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25. 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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26. 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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32. 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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33. Observability Under Sampling for Nonlinear Systems

Author

Sabeur Ammar, Majid Massaoud, and Jean-Claude Vivalda

Subjects
0209 industrial biotechnology, Mathematical optimization, Class (set theory), Property (philosophy), Generalization, Sampling (statistics), 02 engineering and technology, Set (abstract data type), Nonlinear system, 020901 industrial engineering & automation, Mathematics (miscellaneous), Control and Systems Engineering, Simple (abstract algebra), 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, 020201 artificial intelligence & image processing, Observability, Electrical and Electronic Engineering, Mathematics
Abstract

A previous article has investigated the problem of the preservation of the observability under sampling in the framework of compact manifolds. A natural generalization of the cited result would be to extend it to the systems globally Lipschitzian defined on non compact manifolds. A simple representative of this class of systems is constituted by the set of bilinear systems, for this particular class of systems the preservation of the property of observability has been shown in a previous work. In this paper, we deal with the preservation of the observability under sampling for globally Lipschitzian systems defined on Rn.

Published
2016
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34. 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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35. Model based mass soot observer of diesel particle filter*

Author

Fehd Ben-Aicha, Michel Sorine, Karim Bencherif, Jean-Claude Vivalda, Technocentre Renault [Guyancourt], RENAULT, SIgnals and SYstems in PHysiology & Engineering (SISYPHE), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), 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), 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)-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, and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Engineering, active regeneration, 020209 energy, 02 engineering and technology, medicine.disease_cause, Diesel engine, 7. Clean energy, porous wall, Automotive engineering, thermal, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Diesel fuel, Extended Kalman filter, 020401 chemical engineering, 0202 electrical engineering, electronic engineering, information engineering, medicine, passive regeneration, 0204 chemical engineering, pressure drop, Pressure drop, Diesel particulate filter, Dynamometer, business.industry, mass soot estimation, particulate filter, Soot, 13. Climate action, Filter (video), Combustion engine, business
Abstract

International audience; Diesel Particulate Filters (DPF) has now been proven as an efficient solution in order to reduce Diesel PM emissions. Concerned by environment, Renault will equip all serial production Diesel vehicles with this technology. Main issue of such devices is the mandatory periodical regeneration in order to eliminate their soot content. The particulate filter (DPF) is used to store the soot emitted by the combustion engine. When the mass of particles in the filter reaches a certain limit mass, it is regenerated thanks to a temperature rise (Over 600◦C). In this paper, we develop a model that describes the impact of the amount of soot in the filter on the Diesel engine performance. This model is used to determine the optimal amount of soot on which the regeneration of the particulate filter shall start. Then we propose a physical model that describes the pressure drop of particulate filter according to the mass of accumulated soot and inlet DFP temperature and flow conditions. Thus, we improve a literature model so that it takes on account the passive regeneration of the filter. Finally, we design an extended kalman filter using the combination of the simplified model and a pressure drop measurement. All the experimental validations are made thanks to different configurations: engine dynamometer, chassis dynamometer and vehicles.

Published
2011
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36. Endless polarization control using two rotatable wave plates with variable birefringence

Author

Jean-Claude Vivalda, Weifeng Rong, and Laurent Dupont

Subjects
Physics, Birefringence, Control algorithm, business.industry, Optical polarization, Polarization (waves), Waveplate, Atomic and Molecular Physics, and Optics, Electronic, Optical and Magnetic Materials, law.invention, Optics, Polarization controller, law, Electrical and Electronic Engineering, Physical and Theoretical Chemistry, business
Abstract

We present in this article different designs of endless polarization controller based on the concatenation of rotatable wave plates. We show that with these kinds of wave plates, the architecture and the control algorithm of polarization controller are very simple and efficient. The different driving schemes of polarization controller are discussed by studying the limitation of the different possible technologies. Endless polarization control is obtained with two wave plates.

Published
2005
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37. On the genericity of the observability of controlled discrete-time systems

Author

Sabeur Ammar and Jean-Claude Vivalda

Subjects
Discrete system, Computational Mathematics, Nonlinear system, Control and Optimization, Discrete time and continuous time, Control and Systems Engineering, Control theory, Observability, Mathematics
Abstract

In this paper, we prove the genericity of the observability for discrete-time systems with more outputs than inputs.

Published
2005
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38. Observers for Lipschitz non-linear systems

Author

Jean-Claude Vivalda, C. Aboky, and Gauthier Sallet

Subjects
Nonlinear system, Observer (quantum physics), Relation (database), Control and Systems Engineering, Control theory, Convergence (routing), Set (psychology), Lipschitz continuity, Unobservable, Computer Science Applications, Counterexample, Mathematics
Abstract

In an interesting paper R. Rajamani and Y. M. Cho have proposed a systematic methodology to design observers. They have introduced a new problem: relation between distance to unobservability and convergence of 'Luenberger-like' observers. A result for the convergence of the observer has also been given. They have presented a quantity denoted by i, claimed as the distance to unobservability. We show that this number is not actually the distance from the system to the set of unobservable systems. Moreover, the result for the observer is incorrect. We provide a counterexample for the result of convergence. In this paper results for convergence are obtained, with additional strengthened hypothesis, to correct Rajamani and Cho's result. The results are used to design an observer for a, now classical, single-link flexible robot joint. The behaviour of the observer to noisy output is quite satisfactory.

Published
2002
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39. 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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40. Mathematical Analysis of Stability and Drift Behavior of Hydraulic Cylinders Driven by a Servovalve

Author

Jean Claude Vivalda and Edouard Richard

Subjects
Lyapunov function, Invariance principle, Mechanical Engineering, Physical system, Computer Science Applications, Cylinder (engine), law.invention, Hydraulic cylinder, symbols.namesake, Control and Systems Engineering, Control theory, law, Nonlinear model, symbols, Actuator, Instrumentation, Center manifold, Information Systems, Mathematics
Abstract

Hydraulic cylinders are commonly used and many works deal with modeling and control of such devices. This article deals with the stability properties of hydraulic cylinders drift in various situations. The study is based on a classic nonlinear model of these physical systems. The cases of system models without leakages and models with cylinder leakages or servovalve leakages are distinguished and lead to distinct behaviors. The stability properties are proven by various mathematical arguments such as first integrals, Lyapunov theorems, LASALLE invariance principle, BARBALAT’s lemma, and the center manifold theory.

Published
2001
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41. A Separation Result for Nonlinear Systems with Lagged Discrete Time Outputs Measurement

Author

Edouard Richard, Jean-Claude Vivalda, and Marco Pengov

Subjects
Nonlinear system, Stabilization methods, Discrete time and continuous time, Exponential growth, Observer (quantum physics), Control theory, Discrete-time stochastic process, State (functional analysis), Separation result, Mathematics
Abstract

In this article, continuous time nonlinear systems with lagged discrete time outputs are considered. Consider a globally exponentially continuous-discrete observer: an estimation of the whole state is given continuously but only some linear forms of the state are available in discrete time. If there exists a globally exponentially stabilizing continuous time state feedback law then, under some conditions, the feedback law computed with the estimated states still globally exponentially stabilize the system.

Published
1998
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42. A Continuous-Discrete Observer for a Class of Nonlinear Systems

Author

Marco Pengov, Jean-Claude Vivalda, and Edouard Richard

Subjects
Discrete system, Nonlinear system, Discrete time and continuous time, Observer (quantum physics), Exponential growth, Control theory, State estimator, Bioprocess, Mathematics
Abstract

In this article, a state estimator with global exponentially convergence is given. It is based on a continuous time nonlinear system and on output's Ineasurements available in discrete time. For the proof, it is needed a particularity of the system which, as it is shown, usually shared by bioprocesses. A simulation of a classic bioprocess is also given.

Published
1998
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43. 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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44. On the Stabilization of a Class of Bilinear Systems in 3-Space

Author

Jean-Claude Vivalda and Mohamed Oumoun

Subjects
Bilinear systems, Class (set theory), Degree (graph theory), Homogeneous, Control theory, General Engineering, Zero (complex analysis), Applied mathematics, Space (mathematics), Mathematics
Abstract

We investigate the stabilization by means of homogeneous feedbacks of degree zero of a class of bilinear systems in 3-space.

Published
1996
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45. On radial and directional controllability of bilinear systems

Author

Jean Claude Vivalda, Andrea Bacciotti, Dipartimento di Matematica 'Giuseppe Peano' [Torino], Università degli studi di Torino = University of Turin (UNITO), 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), Institut Élie Cartan de Lorraine (IECL), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), CORIDA, Università degli studi di Torino (UNITO), 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), 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
Bilinear systems, Controllability, 0209 industrial biotechnology, General Computer Science, Controllability Gramian, Mechanical Engineering, 010102 general mathematics, Bilinear system, 02 engineering and technology, 01 natural sciences, Switched systems, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Vector field, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Electrical and Electronic Engineering, Mathematics
Abstract

International audience; In this note we study two notions of controllability, called respectively radial controllability and directional controllability. They are both weakened versions of the classical notion of global controllability. We prove that for families of linear vector fields, the two notions are actually equivalent.

Published
2013
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46. 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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47. Stabilization of nonlinear systems: A bilinear approach

Author

Jean-Claude Vivalda, Gauthier Sallet, and Rachid Chabour

Subjects
Bilinear systems, Nonlinear system, Control and Optimization, Planar, Control and Systems Engineering, Control theory, Applied Mathematics, Signal Processing, Bilinear interpolation, Mathematics
Abstract

This paper gives a necessary and sufficient condition for the stabilization of planar bilinear systems. Local stabilization results are obtained for other systems.

Published
1993
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48. 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

49. 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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50. 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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