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

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. High-Gain Dead-Zone Observers for Linear and Nonlinear Plants

Author

Matteo Cocetti, Sophie Tarbouriech, Luca Zaccarian, University of Trento [Trento], 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, Équipe Méthodes et Algorithmes en Commande (LAAS-MAC), Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse 1 Capitole (UT1), Dipartimento di Ingegneria Industriale [Trento], 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), and Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole)

Subjects
LMIs, 0209 industrial biotechnology, Control and Optimization, Observer (quantum physics), Noise measurement, Observers for Linear systems, Linear system, Linear matrix inequality, 02 engineering and technology, Dead zone, Adaptive systems, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Noise, 020901 industrial engineering & automation, Exponential stability, Control and Systems Engineering, Control theory, Adaptive system, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Filtering, Lyapunov methods, Mathematics
Abstract

International audience; We propose an adaptive dead-zone mechanism to robustify observers against high-frequency noise. The construction applies to Luenberger observers and high-gain observers for plants in strict feedback form. The dead-zone improves performances by trimming a portion of the output injection term and trapping the high frequency noise in the dead band. We show that the observer gain and the adaptation parameters can be obtained by solving a linear matrix inequality, whose feasibility only requires detectability of the plant. The parameters obtained through this optimization ensure (in the absence of noise) global exponential stability of the estimation error dynamics, and input-to-state stability (ISS) from the measurement noise to the estimation error.

Published
2019

8. A Class of Hybrid Velocity Observers for Angular Measurements With Jumps

Author

Luca Zaccarian, Paolo Bosetti, Mirko Brentari, University of Trento [Trento], Dipartimento di Ingegneria Industriale [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), 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
0209 industrial biotechnology, Control and Optimization, Observer (quantum physics), Computer science, Capacitive sensing, 020208 electrical & electronic engineering, 02 engineering and technology, Experimental validation, Tracking (particle physics), Class (biology), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Nonlinear system, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, 0202 electrical engineering, electronic engineering, information engineering, Jump
Abstract

International audience; We propose a hybrid nonlinear high-gain observer to estimate the speed of rotary systems equipped with potentiometer-based, capacitive or hall-effect rotary sensors or providing angular measurements evolving in S1, exhibiting unpredictable jumps of 2π. A hybrid measurement model is proposed, based on which a hybrid high-gain observer is synthesized, which does not require the knowledge of the jump times. Asymptotic tracking of the proposed observer is proven. A sampled-data approximation of the proposed observer is developed as well, based on which an experimental validation shows suitability for real-time applications.

Published
2018

9. Representation of Chance-Constraints With Strong Asymptotic Guarantees

Author

Jean B. Lasserre, 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, Institut de Mathématiques de Toulouse UMR5219 (IMT), 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), European Project: 666981,H2020,ERC-2014-ADG,TAMING(2015), 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 Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Discrete mathematics, 0209 industrial biotechnology, Sequence, Polynomial, Control and Optimization, Lebesgue measure, Degree (graph theory), Feasible region, 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, Combinatorics, 020901 industrial engineering & automation, Optimization and Control (math.OC), Control and Systems Engineering, FOS: Mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Representation (mathematics), Mathematics - Optimization and Control, Mathematics, Probability measure, Complement (set theory)
Abstract

Given $\epsilon \in (0,1)$, a probability measure $\mu$ on $\Omega\subset\mathbb{R}^p$ and a semi-algebraic set $K\subset X\times\Omega$, we consider the feasible set $X^*_\epsilon=\{x\in X:{\rm Prob}[(x,\omega)\in K]\geq 1-\epsilon\}$ associated with a chance-constraint. We provide a sequence of outer approximations $X^d_\epsilon=\{x\in X: h_d(x)\geq0\}$, $d\in\mathbb{N}$, where $h_d$ is a polynomial of degree $d$ whose vector of coefficients is an optimal solution of a semidefinite program. The size of the latter increases with the degree $d$. We also obtain the strong and highly desirable asymptotic guarantee that $\lambda(X^d_\epsilon\setminus X^*_\epsilon)\to0$ as $d$ increases, where $\lambda$ is the Lebesgue measure on $X$. Inner approximations with same guarantees are also obtained., Comment: To appear in IEEE Control Systems Letters

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