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345 results on '"Sophie Tarbouriech"'

1. Sophie Tarbouriech [People in Control]

Author: Sophie Tarbouriech
Subjects: Control and Systems Engineering, Modeling and Simulation, Electrical and Electronic Engineering
Published: 2023
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2. A Data-Driven Approach to the L₂ Stabilization of Linear Systems Subject to Input Saturations

Author: Alexandre Seuret and Sophie Tarbouriech
Subjects: Control and Optimization, Control and Systems Engineering
Published: 2023
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3. 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
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4. l2 induced norm analysis of discrete-time LTI systems for nonnegative input signals and its application to stability analysis of recurrent neural networks

Author: Yoshio Ebihara, Ngoc Hoang Anh Mai, Hayato Waki, Dimitri Peaucelle, Victor Magron, and Sophie Tarbouriech
Subjects: Semidefinite programming, General Engineering, Stability (learning theory), 02 engineering and technology, Upper and lower bounds, LTI system theory, Nonlinear system, Recurrent neural network, Discrete time and continuous time, Norm (mathematics), 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, 020201 artificial intelligence & image processing, Mathematics
Abstract: In this paper, we focus on the “positive” l 2 induced norm of discrete-time linear time-invariant systems where the input signals are restricted to be nonnegative. To cope with the nonnegativity of the input signals, we employ copositive programming as the mathematical tool for the analysis. Then, by applying an inner approximation to the copositive cone, we derive numerically tractable semidefinite programming problems for the upper and lower bound computation of the “positive” l 2 induced norm. This norm is typically useful for the stability analysis of feedback systems constructed from an LTI system and nonlinearities where the nonlinear elements provide only nonnegative signals. As a concrete example, we illustrate the usefulness of the “positive” l 2 induced norm for the stability analysis of recurrent neural networks with activation functions being rectified linear units.
Published: 2021
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5. 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
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6. Guest Editorial Introduction to the IEEE Control Systems Letters Special Section on Data-Driven Analysis and Control

Author: Kanat Camlibel, Martin Guay, Sophie Tarbouriech, Simone Baldi, Timm Faulwasser, Francesco Ferrante, Paolo Rapisarda, Henk J. Van Waarde, and Melanie N. Zeilinger
Subjects: Control and Optimization, Control and Systems Engineering
Published: 2023
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7. 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
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8. 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
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9. Energy-based design of dynamic allocation in the presence of saturating actuators

Author: T. Alves Lima, Sophie Tarbouriech, Fabricio Gonzalez Nogueira, Bismark Claude Torrico, Universidade Federal do Ceará = Federal University of Ceará (UFC), 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), Université de Toulouse (UT), and ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018)
Subjects: Scheme (programming language), Computer science, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Stability (learning theory), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Loop (topology), Allocator, Control and Systems Engineering, Control theory, State (computer science), Minification, Actuator, computer, Energy (signal processing), computer.programming_language
Abstract: Cette communication devait être présentée au congrès "24th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2020)" qui a été annulé. Reporté en 2021; International audience; This paper addresses the design of dynamic allocation functions for systems with saturating actuators. The novelty of the proposal relies on the use of an anti-windup loop to drive the state of the allocator, which in some sense dynamically compensates the difference between the computed control signal and the plant input. Furthermore, the co-design of the allocator and anti-windup loop is presented, allowing to deal with the multiple objective of reducing the allocator error and increasing the closed-loop region of stability. Theoretical conditions are derived in terms of linear matrix inequalities (LMIs) and an optimization scheme consisting in the minimization of the energy of the allocator error is proposed. Two examples borrowed from the literature illustrate the proposed technique and show its effectiveness.
Published: 2021
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10. 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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11. Event-triggered control co-design for rational systems

Author: L. G. Moreira, Diógenes José Gusmão Coutinho, J.M. Gomes da Silva, and Sophie Tarbouriech
Subjects: Lyapunov function, 0209 industrial biotechnology, Work (thermodynamics), Computer science, 020208 electrical & electronic engineering, 02 engineering and technology, Set (abstract data type), symbols.namesake, 020901 industrial engineering & automation, Exponential stability, Control and Systems Engineering, Control theory, Convex optimization, 0202 electrical engineering, electronic engineering, information engineering, symbols, Algebraic number, Differential (infinitesimal)
Abstract: This work deals with the problem of designing stabilizing event-triggered state-feedback controllers for rational systems. Using differential algebraic representations and Lyapunov theory techniques, LMI-based conditions are derived to ensure regional asymptotic stability of the origin. These conditions are then cast into a convex optimization problem to the co-design of the event generator parameters and the state-feedback gain in order to reduce the controller updates while ensuring the asymptotic stability of the origin with respect to a given set of admissible initial conditions. The proposed methodology is illustrated by means of a numerical example.
Published: 2020
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12. Event-Triggered Control for Extended Plants of Discrete-Time Linear Systems

Author: Hiroyuki Ichihara, Kenji Sawada, Sophie Tarbouriech, and Koichi Kobayashi
Subjects: 0209 industrial biotechnology, Computer science, 020208 electrical & electronic engineering, Control (management), Linear system, Regular polygon, 02 engineering and technology, 020901 industrial engineering & automation, Exponential stability, Control and Systems Engineering, Filter (video), Control theory, Control system, 0202 electrical engineering, electronic engineering, information engineering, Design methods
Abstract: This paper deals with design methods of event-triggered control systems for discrete-time linear systems. An extended plant consisting of a given plant and a dynamical filter is considered and controlled by an event-triggered static output feedback. The triggering rule uses only the available signals and therefore is based on the difference between the triggered and non-triggered output signals. The paper deals with the co-design problem, that is the design of the triggering condition, the filter, and the controller simultaneously. Sufficient theoretical conditions are proposed in terms of linear matrix inequalities to ensure the asymptotic stability of the closed-loop system. Convex optimizations problems incorporate these conditions in order to optimize the closed-loop performance or to reduce the number of transmissions. Three numerical examples illustrate the design method of the triggering conditions as well as the simultaneous design method of the filter and controller.
Published: 2020
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13. Revisited Anti-Windup Approach for Event-Triggered Control Purpose

Author: Carla de Souza, Sophie Tarbouriech, Isabelle Queinnec, and Antoine Girard
Published: 2022
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14. LMI-Based Stubborn and Dead-Zone Redesign in Linear Dynamic Output Feedback

Author: Sophie Tarbouriech, Angelo Alessandri, Daniele Astolfi, 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), Università degli studi di Genova = University of Genoa (UniGe), 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), University of Trento [Trento], and ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018)
Subjects: Control and Optimization, sector conditions, Noise measurement, Linear matrix inequalities, Linear systems, Vehicle dynamics, Saturation, Output feedback, Symmetric matrices, Control and Systems Engineering, dead-zone, [INFO.INFO-SY]Computer Science [cs]/Systems and Control [cs.SY], Observers, LMI
Abstract: International audience; The redesign of output feedback controllers for linear systems based on adaptive saturation (stubborn) and dead-zone redesign is investigated by showing that input-to-state stability holds in closed loop upon the satisfaction of linear matrix inequalities. Such results are obtained by using sector conditions that are involved in the Lyapunov analysis in order to ensure input-to-state stability. A simulation case study shows the effectiveness of the proposed redesign in denoising and outlier attenuation with increased accuracy and precision.
Published: 2022
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15. Co-design of dynamic allocation functions and anti-windup

Author: Bismark C. Torrico, Sophie Tarbouriech, Fabricio Gonzalez Nogueira, Thiago Alves Lima, Universidade Federal do Ceará = Federal University of Ceará (UFC), 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), 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, LMIs, Control and Optimization, Computer science, 020208 electrical & electronic engineering, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Regular polygon, 02 engineering and technology, Energy consumption, Dynamic priority scheduling, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Allocator, 020901 industrial engineering & automation, Exponential stability, Control and Systems Engineering, Control theory, Dynamic Allocation, 0202 electrical engineering, electronic engineering, information engineering, Saturating Actuators, Symmetric matrix, Minification, Actuator, Anti-windup
Abstract: International audience; This paper addresses the design of dynamic allocation functions for systems with saturating actuators. The allocator can redistribute the desired control effort within the multiple actuators by penalizing each actuator to be more or less used, while also taking into account a criterium for minimization of their total energy consumption over time. Anti-windup gains are added to both the controller and the dynamic allocator state to deal with the saturation condition. Convex conditions for the co-design of both the dynamic allocator and anti-windup gains are expressed in the form of linear matrix inequalities (LMIs). Such conditions allow to deal with the multiple objective problems of enlarging the estimates of the basin of attraction and minimizing the total energy consumption of the actuators. Two examples borrowed from the literature illustrate the proposed technique and show its effectiveness.
Published: 2021
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16. Emulation-based Dynamic Output-Feedback Control of Saturating Discrete-time LPV Systems

Author: Valter J. S. Leite, Eugênio B. Castelan, Carla de Souza, Sophie Tarbouriech, Universidade Federal de Santa Catarina = Federal University of Santa Catarina [Florianópolis] (UFSC), PPGEL and Department of Mechatronics, CEFET-MG/UFJS, 35503-822 Divinópolis, Brazil, 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, ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018), 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: Scheme (programming language), 0209 industrial biotechnology, Control and Optimization, Computer science, Control (management), Actuator saturation, 02 engineering and technology, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Linear parameter-varying systems, 020901 industrial engineering & automation, Exponential stability, Control theory, 0202 electrical engineering, electronic engineering, information engineering, computer.programming_language, Emulation, Linear system, Stability analysis, Emulation-based control, Discrete time and continuous time, Control and Systems Engineering, Convex optimization, 020201 artificial intelligence & image processing, Convex function, Actuator, computer
Abstract: International audience; This paper addresses the problem of emulation-based dynamic output-feedback control for discrete-time linear parameter varying systems under actuator saturation. Sufficient conditions based on linear matrix inequalities (LMI) are derived to design the parameters of two dependent event-triggering rules handling the sensor-to-controller and controller-to-actuator communication and to guarantee the regional asymptotic stability of the closed-loop system. A convex optimization scheme incorporating these conditions is also formulated to reduce the output and control signals' update rate through communication channels. A numerical example illustrates the usefulness of the proposal.
Published: 2021
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17. On the Use of Generalized Holding Devices in Event-Triggered Observer-Based Controllers

Author: Sophie Tarbouriech, Francesco Ferrante, 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), 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, Observer (quantum physics), Computer science, Stability (learning theory), Linear matrix inequalities, 02 engineering and technology, symbols.namesake, 020901 industrial engineering & automation, Exponential stability, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Event-triggered control, Emulation, 020208 electrical & electronic engineering, Hybrid dynamical systems, Computer Science Applications, Control and Systems Engineering, Hybrid system, Global exponential stability, Convex optimization, symbols, Generalized holding devices, Analysis, Observer-based control
Abstract: International audience; This paper deals with the design of output feedback event-triggered controllers equipped with generalized holding devices. Both emulation and co-design settings are explored. Specifically, a robust observer-based event-triggered controller with a dwell time logic is proposed to achieve closed-loop stability. The closed-loop system is modeled as a hybrid system and analyzed via Lyapunov theory for hybrid systems. Sufficient conditions in the form of matrix inequalities are given to ensure global exponential stability and input-to-state stability with respect to measurement disturbances for the closed-loop system. The proposed conditions enable the design of the controller gains, event-triggering mechanism, and of general holding devices, thereby including classical zero-order-holder devices. Convex optimization schemes address the implicit objective consisting of reducing the number of updates of the control input. The effectiveness of the conditions are illustrated through an illustrative example borrowed from the literature.
Published: 2021
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18. Event-based control of a damped linear wave equation

Author: Florent Koudohode, Lucie Baudouin, and Sophie Tarbouriech
Subjects: Control and Systems Engineering, Electrical and Electronic Engineering
Published: 2022
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19. Event-triggered Dynamic Output Feedback Controller for Discrete-time LPV Systems with Constraints

Author: C.E. de Souza, Valter J. S. Leite, Sophie Tarbouriech, Eugênio B. Castelan, Universidade Federal de Santa Catarina = Federal University of Santa Catarina [Florianópolis] (UFSC), 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), PPGEL and Department of Mechatronics, CEFET-MG/UFJS, 35503-822 Divinópolis, Brazil, 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: 0209 industrial biotechnology, Computer science, Control (management), Stability (learning theory), 02 engineering and technology, Function (mathematics), 01 natural sciences, Upper and lower bounds, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Discrete time and continuous time, Exponential stability, Control and Systems Engineering, Control theory, 0103 physical sciences, Convex optimization, 010301 acoustics
Abstract: International audience; This paper examines an event-triggered control design approach for discrete-timelinear parameter-varying (LPV) systems under control constraints. A parameter-dependentdynamic output-feedback controller with an event-triggering condition is designed to ensurethe regional asymptotic stability of the closed-loop system while minimizing a quadratic costfunction. Sufficient conditions are derived in terms of linear matrix inequalities (LMIs) thanksto the use of a parameter-dependent quadratic Lyapunov function. Also, convex optimizationschemes are proposed using these conditions to minimize an upper bound of a given cost functionor to maximize the size of the region of closed-loop stability. Examples illustrate the proposal
Published: 2021
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20. Event-triggered policy for dynamic output stabilization of discrete-time LPV systems under input constraints

Author: Eugênio B. Castelan, Carla de Souza, Valter J. S. Leite, Sophie Tarbouriech, 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: 0209 industrial biotechnology, Emulation, Current (mathematics), General Computer Science, Computer science, Mechanical Engineering, 020208 electrical & electronic engineering, Control (management), Linear matrix inequalities, Saturating actuators, 02 engineering and technology, Dynamic output-feedback control, LPV systems, Event-triggered, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Discrete time and continuous time, Exponential stability, Control and Systems Engineering, Control theory, Convex optimization, 0202 electrical engineering, electronic engineering, information engineering, Co-design, Electrical and Electronic Engineering, Actuator
Abstract: International audience; This paper concerns the event-triggered dynamic output-feedback control of discrete-time linear parameter-varying (LPV) systems subject to saturating actuators. Two independent event-triggering schemes are introduced to determine whether the current signals should be transmitted (a) from the sensor to the controller and (b) from the controller to the actuator. As a result, the communication resources can be significantly saved. Both the emulation-based problem and the co-design problem are addressed. Sufficient conditions based on linear matrix inequalities (LMIs) are derived to ensure the regional asymptotic stability of the origin for the closed-loop system. A convex optimization procedure is proposed to determine the controller matrices and the event-triggering parameters aiming at reducing the number of updates on the independent channels sensor-to-controller and controllerto-actuator. At last, numerical examples are employed to testify to the validity of the proposed methods.
Published: 2021
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21. Guest Editorial Introduction to the Special Issue of the IEEE L-CSS on Learning and Control

Author: Kartik B. Ariyur, Bahman Gharesifard, Kyriakos G. Vamvoudakis, Christian Ebenbauer, Sophie Tarbouriech, Subhrakanti Dey, Christopher M. Kellett, Paolo Frasca, Giovanni Cherubini, Mireille E. Broucke, Antoine Girard, Usman A. Khan, Martin Guay, Giuseppe Notarstefano, João Manoel Gomes da Silva, Lars Grüne, and Luca Scardovi
Subjects: Control and Optimization, Multimedia, Computer science, business.industry, Automotive industry, Complex system, Robotics, Recommender system, computer.software_genre, Control and Systems Engineering, Control theory, Artificial intelligence, Control (linguistics), business, computer
Abstract: Recent advances in machine learning and artificial intelligence have provided astounding performance gains in several domains, including computer vision, natural language processing and recommender systems, in particular when massive data is involved, and large computational power is needed. Similarly, modern control theory techniques have found very successful application in the analysis and control design of complex systems, for example in robotics and in the automotive industry. The connection between machine learning and control theory is more and more pertinent in view of the promise to surpass the potentialities of each discipline.
Published: 2020
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22. 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
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23. Event-triggered damping of a linear wave equation

Author: Sophie Tarbouriech, Swann Marx, and Lucie Baudouin
Subjects: 0209 industrial biotechnology, 020208 electrical & electronic engineering, 02 engineering and technology, Wave equation, Domain (mathematical analysis), Term (time), 020901 industrial engineering & automation, Exponential stability, Control and Systems Engineering, Bounded function, Time derivative, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Partial derivative, Event triggered, Mathematics
Abstract: The paper addresses the design of an event-triggering mechanism for a partial differential wave equation posed in a bounded domain. The wave equation is supposed to be controlled through a classical damping term: the first order time derivative of the solution, distributed in the whole domain. In a continuous framework, such a feedback leads to the global exponential stability of the closed-loop system. Here, sufficient conditions based on the use of a suitable Lyapunov functional are proposed to guarantee that an event-triggered distributed damping ensures the exponential stability. Moreover, the designed event-triggering mechanism allows avoiding the Zeno behavior. The ‘existence and regularity’ prerequisite properties of solutions for the closed loop system are also proven.
Published: 2019
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24. A plug-in procedure for hybridization of PI controllers

Author: Valter J. S. Leite, Sophie Tarbouriech, Mariella M. Quadros, and Ignacio Rubio Scola
Subjects: 0209 industrial biotechnology, Computer science, Settling time, 020208 electrical & electronic engineering, PID controller, 02 engineering and technology, computer.software_genre, Action (physics), Nonlinear system, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Control system, Rise time, 0202 electrical engineering, electronic engineering, information engineering, Plug-in, computer, Energy (signal processing)
Abstract: The nonlinear action of hybrid PI controllers makes possible to achieve almost none overshot with the smallest rise time possible (for the available input energy) and a settling time almost equal to the rise time. However, all of these nice properties require changes on the control loop. Our contribution is the proposition of a plug-in control action that can be added to the classical linear PI to avoid changes in the hardware, and still achieve the same behavior of a recently introduced adaptive hybrid PI controller. Our proposal is illustrated by real-time level control experiments in a nonlinear reservoir. Performance indexes are presented to evaluate the experimental tests.
Published: 2019
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25. LMI conditions for contraction and synchronization

Author: Sophie Tarbouriech and Vincent Andrieu
Subjects: 0209 industrial biotechnology, Contraction analysis, Nonlinear control law, 020208 electrical & electronic engineering, Monotonic function, 02 engineering and technology, Linear matrix, Control function, Nonlinear system, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, 0202 electrical engineering, electronic engineering, information engineering, Closed loop, Contraction (operator theory), Mathematics
Abstract: This paper deals with a systematic way to check if a certain class of nonlinear systems can define a contraction. The proposed approach combines the use of sector bound condition or monotonic condition satisfied by the nonlinearities with the use of an adequate control function matrix. The contraction analysis results are provided under the form of linear matrix inequalities (LMIs). The design of a nonlinear control law (that is a control law depending on nonlinearities) is proposed in order for the closed loop to be a contraction. The adaptation of the contraction results to the synchronization of n identical nonlinear systems is also investigated by considering two kinds of communication graphs (full and general undirected ones).
Published: 2019
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26. Lyapunov Stability Analysis of a Mass-Spring system subject to Friction

Author: Matthieu Barreau, Sophie Tarbouriech, Frédéric Gouaisbaut, Royal Institute of Technology [Stockholm] (KTH ), 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, ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018), 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: 0209 industrial biotechnology, General Computer Science, Friction, 02 engineering and technology, Stability (probability), 020901 industrial engineering & automation, Exponential stability, Subject (grammar), Attractor, 0202 electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Applied mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Electrical and Electronic Engineering, LMI, Mathematics - Optimization and Control, Mathematics, Lyapunov methods, Lyapunov stability, Equilibrium point, Global asymptotic stability, Mechanical Engineering, 020208 electrical & electronic engineering, Regional asymptotic stability, Attraction, Control and Systems Engineering, Optimization and Control (math.OC), [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract: International audience; This paper deals with the stability analysis of a mass-spring system subject to friction using Lyapunov-based arguments. As the described system presents a stick-slip phenomenon, the mass may then periodically stick to the ground. The objective consists in developing numerically tractable conditions ensuring the global asymptotic stability of the unique equilibrium point. The approach proposed merges two intermediate results: The first one relies on the characterization of an attractor around the origin, in which converge the closed-loop trajectories. The second result assesses the regional asymptotic stability of the equilibrium point by estimating its basin of attraction. The main result relies on conditions allowing to ensure that the attractor issued from the first result is included in the basin of attraction of the origin computed form the second result. An illustrative example draws the interest of the approach.
Published: 2021
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27. Tour d’horizon sur les techniques anti-windup pour les systèmes saturés - Commande anti-windup

Author: Isabelle Queinnec and Sophie Tarbouriech
Abstract: Cet article traite de la synthese anti-windup, technique de retouche d’un controleur qui permet de prendre en compte de maniere explicite les phenomenes de saturation des actionneurs et de reduire leur impact negatif sur la dynamique d’un systeme commande. Le procede est decrit par un modele d’etat dynamique lineaire, de meme que son controleur nominal construit a priori sans tenir compte des saturations. Les methodes proposees s’appuient sur l’utilisation de conditions de secteurs afin d’encapsuler la fonction saturation et exploitent la stabilite de Lyapunov au travers de fonctions quadratiques permettant d’exprimer les conditions de stabilite et de performances par des inegalites matricielles lineaires.
Published: 2020
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28. Un tour d'horizon sur les techniques anti-windup pour les systèmes saturés

Author: Sophie Tarbouriech, Isabelle Queinnec, 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, and Queinnec, Isabelle
Subjects: [SPI.AUTO] Engineering Sciences [physics]/Automatic, saturations, anti-windup, actuators, control, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract: National audience; Cet article traite de la synthèse anti-windup, technique de retouche d'un contrôleur qui permet de prendre en compte de manière explicite les phénomènes de saturation des actionneurs et de réduire leur impact négatif sur la dynamique d'un système commandé. Le procédé est décrit par un modèle d'état dynamique linéaire, de même que son contrôleur nominal construit a priori sans tenir compte des saturations. Les méthodes proposées s'appuient sur l'utilisation de conditions de secteurs afin d'encapsuler la fonction saturation et exploitent la stabilité de Lyapunov au travers de fonctions quadratiques permettant d'exprimer les conditions de stabilité et de performances par des inégalités matricielles linéaires.
Published: 2020

29. Dead-zone observer-based control for anesthesia subject to noisy BIS measurement

Author: Germain Garcia, Isabelle Queinnec, Sophie Tarbouriech, Michel Mazerolles, Queinnec, Isabelle, 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, CHU Toulouse [Toulouse], 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 Hospitalier Universitaire de Toulouse (CHU Toulouse), and ANR-18-CE40-0010,HANDY,Systèmes Dynamiques Hybrides et en Réseau(2018)
Subjects: 0209 industrial biotechnology, noise, Observer (quantum physics), Property (programming), Computer science, saturation, 0206 medical engineering, Control (management), Linear matrix inequality, observer, 02 engineering and technology, Dead zone, 020601 biomedical engineering, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Noise, 020901 industrial engineering & automation, [SPI.AUTO] Engineering Sciences [physics]/Automatic, Exponential stability, Control and Systems Engineering, Anesthesia, hypnosis, Observer based, control
Abstract: International audience; This paper deals with the maintenance phase control of general anesthesia during surgery, involving saturated input and noisy output. The objective is to maintain the patient to some given depth of hypnosis, measured by the BIS. The control law is an observer-based control, where a dead-zone observer is built in order to mitigate the presence of the output noise. The global exponential stability of the complete closed-loop system in the noise-free case is guaranteed thanks to a linear matrix inequality condition and an input-to-state property in presence of the noise is also proven. A three-steps optimization algorithm is proposed to determine the parameters of the control law and then evaluated on a patient case.
Published: 2020

30. Feedback law with probabilistic certification for Propofol-based control of BIS during anesthesia

Author: Mirko Fiacchini, Isabelle Queinnec, Michel Mazerolles, Mazen Alamir, and Sophie Tarbouriech
Subjects: 0209 industrial biotechnology, General Chemical Engineering, Control (management), Biomedical Engineering, Aerospace Engineering, 02 engineering and technology, Certification, Interval (mathematics), Industrial and Manufacturing Engineering, 03 medical and health sciences, 020901 industrial engineering & automation, 0302 clinical medicine, 030202 anesthesiology, Medicine, Electrical and Electronic Engineering, business.industry, Mechanical Engineering, Probabilistic logic, Variable (computer science), Control and Systems Engineering, Feature (computer vision), Bispectral index, Anesthesia, business, Propofol, medicine.drug
Abstract: This paper proposes a new control strategy for Propofol injection during anesthesia in patients undergoing surgery and where the bispectral index (BIS) is considered to be the regulated variable. The proposed control shows the nice feature of being completely independent of the knowledge of the pharmacokinetics that govern the diffusion of the drug. The paper also proposes a certification framework that gives a probabilistic guarantee regarding the containment of the BIS inside the desired interval as well as for the time needed for the BIS to be steered to this interval. Moreover, this certification is given for realistic (and hence very high) level of uncertainties on the parameters that define the unknown-to-the-controller dynamics. This last feature is checked using a widely employed model.
Published: 2018
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31. Invariant set analysis for SISO discrete-time polynomial systems with dynamic quantizers

Author: Hiroyuki Ichihara, Sophie Tarbouriech, and Kenji Sawada
Subjects: 0209 industrial biotechnology, Mechanical Engineering, General Chemical Engineering, Quantization (signal processing), 020208 electrical & electronic engineering, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, Biomedical Engineering, Aerospace Engineering, Data_CODINGANDINFORMATIONTHEORY, 02 engineering and technology, Upper and lower bounds, Performance index, Industrial and Manufacturing Engineering, 020901 industrial engineering & automation, Discrete time and continuous time, Control and Systems Engineering, Bounded function, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Electrical and Electronic Engineering, Mathematics
Abstract: This paper deals with the stability analysis problem of discrete‐time polynomial systems subject to input quantization. The quantizer under consideration is supposed to be dynamic. Indeed, considering the quantization error as bounded disturbances, the regional input‐to‐state stability is studied. The approach developed consists in characterizing two nested invariant sets where the outer one is a region of attraction and the inner one is the robust invariant set with respect to the quantization error. By defining a performance index between the quantized system and the quantizer‐free system, a quasi‐convex problem is formulated to minimize an upper bound on such a performance index.
Published: 2018
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32. A new methodology to compute stabilizing control laws for continuous-time LTV systems

Author: Sophie Tarbouriech, Germain Garcia, Cristiano M. Agulhari, and Pedro L. D. Peres
Subjects: Lyapunov stability, 0209 industrial biotechnology, Sequence, Computer science, Mechanical Engineering, General Chemical Engineering, Computation, Control (management), Biomedical Engineering, Stochastic matrix, Stability (learning theory), Aerospace Engineering, 010103 numerical & computational mathematics, 02 engineering and technology, 01 natural sciences, Industrial and Manufacturing Engineering, Set (abstract data type), 020901 industrial engineering & automation, Transformation (function), Control and Systems Engineering, Law, 0101 mathematics, Electrical and Electronic Engineering
Abstract: This paper is devoted to the problem of computing control laws for the stabilization of continuous‐time linear time‐varying systems. First, a necessary and sufficient condition to assess the stability of a linear time‐varying system based on the norm of the transition matrix computed over a sequence of successive finite‐time intervals is proposed. A link with a stability condition for an equivalent discrete‐time model is also established. Then, 3 approaches for the computation of stabilizing state‐feedback gains are proposed: a continuous‐time technique, ie, directly derived from the stability condition, not suitable for numerical implementation; a method based on the stabilization of the discrete‐time equivalent model along with a transformation to generate the desired continuous‐time gain; and the computation of stabilizing gains for a set of periodic discrete‐time systems. Finally, by adapting one of the existing methods for the stabilization of periodic discrete‐time systems, an algorithm for the computation of a stabilizing state‐feedback continuous‐time gain is proposed. A numerical example illustrates the validity of the technique.
Published: 2018
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33. Some Results on Exponential Synchronization of Nonlinear Systems

Author: Vincent Andrieu, Bayu Jayawardhana, Sophie Tarbouriech, Laboratoire d'automatique et de génie des procédés (LAGEP), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-École Supérieure Chimie Physique Électronique de Lyon-Centre National de la Recherche Scientifique (CNRS), Engineering and Technology Institute Groningen (ENTEG), University of Groningen [Groningen], 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, ANR-12-BS03-0005,LimICoS,Synthèse et analyse des systèmes avec informations limitées(2012), Université de Lyon-Université de Lyon-École Supérieure de Chimie Physique Électronique de Lyon (CPE)-Centre National de la Recherche Scientifique (CNRS), 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), Discrete Technology and Production Automation, and Robotics and image-guided minimally-invasive surgery (ROBOTICS)
Subjects: Lyapunov stability, 0209 industrial biotechnology, COORDINATION, Mathematical analysis, Linear system, 02 engineering and technology, Computer Science Applications, Exponential function, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Synchronizer, Exponential stability, Control and Systems Engineering, lyapunov methods, Backstepping, Synchronization (computer science), 0202 electrical engineering, electronic engineering, information engineering, Symmetric matrix, 020201 artificial intelligence & image processing, multi-agent systems, Electrical and Electronic Engineering, synchronization, OUTPUT SYNCHRONIZATION, Mathematics
Abstract: International audience; Based on recent works on transverse exponential stability, we establish some necessary and sufficient conditions for the existence of a (locally) exponential synchronizing control law. We show that the existence of a structured synchronizer is equivalent to the existence of a stabilizer for the individual linearized systems (on the synchronization manifold) by a linear state feedback. This, in turn, is also equivalent to the existence of a symmetric covariant tensor field, which satisfies a Control Matrix Function inequality. Based on this result, we provide the construction of such synchronizer via backstepping approaches. In some particular cases, we show how global exponential synchronization may be obtained.
Published: 2018
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34. Stabilisation of discrete‐time systems with finite‐level uniform and logarithmic quantisers

Author: Carlos Eduardo Pereira, Sophie Tarbouriech, Gustavo Cruz Campos, João Manoel Gomes da Silva, Departamento de Engenharia Eletrica (UFRGS), Universidade Federal do Rio Grande do Sul [Porto Alegre] (UFRGS), 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: 0209 industrial biotechnology, Control and Optimization, Logarithm, 020208 electrical & electronic engineering, Linear system, Linear matrix inequality, Admissible set, 02 engineering and technology, State (functional analysis), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science Applications, Human-Computer Interaction, 020901 industrial engineering & automation, Discrete time and continuous time, Control and Systems Engineering, Control theory, Attractor, Convergence (routing), 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, Mathematics
Abstract: International audience; This study deals with the stabilisation of discrete-time linear systems subject to static finite-level quantisation on thecontrol inputs. Two kinds of quantisers are considered: uniform and logarithmic. The modelling of the finite-level quantisation isobtained by the application of deadzone and saturation maps to an infinite-level quantiser. From this model, conditions for thesynthesis of state feedback control laws guaranteeing the convergence of the trajectories to an attractor around the originprovided that the initial state belongs to a certain admissible set are proposed. These conditions can thus be incorporated inlinear matrix inequality-based optimisation schemes to compute the stabilising gain while minimising the size of the attractor.
Published: 2018
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35. Analysis and Synthesis of Reset Control Systems

Author: Luca Zaccarian, Sophie Tarbouriech, Isabelle Queinnec, Christophe Prieur, GIPSA - Systèmes non linéaires et complexité (GIPSA-SYSCO), Département Automatique (GIPSA-DA), Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), 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: 0209 industrial biotechnology, 020901 industrial engineering & automation, Control and Optimization, Control and Systems Engineering, 020208 electrical & electronic engineering, 0202 electrical engineering, electronic engineering, information engineering, 02 engineering and technology, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract: International audience; This survey monograph overviews a large core of research results produced by the authors in the past decade about reset controllers for linear and nonlinear plants. The corresponding feedback laws generalize classical dynamic controllers because of the interplay of mixed continuous/discrete dynamics. The obtained closed-loop system falls then within the category of hybrid dynamical systems, with the specific feature that the hybrid nature arises from the nature of the controller, rather than the nature of the plant, which is purely continuous-time. Due to this fact, the presented results focus on performance and stability notions that prioritize continuous-time evolution as compared to the discrete-time one. Dwell-time logics (namely, conditions preventing consecutive jumps that are too close to each other) are indeed enforced on solutions, to ensure that the continuous evolution of solutions is complete (no Zeno solutions occur).After presenting a historical motivation and an overview of the results on this topic in Part I, several results on stability and performance analysis and on control design for general linear continuous-time plants are developed in Part II. These results are developed by exploiting the well-established formalism for nonlinear hybrid dynamical systems introduced by Andy Teel and co-authors around 2004. With this formalism, by ensuring sufficient regularity of the reset controller dynamics, we ensure robustness of stability with respect to small disturbances and uncertainties together with suitable continuity of solutions, generally regarded as well-posedness of the hybrid closed loop. Throughout Part II, we provide several simulation studies showing that reset control strategies may allow to attain better performance with respect to the optimal ones obtained by classical continuous-time controllers.Finally, in Part III we focus on planar systems, that is reset closed loops involving a one-dimensional linear plant and a one-dimensional reset controller. For this simple interconnection interesting stability conditions can be drawn and relevant extensions addressing the reference tracking problem are introduced, illustrating them on a few relevant case studies emerging in the automotive field.
Published: 2018
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36. Observer-based event-triggered control for linear systems subject to cone-bounded nonlinearities

Author: L. G. Moreira, Alexandre Seuret, Sophie Tarbouriech, and J.M. Gomes da Silva
Subjects: 0209 industrial biotechnology, Observer (quantum physics), Quantization (signal processing), 020208 electrical & electronic engineering, Linear system, Context (language use), 02 engineering and technology, Stability (probability), 020901 industrial engineering & automation, Exponential stability, Control and Systems Engineering, Control theory, Bounded function, Convex optimization, 0202 electrical engineering, electronic engineering, information engineering, Mathematics
Abstract: The paper presents an observer-based event-triggered control strategy for linear systems subject to input cone-bounded nonlinearities by using only available measurable variables. Sufficient conditions based on linear matrix inequalities are proposed to ensure the asymptotic stability of the closed loop and the avoidance of Zeno behavior in an emulation context. Based on these conditions, a convex optimization problem to compute the parameters of the event-trigger rule aiming at reducing the number of control updates is proposed. The approach is illustrated on a numerical example that considers the control of a linear system with a logarithmic input quantization constraint.
Published: 2017
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37. Stability analysis of linear impulsive delay dynamical systems via looped-functionals

Author: Sophie Tarbouriech, Alexandre Seuret, Alfonso Baos, Miguel A. Dav, Frédéric Gouaisbaut, SYSCO ( GIPSA-SYSCO ), Département Automatique ( GIPSA-DA ), Grenoble Images Parole Signal Automatique ( GIPSA-lab ), Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Grenoble Images Parole Signal Automatique ( GIPSA-lab ), Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ) -Université Pierre Mendès France - Grenoble 2 ( UPMF ) -Université Stendhal - Grenoble 3-Université Joseph Fourier - Grenoble 1 ( UJF ) -Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique ( CNRS ) -Université Grenoble Alpes ( UGA ), Departamento de Informática y Sistemas [Murcia] ( Modelum ), Universidad de Murcia, Équipe Méthodes et Algorithmes en Commande ( LAAS-MAC ), Laboratoire d'analyse et d'architecture des systèmes [Toulouse] ( LAAS ), Institut National Polytechnique [Toulouse] ( INP ) -Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Université Paul Sabatier - Toulouse 3 ( UPS ) -Centre National de la Recherche Scientifique ( CNRS ) -Institut National Polytechnique [Toulouse] ( INP ) -Institut National des Sciences Appliquées - Toulouse ( INSA Toulouse ), Institut National des Sciences Appliquées ( INSA ) -Institut National des Sciences Appliquées ( INSA ) -Université Paul Sabatier - Toulouse 3 ( UPS ) -Centre National de la Recherche Scientifique ( CNRS ), GIPSA - Systèmes non linéaires et complexité (GIPSA-SYSCO), Département Automatique (GIPSA-DA), Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Departamento de Informática y Sistemas [Murcia] (Modelum), 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: 0209 industrial biotechnology, Dynamical systems theory, Discrete dynamics, 02 engineering and technology, Linear matrix, Base (topology), Stability (probability), [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Exponential stability, Computer Science::Systems and Control, Control and Systems Engineering, Control theory, [ SPI.AUTO ] Engineering Sciences [physics]/Automatic, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Electrical and Electronic Engineering, Mathematics
Abstract: International audience; This article investigates the asymptotic stability of impulsive delay dynamical systems (IDDS) by using the Lyapunov-Krasovskii method and looped-functionals. The proposed conditions reduce the conservatism of the results found in the literature by allowing the functionals to grow during both the continuous dynamics and the discrete dynamics. Sufficient conditions for asymptotic stability in the form of linear matrix inequalities (LMI) are provided for the case of impulsive delay dynamical systems with linear and time-invariant (LTI) base systems (non-impulsive actions). Several numerical examples illustrate the effectiveness of the method.
Published: 2017
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38. Nouvelle approche pour la commande de l’anesthésie basée sur un découplage de la dynami

Author: Isabelle Queinnec, Michel Mazerolles, Germain Garcia, Sophie Tarbouriech, and Said Zabi
Subjects: Control and Systems Engineering, Electrical and Electronic Engineering, Industrial and Manufacturing Engineering, Computer Science Applications
Abstract: Dans cet article une nouvelle strategie est presentee pour la commande de l'anesthesie, tenant compte des saturations des actionneurs, de l'intervalle cible pour la profondeur d'endormissement du patient et permettant de suivre une reference constante pour cette profondeur d'endormissement via l'ajout d'un integrateur. Par ailleurs, pour tenir compte de la dispersion des dynamiques qui composent les modeles d'anesthesie, le systeme est re-exprime en decouplant les dynamiques rapides des dynamiques lentes. Ces dernieres sont ainsi considerees comme des perturbations du sous-systeme rapide et vice versa. La variabilite des patients est prise en compte via l'utilisation d'incertitudes polytopiques et la synthese d'un correcteur robuste est proposee a travers la resolution d'un probleme d'optimisation sous contraintes exprimees sous forme d'inegalites matricielles lineaires.
Published: 2017
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39. Stability analysis of systems with nested saturation and backlash in the loop via nonstandard anti-windup compensation

Author: Sophie Tarbouriech, Christophe Prieur, Isabelle Queinnec, 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), GIPSA - Systèmes non linéaires et complexité (GIPSA-SYSCO), Département Automatique (GIPSA-DA), Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), 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, and Prieur, Christophe
Subjects: 0209 industrial biotechnology, Computer science, 02 engineering and technology, Stability (probability), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Loop (topology), [SPI.AUTO] Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Exponential stability, Control theory, Stability theory, Control system, Attractor, Saturation (chemistry), Backlash, ComputingMilieux_MISCELLANEOUS
Abstract: This paper deals with control systems subject to backlash and saturation in the loop. One of the goals is to characterize, or at least to approximate, the attractor of such nonlinear dynamical systems. Then, the regional or global asymptotic stability of the closed loop with respect to this attractor is handled. An anti-windup inspired loops is added aiming at improving the quality of the attractor approximation in which converge the closed-loop trajectories and of the basin of attraction of such an attractor. Numerically tractable algorithms with feasibility guarantee are provided, as soon as the linear closed-loop system, obtained by neglecting the backlash and saturation effects, is asymptotically stable. The interest of the results is drawn through an illustrative example.
Published: 2019

40. Observer-based event-triggered control in the presence of cone-bounded nonlinear inputs

Author: Alexandre Seuret, L. G. Moreira, Sophie Tarbouriech, J.M. Gomes da Silva, Universidade Federal do Rio Grande do Sul [Porto Alegre] (UFRGS), 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, Logarithm, Observer (quantum physics), Computer science, Linear system, 02 engineering and technology, stability, cone-bounded nonlinearities, Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Nonlinear system, Dwell time, observer-based control, 020901 industrial engineering & automation, Exponential stability, Control and Systems Engineering, Control theory, Bounded function, Convex optimization, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Event-triggered control, LMI, Analysis
Abstract: International audience; This paper presents an observer-based event-triggered strategy for linear systems subject to input cone-bounded nonlinearities. Both the emulation and co-design problems are addressed. Considering a Lyapunov approach and the cone-bound property of the input nonlinearity, sufficient conditions based on linear matrix inequalities are derived to ensure regional or global asymptotic stability of the origin of the closed-loop system. These conditions are incorporated into convex optimization problems to optimally determine the event generator parameters and the controller gain (in the co-design case) aiming at reducing the number of control updates with respect to periodic implementations for a prescribed observer gain. The event-triggering strategy considers a dwell time to cope with Zeno behaviors. Numerical examples, considering systems with quantized logarithmic inputs and saturating inputs, illustrate the potentialities of the approach.
Published: 2019
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41. $\mathcal{L}_2$ State Estimation with Guaranteed Convergence Speed in the Presence of Sporadic Measurements

Author: Francesco Ferrante, Frédéric Gouaisbaut, Ricardo G. Sanfelice, Sophie Tarbouriech, GIPSA - Systèmes non linéaires et complexité (GIPSA-SYSCO), Département Automatique (GIPSA-DA), Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), 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, Computer Engineering Department (UCSC Department of Computer Engineering), University of California [Santa Cruz] (UCSC), University of California-University of California, 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 California [Santa Cruz] (UC Santa Cruz), and University of California (UC)-University of California (UC)
Subjects: 0209 industrial biotechnology, sampled-data systems, Hybrid systems, Observer (quantum physics), Computer science, Bioengineering, 02 engineering and technology, observer design, Systems and Control (eess.SY), Stability (probability), Electrical Engineering and Systems Science - Systems and Control, Linear dynamical system, 020901 industrial engineering & automation, Control theory, Robustness (computer science), [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Convergence (routing), FOS: Electrical engineering, electronic engineering, information engineering, Sampled -data systems, Electrical and Electronic Engineering, Sampled data systems, LMIs, Applied Mathematics, Mechanical Engineering, 16. Peace & justice, cs.SY, Linear matrix In- equalities LMIs, Computer Science Applications, Nonlinear system, Industrial Engineering & Automation, Control and Systems Engineering, Hybrid system, Measurement uncertainty, State estimation
Abstract: This paper deals with the problem of estimating the state of a linear time-invariant system in the presence of sporadically available measurements and external perturbations. An observer with a continuous intersample injection term is proposed. Such an intersample injection is provided by a linear dynamical system, whose state is reset to the measured output estimation error at each sampling time. The resulting system is augmented with a timer triggering the arrival of a new measurement and analyzed in a hybrid system framework. The design of the observer is performed to achieve global exponential stability with a given decay rate to a set wherein the estimation error is equal to zero. Robustness with respect to external perturbations and $\mathcal{L}_2$-external stability from the plant perturbation to a given performance output are considered. Moreover, computationally efficient algorithms based on the solution to linear matrix inequalities are proposed to design the observer. Finally, the effectiveness of the proposed methodology is shown in three examples., Comment: Extended version of "$\mathcal{L}_2$ State Estimation with Guaranteed Convergence Speed in the Presence of Sporadic Measurements". This version contains fixes to some minor typos
Published: 2019
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42. A Hybrid Adaptive Inverse for Uncertain SISO Linear Plants with Full Relative Degree *

Author: Luca Zaccarian, Matteo Ragni, Sophie Tarbouriech, Matteo Cocetti, 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, Dipartimento di Ingegneria Industriale [Trento], University of Trento [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)-Université Toulouse Capitole (UT Capitole), and Université de Toulouse (UT)
Subjects: 0209 industrial biotechnology, Degree (graph theory), Basis (linear algebra), 020208 electrical & electronic engineering, Regulator, Inverse, 02 engineering and technology, Action (physics), [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Discrete time and continuous time, Control theory, Hybrid system, 0202 electrical engineering, electronic engineering, information engineering, Full Relative, Mathematics
Abstract: International audience; We propose a hybrid adaptive feed-forward regulator for single-input single-output linear plants with full relative degree. The scheme includes an adaptive law that estimates the inverse of the plant and provides a feed-forward control calculated on the basis of the desired output and its derivatives. The adaptation is performed during discrete time events, called jumps, while the feed-forward action is continuous. This combination leads to a full hybrid system. The advantage of this framework is a conceptual separation between the adaptation dynamics, which is discrete, and the plant dynamics, which is continuous. Under an assumption of a persistence of excitation, we show through examples that the output asymptotically tracks the desired reference and that the estimate of the parameters of the inverse converges.
Published: 2019
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43. PI event-triggered control under saturating actuators

Author: L. G. Moreira, L. B. Groff, João Manoel Gomes da Silva, Sophie Tarbouriech, 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), Departamento de Engenharia Eletrica (UFRGS), Universidade Federal do Rio Grande do Sul [Porto Alegre] (UFRGS), 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, Computer science, PID controller, Sampling (statistics), 02 engineering and technology, Function (mathematics), Stability (probability), Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Set (abstract data type), symbols.namesake, 020901 industrial engineering & automation, Exponential stability, Control and Systems Engineering, Control theory, 0202 electrical engineering, electronic engineering, information engineering, symbols, 020201 artificial intelligence & image processing, Actuator
Abstract: International audience; This paper proposes a methodology to design stabilising event-trigger strategies for PI-controlled linear continuous-time plants subject to input saturation. Using Lyapunov theory techniques, conditions based on linear matrix inequalities (LMI) are derived to guarantee regional (or global, when possible) asymptotic stability of the equilibrium. These conditions can be incorporated in optimisation problems to choose the parameters of the trigger function aiming at reducing the sampling activity, while ensuring the regional stability of the equilibrium with respect to a given set of admissible initial states. Simulation results illustrate the application and potentialities of the method.
Published: 2019
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44. Hierarchical estimation of the region of attraction for systems subject to a state delay and a saturated input

Author: Alexandre Seuret, Swann Marx, Sophie Tarbouriech, 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), Université de Toulouse (UT), 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), and Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse Capitole (UT Capitole)
Subjects: 0209 industrial biotechnology, 020208 electrical & electronic engineering, Linear system, 02 engineering and technology, Linear matrix, Attraction, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Convex optimization, 0202 electrical engineering, electronic engineering, information engineering, Initial value problem, Applied mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Saturation (chemistry), Legendre polynomials, Mathematics
Abstract: International audience; This paper addresses the local stability analysis problem for linear systems subject to input saturation and state delay. Thanks to the construction of a Lyapunov-Krasovskii functional associated to Legendre polynomials and the use of generalized sector conditions, sufficient linear matrix inequalities (LMIs) are derived to guarantee the local stability of the origin for the closed-loop system. In addition, an estimate of the basin of attraction of the origin is provided, which does not include the derivative of the initial condition. A convex optimization problem leans on these conditions to maximize the size of the estimate of the basin of attraction. Optimal LMIs form a hierarchy, which is competitive to improve the size criterium of the estimate of the basin of attraction. An example illustrates the potential of the technique.
Published: 2019
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45. Discontinuous model recovery anti-windup for image based visual servoing

Author: Henry de Plinval, Laurent Burlion, Sophie Tarbouriech, Luca Zaccarian, 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 - 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, ONERA - The French Aerospace Lab [Toulouse], ONERA, 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: 0209 industrial biotechnology, Invariance principle, Computer science, 020208 electrical & electronic engineering, 02 engineering and technology, Time-varying systems, Space (mathematics), Object (computer science), Visual servoing, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Double integrator, 020901 industrial engineering & automation, Exponential stability, Model recovery anti-windup, Control and Systems Engineering, Control theory, Position (vector), 0202 electrical engineering, electronic engineering, information engineering, Uncertain systems, Electrical and Electronic Engineering, Image-based visual servo control, Anti windup
Abstract: International audience; A discontinuous model recovery anti-windup technique is proposed for a double integrator with the output measurement corrupted by a time-varying scaling factor. This challenging measurement configuration arises in vision-based control, where the position of an object moving in the three-dimensional space is determined using two-dimensional images. We prove uniform global asymptotic stability of the closed loop by applying an invariance principle argument to the regularized dynamics. The effectiveness of the proposed approach is illustrated on a visual aircraft landing simulation example.
Published: 2019
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46. A nonsmooth hybrid invariance principle applied to robust event-triggered design

Author: Christophe Prieur, Alexandre Seuret, Luca Zaccarian, Sophie Tarbouriech, Andrew R. Teel, 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, GIPSA - Systèmes non linéaires et complexité (GIPSA-SYSCO), Département Automatique (GIPSA-DA), Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Department of Electrical and Computer Engineering [Santa Barbara] (ECE-UCSB), University of California [Santa Barbara] (UCSB), University of California-University of California, 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 California [Santa Barbara] (UC Santa Barbara), and University of California (UC)-University of California (UC)
Subjects: 0209 industrial biotechnology, Mathematical optimization, non-smooth Lyapunov function, hybrid dynamical systems, Invariance principle, Tangent cone, 02 engineering and technology, Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Exponential stability, uncertain systems, Control and Systems Engineering, Robustness (computer science), Control theory, Control system, Jump, Symmetric matrix, LaSalle invariance principle, Electrical and Electronic Engineering, Event-triggered control, Mathematics
Abstract: International audience; We first propose a nonsmooth hybrid invariance principle with relaxed conditions stemming from the fact that flowing solutions evolve only in the tangent cone, and complete jumping solutions cannot jump ouside the jump and flow sets. We then show an application consisting in the design of event-triggered rules to stabilize a class of uncertain linear control systems. The event-triggering rule depends only on local information, that is it uses only the output signals available to the controller. The approach proposed combines a hybrid framework to describe the closed-loop system with looped functionals based techniques. The proposed design conditions are formulated in terms of linear matrix inequalities (LMIs) ensuring global robust asymptotic stability of the closed-loop system. A tunable parameter is also available to guarantee an adjustable dwell-time property of the solutions. The effectiveness of the approach is evaluated through an example borrowed from the literature.
Published: 2019
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47. A switched control strategy including time optimal control and robust dynamic output feedback for anesthesia

Author: Isabelle Queinnec, Sophie Tarbouriech, Michel Mazerolles, Germain Garcia, Said Zabi, 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, Service d'Anesthésie - Réanimation, Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-CHU Toulouse [Toulouse]-Hôpital de Rangueil, CHU Toulouse [Toulouse], 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)-Université de Toulouse (UT)-Centre Hospitalier Universitaire de Toulouse (CHU Toulouse)
Subjects: 0209 industrial biotechnology, Control and Optimization, Computer science, Control (management), Stability (learning theory), Phase (waves), 02 engineering and technology, Interval (mathematics), Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Human-Computer Interaction, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Bispectral index, Anesthesia, State (computer science), Electrical and Electronic Engineering, Robust control, Actuator
Abstract: International audience; Mimicking the medical practice, this paper deals with the control of hypnosis during a surgical intervention thanks to a switched control strategy. The key idea consists in starting with an initial minimum time control for the induction phase followed by a dynamic output feedback for the maintenance phase. The objective during the first phase is to bring the patient from its awake state to a final state corresponding to some given depth of hypnosis, measured by the BIS, within a minimum time. Then, once the patient state is close to the desired target, the control is switched to a dynamic output feedback ensuring that the BIS stays in a given interval taking into account the saturation of the actuator and the multi-time scale dynamics in the anesthesia model. Positivity of the system is also preserved thanks to the use of input saturation and state constraints. The stability of the switched control strategy is addressed and the theoretical conditions are evaluated on different case studies.
Published: 2019
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48. Hybrid models of opinion dynamics with opinion-dependent connectivity

Author: Sophie Tarbouriech, Luca Zaccarian, Paolo Frasca, Systèmes Commandés en Réseau (NECS-POST), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Département Automatique (GIPSA-DA), Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), 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], University of Trento [Trento], 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, Physics::Physics and Society, 0209 industrial biotechnology, Computer science, Lyapunov analysis, Stability (learning theory), 02 engineering and technology, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Convergence (routing), 0202 electrical engineering, electronic engineering, information engineering, Hybrid dynamical systems, Opinion dynamics, Statistical physics, Electrical and Electronic Engineering, 020208 electrical & electronic engineering, Interaction model, n/a OA procedure, Flow (mathematics), Control and Systems Engineering, Hybrid system, Ordinary differential equation, symbols, Pairwise comparison, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract: International audience; This paper is a first attempt at using tools from the theory of hybrid systems to study opinion dynamics on networks with opinion-dependent connectivity. According to the hybrid framework, our dynamics are represented by the combination of continuous flow dynamics and discrete jump dynamics. The flow embodies the attractive forces between the agents and is defined by an ordinary differential equation whose right-hand side is a Laplacian, whereas the jumps describe the activation or deactivation of the pairwise interactions between agents. We first reformulate the classical Hegselmann–Krause model in this framework and then define a novel interaction model, which has the property of being scale-invariant. We study the stability and convergence properties of both models by a Lyapunov analysis, showing convergence and clusterization of opinions.
Published: 2019
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49. On Sensor Quantization in Linear Control Systems: Krasovskii Solutions meet Semidefinite Programming

Author: Frédéric Gouaisbaut, Francesco Ferrante, Sophie Tarbouriech, GIPSA - Systèmes non linéaires et complexité (GIPSA-SYSCO), Département Automatique (GIPSA-DA), Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), 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: 0209 industrial biotechnology, Control and Optimization, Computer science, Differential equation, Linear Matrix Inequalities, Stability (learning theory), Systems and Control (eess.SY), 02 engineering and technology, Discontinuous-Control, Electrical Engineering and Systems Science - Systems and Control, Matrix (mathematics), 020901 industrial engineering & automation, Exponential stability, Stability theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Quantization, FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Mathematics - Optimization and Control, Semidefinite programming, Applied Mathematics, Quantization (signal processing), 020208 electrical & electronic engineering, Optimization and Control (math.OC), Control and Systems Engineering, Control system, Krasovksii Solutions
Abstract: Stability and stabilization for linear state feedback control systems in the presence of sensor quantization are studied. As the closed-loop system is described by a discontinuous right-hand side differential equation, Krasovskii solutions (to the closed-loop system) are considered. Sufficient conditions in the form of matrix inequalities are proposed to characterize uniform global asymptotic stability of a compact set containing the origin. Such conditions are shown to be always feasible whenever the quantization-free closed-loop system is asymptotically stable. Building on the obtained conditions, computationally affordable algorithms for the solution to the considered problems are illustrated. The effectiveness of the proposed methodology is shown in three examples., V1 fixes some minor typos in the published version. Corrections are colored in blue
Published: 2019
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50. Regional Hinfinity Synchronization of Identical Linear Multi-agent Systems under Input Saturation

Author: Laura Dal Col, Sophie Tarbouriech, Isabelle Queinnec, 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), Dipartimento di Informatica, Sistemi e Produzione [Roma] (DISP), Università degli Studi di Roma Tor Vergata [Roma], 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: Output feedback, Controller design, 0209 industrial biotechnology, Control and Optimization, Computer Networks and Communications, Computer science, Multi-agent system, 020208 electrical & electronic engineering, Bilinear matrix inequality, Regular polygon, 02 engineering and technology, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science::Multiagent Systems, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Signal Processing, 0202 electrical engineering, electronic engineering, information engineering, Symmetric matrix, Saturation (magnetic)
Abstract: International audience; This paper addresses the local synchronization problem of identical linear multi-agent systems subject to input saturation constraints and exogenous disturbances with guaranteed region of attraction. A dynamic output feedback controller is proposed, while the information exchanged through the network is the relative input mismatch of each agent with respect to the neighbors. Using a suitable incremental sector condition we cast the synchronization of multi-agent systems with general undirected topology in terms of Bilinear Matrix Inequalities (BMIs). Based on a multi-step convex controller design procedure, the effectiveness of the theoretical results is demonstrated through numerical simulations of a fleet of quadrotors.
Published: 2019
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