation in linear output feedback closed loops. The design is conducted with the help of a non-quadratic Lyapunov function involving sign-indefinite quadratic forms, which allows for additional degrees of freedom to be exploited, for the anti-windup gain design. Synthesis conditions, combining the use of sign-indefinite quadratic forms and several sector bound properties are stated in the form of bilinear matrix inequalities ensuring global exponential stability of the closed-loop system. An iterative design algorithm is then devised, based on the resolution of a sequence of semidefinite programs. The superiority of the proposed technique over classical quadratic constructions is illustrated on an example borrowed from the literature, where quadratic positive definite functions are ineffective.

Published
2022

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