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19 results on '"Jean-Claude Vivalda"'

1. Strong differential observability for sampled systems

Author

Sabeur Ammar, Basma Zitouni, Jean-Claude Vivalda, Institut Supérieur de l'Informatique et Multimédia de Sfax, Université de Sfax - University of Sfax, Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Faculté des Sciences de Sfax, and ANR-19-CE48-0004,ODISSE,Synthèse d'observateur pour des systèmes de dimension infinie(2019)

Subjects
0209 industrial biotechnology, sampled systems, Control and Optimization, Transversality, observability, Applied Mathematics, 010102 general mathematics, Observable, 02 engineering and technology, 93C57, 01 natural sciences, 020901 industrial engineering & automation, transversality AMS subject classifications. 93B07, Applied mathematics, Observability, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, genericity, Differential (mathematics), Mathematics, transversality
Abstract

International audience; In this paper we prove that, generically, a sampled data system is strongly differentially observable provided that the number of outputs is greater than the number of inputs plus one.

Published
2020
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2. Analysis and Output Tracking Design for the Direct Contact Membrane distillation parabolic system

Author

Jean-Claude Vivalda, Mohamed Ghattassi, Taous-Meriem Laleg, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), King Abdullah University of Science and Technology (KAUST), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Noise (signal processing), Applied Mathematics, 010102 general mathematics, Boundary (topology), Servomechanism, 01 natural sciences, Parabolic partial differential equation, law.invention, 010101 applied mathematics, Tracking error, Mathematics - Analysis of PDEs, Optimization and Control (math.OC), Control theory, law, FOS: Mathematics, State observer, Uniqueness, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, MESH: Direct Contact Membrane Distillation System, Well-Posedness Criteria, disturbance rejection, disturbance rejection control, Mathematics - Optimization and Control, Analysis, Analysis of PDEs (math.AP), Mathematics
Abstract

This paper considers the performance output tracking for a boundary controlled Direct Contact Membrane Distillation (DCMD) system. First, the mathematical properties of a recently developed mathematical model of the DCMD system are discussed. This model consists of parabolic equations coupled at the boundary. Then, the existence and uniqueness of the solutions are analyzed, using the theory of operators. Some regularity results of the solution are also established. A particular case showing the diagonal property of the principal operator is studied. Then, based on one-side feedback law the control problem, which consists of tracking both the feed and permeate outlet temperatures of the membrane distillation system is formulated. A servomechanism and an output feedback controller are proposed to solve the control problem. In addition, an extended state observer aimed at estimating both the system state and disturbance, based on the temperature measurements of the inlet is proposed. Thus, by some regularity for the reference signal and when the disturbance vanishes, we prove the exponential decay of the output tracking error. Moreover, we show the performance of the control strategy in presence of the flux noise., 32 pages, 4 figures

Published
2020
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3. State observer design for Direct Contact Membrane Distillation Parabolic systems

Author

Jean-Claude Vivalda, Mohamed Ghattassi, Taous-Meriem Laleg-Kirati, King Abdullah University of Science and Technology (KAUST), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Lyapunov function, 0209 industrial biotechnology, Partial differential equation, Observer (quantum physics), Computer science, Exponential convergence, 02 engineering and technology, Membrane distillation, Desalination, 6. Clean water, symbols.namesake, 020901 industrial engineering & automation, 020401 chemical engineering, Control theory, Heat transfer, symbols, State observer, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0204 chemical engineering
Abstract

International audience; This paper proposes a state observer for a coupled two dimensional partial differential equations (PDEs) system used to describe the heat transfer in a membrane distillation system for water desalination. The mathematical model based on reaction-diffusion system is introduced. Sufficient conditions for the exponential convergence of the estimation error is presented using Lyapunov method. A numerical example is also provided to illustrate the effectiveness of the proposed observer.

Published
2018
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4. On the stabilization of quadratic nonlinear systems

Author

Jean-Claude Vivalda, Mohamed Oumoun, Lahcen Maniar, Université Cadi Ayyad [Marrakech] (UCA), Systems with physical heterogeneities : inverse problems, numerical simulation, control and stabilization (SPHINX), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, 020208 electrical & electronic engineering, General Engineering, 02 engineering and technology, Nonlinear system, 020901 industrial engineering & automation, Quadratic equation, Control theory, Quadratic control systems, Control Lyapunov function, 0202 electrical engineering, electronic engineering, information engineering, Continuous feedback, Global stabilization, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Lyapunov redesign, Control (linguistics), Control-Lyapunov function, Mathematics
Abstract

International audience; The aim of this paper is to study the problem of stabilization of nonlinear systems with a quadratic control. Under the assumption that a control Lyapunov function (CLF) is known, we derive necessary and sufficient conditions for the stabilization by continuous feedback controls explicitly computed. Illustrative examples are presented.

Published
2017
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5. Self-triggered Continuous Discrete Observer with Updated Sampling Period

Author

Vincent Andrieu, Madiha Nadri, Jean-Claude Vivalda, Ulysse Serres, SNLEP, 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)-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), Arbeitsgruppe Funktionalanalysis, Bergische Universität Wuppertal, Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), and ANR-12-BS03-0005,LimICoS,Synthèse et analyse des systèmes avec informations limitées(2012)

Subjects
Nonlinear system, Variable (computer science), Observer (quantum physics), Dynamical systems theory, Control and Systems Engineering, Control theory, Convergence (routing), State observer, Electrical and Electronic Engineering, Lipschitz continuity, Alpha beta filter, Mathematics, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; This paper deals with the design of high gain observers for a class of continuous-time dynamical systems with discrete-time measurements. Dierent approaches based on high gain techniques have been followed in the literature to tackle this problem. Contrary to these works, the measurement sampling time is considered to be variable. Moreover, the new idea of the proposed work is that the use of the output measurements by the observer follows an event based on an extended observer state component. Assuming that the vector elds related to the considered system are globally Lipschitz, the asymptotic convergence of the observation error is established. As an application of this approach, a state estimation problem of an academic bioprocess is studied, and its simulation results are discussed.

Published
2015
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6. Dynamic output feedback for switched linear systems based on a LQG design

Author

Pierre Riedinger, Jean-Claude Vivalda, Centre de Recherche en Automatique de Nancy (CRAN), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), Robust control of infinite dimensional systems and applications (CORIDA), Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Engineering, business.industry, Linear system, Control engineering, Linear-quadratic regulator, DC-DC Power converters, Converters, Linear-quadratic-Gaussian control, Power (physics), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Output feedback, Control and Systems Engineering, Control theory, [INFO.INFO-IR]Computer Science [cs]/Information Retrieval [cs.IR], Convex combination, Optimal projection equations, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Electrical and Electronic Engineering, business, LQG, Switched systems, Control-Lyapunov function
Abstract

International audience; The aim of this paper is the extend of the LQG design for linear system to the case of switched linear systems in continuous time. The main result provides a control Lyapunov function and a dynamic output feedback law leading to sub-optimal solutions. Practically, the dynamic output feedback is easy to apply and the design procedure is effective if there exists at least one controllable and observable convex combination of the subsystems. Practical applications concern the large class of power converters.

Published
2015
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7. A separation principle for linear impulsive systems

Author

Imen Ellouze, Mohamed Hammami, Jean-Claude Vivalda, Département de Mathematiques [Sfax], Faculté des Sciences de Sfax, Université de Sfax - University of Sfax-Université de Sfax - University of Sfax, Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, and Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM)

Subjects
0209 industrial biotechnology, 010102 general mathematics, General Engineering, 02 engineering and technology, Kalman filter, State (functional analysis), Separation principle, 01 natural sciences, Controllability, 020901 industrial engineering & automation, Control theory, Observability, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Observer based, Mathematics
Abstract

International audience; In this paper, we deal with the problem of the stabilization and the estimation of the state for a class of linear impulsive systems. We show that, under the classical Kalman's conditions of controllability and observability it is possible to design an observer based controller for the linear \emph{impulsive} system.

Published
2014
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8. An LQ sub-optimal stabilizing feedback law for switched linear systems

Author

Jean-Claude Vivalda, Pierre Riedinger, Centre de Recherche en Automatique de Nancy (CRAN), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), CORIDA, European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est

Subjects
Lyapunov function, 0209 industrial biotechnology, Optimization problem, Existential quantification, Linear system, 02 engineering and technology, Upper and lower bounds, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, switched linear systems, Control theory, Law, Bellman equation, 0202 electrical engineering, electronic engineering, information engineering, symbols, 020201 artificial intelligence & image processing, Convex combination, LQ regulator, Control-Lyapunov function, Mathematics
Abstract

International audience; The aim of this paper is the design of a stabilizing feedback law for contin- uous time linear switched system based on the optimization of a quadratic criterion. The main result provides a control Lyapunov function and a feed- back switching law leading to sub optimal solutions. As the Lyapunov func- tion defines a tight upper bound on the value function of the optimization problem, the sub optimality is guaranteed. Practically, the switching law is easy to apply and the design procedure is effective if there exists at least a controllable convex combination of the subsystems.

Published
2014
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9. Continuous discrete observer with updated sampling period

Author

Ulysse Serres, Vincent Andrieu, Jean-Claude Vivalda, Madiha Nadri, 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), SNLEP, Université de Lyon-Université de Lyon-École Supérieure Chimie Physique Électronique de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), IFAC, Tarbouriech, Sophie and Krstic, Miroslav, CORDIA, 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), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est

Subjects
0209 industrial biotechnology, Class (computer programming), Observer (quantum physics), Dynamical systems theory, 020208 electrical & electronic engineering, 02 engineering and technology, Lipschitz continuity, continuous-discrete time observers, high gain observer, Nonlinear system, Variable (computer science), 020901 industrial engineering & automation, Control theory, Convergence (routing), 0202 electrical engineering, electronic engineering, information engineering, Nonlinear systems, sampled-data, State (computer science), updated sampled-data, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics
Abstract

International audience; This paper deals with the design of high gain observers for a class of continuous dynamical systems with discrete-time measurements. Indeed, different approaches based on high gain techniques have been followed in the literature to tackle this problem. Contrary to these works, the measurement sampling time is considered to be variable. Moreover, the new idea of the proposed work is to synthesize an observer requiring the less knowledge as possible from the output measurements. This is done by using an updated sampling time observer. Under the global Lipschitz assumption, the asymptotic convergence of the observation error is established. As an application of this approach, an estimation problem of state of an academic bioprocess is studied, and its simulation results are discussed.

Published
2013
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10. On the convergence of linear switched systems

Author

Jean-Claude Vivalda, Pierre Riedinger, Ulysse Serres, 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), Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM), Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Centre de Recherche en Automatique de Nancy (CRAN), Université Henri Poincaré - Nancy 1 (UHP)-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), CPER AOC (Automatique Optimisation et Contrôle) SC2 (Stabilité et Commande des Systèmes à Commutations), Université de Lyon-Université de Lyon-École Supérieure de Chimie Physique Électronique de Lyon (CPE)-Centre National de la Recherche Scientifique (CNRS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est

Subjects
0209 industrial biotechnology, three-cell converter, Differential equation, 02 engineering and technology, Dynamical system, Stability (probability), Quantitative Biology::Subcellular Processes, 020901 industrial engineering & automation, Control theory, Stopping time, Convergence (routing), 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, Switched systems, Mathematics, 020208 electrical & electronic engineering, Linear system, stability, Computer Science Applications, Control and Systems Engineering, Hybrid system, omega-limit set, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], human activities, Counterexample, dwell-time
Abstract

International audience; This paper investigates sufficient conditions for the convergence to zero of the trajectories of linear switched systems. We provide a collection of results that use weak dwell-time, dwell-time, strong dwell-time, permanent and persistent excitation hypothesis. The obtained results are shown to be tight by counterexample. Finally, we apply our result to the three-cell converter.

Published
2011
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11. On a class of switched linear systems

Author

Jean-Claude Vivalda, Pierre Riedinger, Ulysse Serres, Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Automatique de Nancy (CRAN), Université Henri Poincaré - Nancy 1 (UHP)-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), CPER MISN: AOC action SC2, European Project: 232501,EC:FP7:SME,FP7-SME-2008-1,HYCON(2009), Riedinger, Pierre, Hygienic and Energy Optimized Conveyor Belt for the Slaughtering Industry - HYCON - - EC:FP7:SME2009-10-01 - 2012-03-31 - 232501 - VALID, and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est

Subjects
0209 industrial biotechnology, Class (set theory), three-cell converter, Linear system, Zero (complex analysis), 02 engineering and technology, stability, 01 natural sciences, Stability (probability), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Quantitative Biology::Subcellular Processes, Dwell time, 020901 industrial engineering & automation, [SPI.AUTO] Engineering Sciences [physics]/Automatic, Control theory, 0103 physical sciences, Convergence (routing), omega-limit set, 010307 mathematical physics, human activities, Switched systems, Mathematics, Counterexample, dwell-time
Abstract

International audience; This paper investigates sucient conditions for the convergence to zero of the trajectories of linear switched systems. We provide a collection of results that use weak dwell-time, dwell-time, strong dwell-time, permanent and persistent activation hypothesis. The obtained results are shown to be tight by counterexample. Finally, we apply our result to the three-cell converter.

Published
2010

12. Controllability properties of a class of systems modeling swimming microscopic organisms

Author

Mario Sigalotti, Jean-Claude Vivalda, Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), Robust control of infinite dimensional systems and applications (CORIDA), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), INRIA Lorraine, Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Surface (mathematics), Physics, Control and Optimization, 010102 general mathematics, Systems modeling, Rigid body, Space (mathematics), 01 natural sciences, Action (physics), 010101 applied mathematics, Controllability, Computational Mathematics, Nonlinear system, Classical mechanics, Mathematics Subject Classification, Control and Systems Engineering, Optimization and Control (math.OC), FOS: Mathematics, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Mathematics - Optimization and Control
Abstract

We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploits the action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body, with Stokes equations governing the surrounding fluid. The action of the cilia is described by a set of controlled velocity fields on the surface of the organism. The first contribution of the paper is the proof that such a system is generically controllable when the space of controlled velocity fields is at least three-dimensional. We also provide a complete characterization of controllable systems in the case in which the organism has a spherical shape. Finally, we offer a complete picture of controllable and non-controllable systems under the additional hypothesis that the organism and the fluid have densities of the same order of magnitude. Mathematics Subject Classification. 37C20, 70Q05, 76Z10, 93B05, 93C10.

Published
2010
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13. Separation principle for a sampled bilinear system

Author

M. A. Hammami, Houssem Jerbi, S. Ammar, Jean-Claude Vivalda, Institut Supérieur d'Informatique et de Multimédia de Sfax (ISIMS), Université de Sfax - University of Sfax, Faculté des Sciences de Sfax, Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), CORIDA, and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est

Subjects
Bilinear systems, 0209 industrial biotechnology, Numerical Analysis, Control and Optimization, Algebra and Number Theory, Observer (quantum physics), observability, observer, 010103 numerical & computational mathematics, 02 engineering and technology, 93B07, 93C57, 93D15, Under sampling, Separation principle, 01 natural sciences, stabilization, Continuation, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, State observer, Observability, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Sampled bilinear system, Mathematics
Abstract

International audience; This work is a continuation of [2] and [1] in which the authors studied the preservation of the observability and observer under sampling. In this paper, by relaxing some hypotheses, we study the observability and stabilization problems for a sampled bilinear system. We give a characterization of the observability for such systems. Moreover, under some sufficient conditions, we show that the sampled of the bilinear system can be globally asymptotically stabilizable using a state observer.

Published
2010
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14. Observer and global output feedback stabilisation for some mechanical systems

Author

Sabeur Ammar, Mohamed Mabrouk, Jean Claude Vivalda, Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), CORIDA, and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est

Subjects
Output feedback, 0209 industrial biotechnology, Euler-Lagrange systems, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Triangular systems, 02 engineering and technology, Nonlinear control, 01 natural sciences, Feedback regulation, overhead crane, 020901 industrial engineering & automation, Control theory, 0103 physical sciences, output feedback stabilisation, 010301 acoustics, Gantry crane, non-linear observer, Mathematics, System identification, Control engineering, Overhead crane, Computer Science Applications, global asymptotic stabilisation, Mechanical system, 70Q05, 93D15, Control and Systems Engineering, two-link manipulator, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

International audience; The objective of the work is two-fold. A first part is devoted to the problem of constructing an observer to the practical system called overhead crane with the position as output. In a second part, the problem of global output feedback stabilisation is solved for a class of Euler-Lagrange systems when the variables of velocity are the unmeasured part of the state. The equations of these systems are non-linear with respect to the velocities. A new output feedback control scheme is proposed. It relies on the determination of a change of coordinates which gives to the systems a triangular form. To illustrate the approach, it is applied to a two-link manipulator.

Published
2009
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15. On practical observers for nonlinear uncertain systems

Author

Jean-Claude Vivalda, Thouraya Kharrat, Amel Benabdallah, Université de Sfax - University of Sfax, Robust control of infinite dimensional systems and applications (CORIDA), Institut Élie Cartan de Nancy (IECN), Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS)-Laboratoire de Mathématiques et Applications de Metz (LMAM), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Inria Nancy - Grand Est, Institut National de Recherche en Informatique et en Automatique (Inria), CORIDA, and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Inria Nancy - Grand Est

Subjects
0209 industrial biotechnology, General Computer Science, Observer (quantum physics), Mechanical Engineering, 93B07, 93B17, System identification, Uncertain systems, Observable, 02 engineering and technology, Nonlinear control, Triangular form, Unknown inputs, Practical observers, Nonlinear system, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, 0202 electrical engineering, electronic engineering, information engineering, Nonlinear systems, 020201 artificial intelligence & image processing, Affine transformation, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Electrical and Electronic Engineering, Observers, Mathematics
Abstract

International audience; In this paper, we show firstly that a differentially observable system affine with respect to the unknown input can be put into a triangular form. For systems under this form, we propose two strong practical observers. The first one has a constant gain while the second has a time-varying gain.

Published
2008
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16. State estimation for a fish population via a nonlinear observer

Author

M. Oumoun, Jean-Claude Vivalda, Abderrahman Iggidr, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paul Verlaine - Metz (UPVM), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
age-structured model, 0209 industrial biotechnology, Observer (quantum physics), [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], stock-recruitment function, 02 engineering and technology, 01 natural sciences, discrete time systems, nonlinear control systems, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Control theory, nonlinear observer, exponential observer, population dynamics, Quantitative Biology::Populations and Evolution, 14. Life underwater, State observer, 0101 mathematics, natural resources, Population dynamics of fisheries, Mathematics, Estimation, observers, estimation, 010102 general mathematics, observer, Function (mathematics), State (functional analysis), difference equations, exploited fish population, Exponential function, non- linear control systems, Nonlinear system, discrete-time systems, fish population
Abstract

International audience; This paper focuses on the construction of an exponential observer for an age-structured model of an exploited fish population in order to get an estimation of the number of fishes by age class. The considered model is nonlinear and involves a stock-recruitment function which is not well known. The observer that we construct is independent of this function.

Published
2000
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17. A simple observer for nonlinear discrete-time systems, application to a population dynamics model

Author

Jean-Claude Vivalda, Abderrahman Iggidr, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine

Subjects
0209 industrial biotechnology, demography, Observer (quantum physics), Computer science, Population, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, Constructive, discrete time systems, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 03 medical and health sciences, 020901 industrial engineering & automation, Control theory, Simple (abstract algebra), dead-beat observer, population dynamics, State observer, education, state feedback, 030304 developmental biology, nonlinear discrete-time systems, 0303 health sciences, education.field_of_study, observers, difference equations, dynamics, Nonlinear system, Discrete time and continuous time, nonlinear systems
Abstract

International audience; A constructive dead-beat observer design method for nonlinear discrete systems is given and illustrated with an application to a model of population dynamics.

Published
2000
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18. On the regulation of the state of a harvested fish population

Author

Jean-Claude Vivalda, M. El Bagdouri, A. Ouahbi, Abderrahman Iggidr, Laboratoire d'Automatique et d'Etude des Procédés, Université Cadi Ayyad [Marrakech] (UCA), Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
0209 industrial biotechnology, Engineering, Steady state (electronics), [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, Quantitative Biology::Other, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Aquaculture, Control theory, Quantitative Biology::Populations and Evolution, 14. Life underwater, 0101 mathematics, natural resources, Population dynamics of fisheries, asymptotic stability, business.industry, 010102 general mathematics, Fishery, aquaculture, fish population, State (computer science), nonlinear systems, business, fishery model
Abstract

International audience; The goal of this paper is to apply some tools of control theory to an age-structured fishery model in order to stabilize an exploited fish population around a nontrivial steady state.

Published
2000
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19. Stabilization of a class of multi-inputs nonlinear systems

Author

Abderrahman Iggidr, Jean-Claude Vivalda, Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM), INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria), Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Pure mathematics, Class (set theory), General Computer Science, Mechanical Engineering, 010102 general mathematics, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, State (functional analysis), 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Nonlinear system, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Affine transformation, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Electrical and Electronic Engineering, Equivalence (measure theory), ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

In this paper, we investigate the local stabilization of affine analytic systems x = f(x) + ∑ i = 1 n − 1 u i g i (x) with n − 1 inputs. We state a sufficient condition on the first approximation of f for which the local asymptotic stabilizability can be achieved; furthermore, we give explicitly the stabilizing feedback.

Published
1994
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