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54 results on '"European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010)"'

1. A robust stability framework for LTI systems with time-varying sampling

Author

Christophe Fiter, Laurentiu Hetel, Jean-Pierre Richard, Wilfrid Perruquetti, Systèmes Non Linéaires et à Retards (SyNeR), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Non-Asymptotic estimation for online systems (NON-A), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Région Nord - Pas de Calais project ARCIR ESTIREZ, ANR-14-CE27-0008,ROCC-SYS,Commande Robuste des Systèmes Cyber-Physiques(2014), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Linear matrix inequality, Sampling (statistics), state-dependent sampling, Stability (probability), event-triggered control, LTI system theory, Stability conditions, self-triggered control, sampled-data control, sampling jitter, Exponential stability, time-varying sampling, Control and Systems Engineering, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Lyapunov-Razumikhin, State space, Electrical and Electronic Engineering, linear matrix inequality, Importance sampling, convex embedding, Mathematics
Abstract

International audience; This work aims at enlarging the sampling intervals in several state feedback control situations by designing a sampling map in the state space. We consider the case of linear time invariant (LTI) systems with state-bounded perturbations, and guarantee their exponential stability for a chosen decay-rate. The approach is based on linear matrix inequalities (LMIs) obtained thanks to Lyapunov-Razumikhin stability conditions and convexification arguments. First, it enables to optimize the lower-bound of the sampling maps by computing the adequate Lyapunov-Razumikhin function. This result can be interpreted as a robust stability analysis with respect to arbitrary time-varying sampling intervals, which may be useful in the case of uncontrolled sampling, or in the presence of phenomenon such as sampling jitter. Then, the obtained results are extended to design the sampling map in three dynamic sampling control situations: event-triggered control, self-triggered control, and state-dependent sampling. The results are illustrated with a numerical example from the literature.

Published
2015
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2. A hyperbolic model of chemotaxis on a network: a numerical study

Author

Gabriella Bretti, Magali Ribot, Roberto Natalini, Istituto per le Applicazioni del Calcolo 'Mauro Picone' (IAC), Consiglio Nazionale delle Ricerche [Roma] (CNR), Laboratoire Jean Alexandre Dieudonné (JAD), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), COmplex Flows For Energy and Environment (COFFEE), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (JAD), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), This work has also been partially supported by the PRIN project 2008-2009 'Equazioni iperboliche non lineari e fluidodinamica', ANR-10-JCJC-0103,MONUMENTALG,MOdélisation mathématique et simulations NUMériques pour la dégradation biologique des MONUMENTs et pour la prolifération des ALGues.(2010), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), National Research Council of Italy | Consiglio Nazionale delle Ricerche (CNR), Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Alexandre Dieudonné (LJAD), and COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS)

Subjects
Quantitative Biology::Tissues and Organs, Space dimension, transmission conditions, Stability (probability), finite difference schemes, Quantitative Biology::Cell Behavior, Mathematics - Analysis of PDEs, hyperbolic system on network, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Applied mathematics, asymptotic behavior, Mathematics - Numerical Analysis, Numerical tests, chemotaxis, initial-boundary value problem, Mathematics, Numerical Analysis, Applied Mathematics, 65M06, 35L50, 92B05, 92C17, 92C42, Chemotaxis, Numerical Analysis (math.NA), Term (time), Computational Mathematics, Transmission (telecommunications), Modeling and Simulation, Scheme (mathematics), [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA], Analysis, Analysis of PDEs (math.AP)
Abstract

25 pages; International audience; In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the behavior of solutions and to discuss the stability and the accuracy of our approximation.

Published
2014
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3. Min-switching local stabilization for discrete-time switching systems with nonlinear modes

Author

Marc Jungers, Jamal Daafouz, Carlos Alberto Cavichioli Gonzaga, Centre de Recherche en Automatique de Nancy (CRAN), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Lyapunov function, 0209 industrial biotechnology, Optimization problem, Quadratic lyapunov function, 02 engineering and technology, Domain (mathematical analysis), [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, 0203 mechanical engineering, Control theory, Min-switching local stabilization, Basin of attraction estimate, Cone bounded nonlinearity, Mathematics, 020301 aerospace & aeronautics, Lyapunov-Metzler inequalities, Input saturation, Maximization, Computer Science Applications, Nonlinear system, Modal, Discrete time and continuous time, Control and Systems Engineering, symbols, Analysis
Abstract

International audience; This paper deals with the discrete-time switched Lur'e problem in finite domain. The aim is to provide a stabilization inside an estimate of the origin's basin of attraction, as large as possible, via a suitable switching rule. The design of this switching rule is based on the min-switching policy and can be induced by sufficient conditions given by Lyapunov-Metzler inequalities. Nevertheless instead of intuitively considering a switched quadratic Lyapunov function for this approach, a suitable switched Lyapunov function including the modal nonlinearities is proposed. The assumptions required to characterize the nonlinearities are only mode-dependent sector conditions, without constraints related to the slope of the nonlinearities. An optimization problem is provided to allow the maximization of the size of the basin of attraction estimate - which may be composed of disconnected sets - under the stabilization conditions. A numerical example illustrates the efficiency of our approach and emphasizes the specificities of our tools.

Published
2013
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4. Strong iISS for a class of systems under saturated feedback

Author

Remi Azouit, Antoine Chaillet, Yacine Chitour, Luca Greco, QUANTum Information Circuits (QUANTIC), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre Automatique et Systèmes (CAS), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Pierre et Marie Curie - Paris 6 (UPMC)-MINES ParisTech - École nationale supérieure des mines de Paris, MINES ParisTech - École nationale supérieure des mines de Paris, Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Pierre et Marie Curie - Paris 6 (UPMC)

Subjects
0209 industrial biotechnology, Spacecraft, business.industry, 010102 general mathematics, Angular velocity, 02 engineering and technology, Stability and robustness of nonlinear systems, 01 natural sciences, Stability (probability), saturated feedback, [SPI.AUTO]Engineering Sciences [physics]/Automatic, input-to-state stability, Nonlinear system, 020901 industrial engineering & automation, Amplitude, Control and Systems Engineering, Control theory, Bounded function, 0101 mathematics, Electrical and Electronic Engineering, Actuator, business, Harmonic oscillator, Mathematics
Abstract

International audience; This paper proposes sufficient conditions under which a system can be made Strongly iISS in the presence of actuator saturation. This property was recently proposed as a compromise between the strength of ISS and the generality of iISS. It ensures in particular that solutions are bounded provided that the disturbance magnitude is below a certain threshold, and that they tend to the origin in response to any vanishing disturbance. We show that, under a growth rate condition, the bounded feedback law proposed by Lin and Sontag for the stabilization of the disturbance-free system based on the knowledge of a control Lyapunov function, ensures Strong iISS in the presence of perturbations. We illustrate our findings on the angular velocity control of a spacecraft with limited-power thrusters. In the specific case of linear time-invariant systems with neutrally stable internal dynamics, we provide a simple static state-feedback that ensures Strong iISS in presence of actuator saturations. This second result is illustrated by the robust stabilization of the harmonic oscillator. In both cases, we provide an estimate of the maximum disturbance amplitude that can be tolerated without compromising solutions' boundedness.

Published
2016
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5. Anti-windup strategies for discrete-time switched systems subject to input saturation

Author

Sophie Tarbouriech, Marc Jungers, Centre de Recherche en Automatique de Nancy (CRAN), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), 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, Région Lorraine, ANR-08-SEGI-0004,ArHyCo,Architectures Hybrides et Contraintes(2008), ANR-13-BS03-0004,COMPACS,Computation Aware Control Systems(2013), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Université de Lorraine (UL)-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), and Université de Toulouse (UT)

Subjects
Lyapunov function, 0209 industrial biotechnology, Mathematical optimization, Lyapunov–(Metzler) inequalities, 02 engineering and technology, Dead zone, anti-windup, Constructive, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Control theory, Subject (grammar), 0202 electrical engineering, electronic engineering, information engineering, Switched systems, Mathematics, Lyapunov functions, saturation, deadzone, Regular polygon, Computer Science Applications, Discrete time and continuous time, Control and Systems Engineering, symbols, 020201 artificial intelligence & image processing, Saturation (chemistry), Anti windup
Abstract

International audience; This paper deals with the design of anti-windup compensator for discrete-time switched systems subject to input saturation. The cases of static and dynamic anti-windup controllers are addressed aiming at maximising the estimate of the basin of attraction of the origin for the closed-loop system. Two aspects of the switching law are taken into account during the design: either it is arbitrary or it is a part of the complete control law. Theoretical conditions allowing to synthesise the anti-windup compensator are mainly described through linear matrix inequalities. Computational oriented conditions are then provided to solve convex optimisation problems that are able to give a constructive solution.

Published
2016
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6. On the stabilizability of discrete-time switched linear systems: novel conditions and comparisons

Author

Marc Jungers, Mirko Fiacchini, Antoine Girard, 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]), Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), ANR-13-BS03-0004,COMPACS,Computation Aware Control Systems(2013), ANR-11-LABX-0025,PERSYVAL-lab,Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), and Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)

Subjects
0209 industrial biotechnology, Generality, Property (programming), Linear system, Mathematics::Optimization and Control, stabilizability, 02 engineering and technology, Characterization (mathematics), Ellipsoid, Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Discrete time and continuous time, Control and Systems Engineering, Control theory, Computer Science::Systems and Control, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Set theory, Electrical and Electronic Engineering, LMI, Switched systems, Mathematics
Abstract

International audience; In this paper we deal with the stabilizability property for discrete-time switched linear systems. A recent necessary and sufficient characterization of stabilizability, based on set theory, is considered as the reference for comparing the computation-oriented sufficient conditions. The classical BMI conditions based on Lyapunov-Metzler inequalities are considered and extended. Novel LMI conditions for stabilizability, derived from the geometric ones, are presented that permit to combine generality with computational affordability. For the different conditions, the geometrical interpretations are provided and the induced stabilizing switching laws are given. The relations and the implications between the stabilizability conditions are analyzed to infer and compare their conservatism and their complexity.

Published
2016
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7. What population reveals about individual cell identity: Single-cell parameter estimation of models of gene expression in yeast

Author

Cristian Versari, Pascal Hersen, Giancarlo Ferrari-Trecate, Eugenio Cinquemani, Andrés M. González-Vargas, Gregory Batt, Artémis Llamosi, Computational systems biology and optimization (Lifeware), 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), Matière et Systèmes Complexes (MSC (UMR_7057)), Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7), Dipartimento di Informatica e Sistemistica (DIS), Università degli Studi di Pavia, BioComputing, Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Modeling, simulation, measurement, and control of bacterial regulatory networks (IBIS), Laboratoire Adaptation et pathogénie des micro-organismes [Grenoble] (LAPM), Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Jean Roget, Mechanobiology Institute [Singapore] (MBI), National University of Singapore (NUS), C’Nano program (région Ile de France), ANR-10-BINF-0006,Iceberg,Des modèles de population aux populations de modèles: observation, modélisation et contrôle de l'expression génique au niveau de la cellule unique(2010), ANR-11-LABX-0071,WHO AM I,Determinants de l'Identité : de la molécule à l'individu(2011), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Matière et Systèmes Complexes (MSC), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Università degli Studi di Pavia = University of Pavia (UNIPV), Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Université Joseph Fourier - Grenoble 1 (UJF)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Università di Pavia, Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189 (CRIStAL), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Ecole Centrale de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Ecole Centrale de Lille, ANR-10-BINF-06-01/10-BINF-0006,Iceberg,Iceberg(2010), and ANR-11-LABX-0071_WHOAMI,WHOAMI,Who am I?

Subjects
0301 basic medicine, Microfluidics, Gene Expression, Biochemistry, 0302 clinical medicine, Single-cell analysis, Transcription (biology), Gene expression, Statistical inference, Cell Cycle and Cell Division, lcsh:QH301-705.5, Genetics, education.field_of_study, Covariance, Ecology, Messenger RNA, Microfluidic Analytical Techniques, Nucleic acids, Computational Theory and Mathematics, Cell Processes, Modeling and Simulation, Physical Sciences, Engineering and Technology, Probability distribution, Fluidics, Single-Cell Analysis, Biological system, Research Article, Statistical Distributions, DNA transcription, Population, Saccharomyces cerevisiae, Biology, Models, Biological, 03 medical and health sciences, Cellular and Molecular Neuroscience, DNA-binding proteins, Gene Regulation, education, Molecular Biology, Ecology, Evolution, Behavior and Systematics, Computational Biology, Biology and Life Sciences, Proteins, Random Variables, Cell Biology, Probability Theory, biology.organism_classification, Regulatory Proteins, 030104 developmental biology, lcsh:Biology (General), RNA, [INFO.INFO-BI]Computer Science [cs]/Bioinformatics [q-bio.QM], Mathematics, 030217 neurology & neurosurgery, Transcription Factors
Abstract

Significant cell-to-cell heterogeneity is ubiquitously observed in isogenic cell populations. Consequently, parameters of models of intracellular processes, usually fitted to population-averaged data, should rather be fitted to individual cells to obtain a population of models of similar but non-identical individuals. Here, we propose a quantitative modeling framework that attributes specific parameter values to single cells for a standard model of gene expression. We combine high quality single-cell measurements of the response of yeast cells to repeated hyperosmotic shocks and state-of-the-art statistical inference approaches for mixed-effects models to infer multidimensional parameter distributions describing the population, and then derive specific parameters for individual cells. The analysis of single-cell parameters shows that single-cell identity (e.g. gene expression dynamics, cell size, growth rate, mother-daughter relationships) is, at least partially, captured by the parameter values of gene expression models (e.g. rates of transcription, translation and degradation). Our approach shows how to use the rich information contained into longitudinal single-cell data to infer parameters that can faithfully represent single-cell identity., Author Summary Because of non-genetic variability, cells in an isogenic population respond differently to a same stimulation. Therefore, the mean behavior of a cell population does not generally correspond to the behavior of the mean cell, and more generally, neglecting cell-to-cell differences biases our quantitative representation and understanding of the functioning of cellular systems. Here we introduce a statistical inference approach allowing for the calibration of (a population of) single cell models, differing by their parameter values. It enables to view time-lapse microscopy data as many experiments performed on one cell rather than one experiment performed on many cells. By harnessing existing cell-to-cell differences, one can then learn how environmental cues affect (non-observed) intracellular processes. Our approach is generic and enables to exploit in unprecedented manner the high informative content of single-cell longitudinal data.

Published
2016
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8. Desynchronization and inhibition of Kuramoto oscillators by scalar mean-field feedback

Author

Françoise Lamnabhi-Lagarrigue, Elena Panteley, Antoine Chaillet, Alessio Franci, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), CNRS PEPS project TREMBATIC, and European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010)

Subjects
0209 industrial biotechnology, Control and Optimization, Quantitative Biology::Neurons and Cognition, Oscillation, Applied Mathematics, Scalar (mathematics), Zero (complex analysis), Topology (electrical circuits), 02 engineering and technology, Fixed point, Topology, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 03 medical and health sciences, Coupling (physics), 020901 industrial engineering & automation, 0302 clinical medicine, Mean field theory, Control and Systems Engineering, Control theory, Stability theory, Signal Processing, 030217 neurology & neurosurgery, Mathematics
Abstract

International audience; Motivated by neuroscience applications, and in particular by the deep brain stimulation treatment for Parkinson's disease, we have recently derived a simplified model of an interconnected neuronal population under the effect of its mean-field proportional feedback. In this paper, we rely on that model to propose conditions under which proportional mean-field feedback achieves either oscillation inhibition or desynchronization. More precisely, we show that for small natural frequencies, this scalar control signal induces an inhibition of the collective oscillation. For the closed-loop system, this situation corresponds to a fixed point which is shown to be almost globally asymptotically stable in the fictitious case of zero natural frequencies and all-to-all coupling and feedback. In the case of an odd number of oscillators, this property is shown to be robust to small natural frequencies and heterogencities in both the coupling and feedback topology. On the contrary, for large natural frequencies, we show that scalar proportional mean-field feedback is able to induce desynchronization. After having recalled a formal definition for desynchronization, we show how it can be induced in a network of originally synchronized oscillators.

Published
2012
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9. A numerical framework for optimal control of switched affine systems with state constraint

Author

Pierre Riedinger, Irinel-Constantin Morarescu, 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), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), cper misn region Lorraine, European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), Riedinger, Pierre, and CPER Région Lorraine

Subjects
0209 industrial biotechnology, Mathematical optimization, Optimization problem, Numerical analysis, numerical method, 010103 numerical & computational mathematics, 02 engineering and technology, Singular optimal control, Optimal control, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Hamiltonian system, Slack variable, [SPI.AUTO] Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, complementarity system, Singular solution, Control theory, switched systems, Affine transformation, 0101 mathematics, Mixed complementarity problem, Mathematics
Abstract

In this paper, we address the problem of numerical implementation of optimal control for switched affine systems with state constraint. In order to solve the problem we introduce a relaxed system and establish the connection between the solution of this system and the solution of the initial one. One of the main difficulties is then related to the fact that the optimal solution of the relaxed system is generally singular. We show that, using slack variables, a set of complementarity constraints can be used to take into account the singular nature of the solution. This formulation does not requires a priori knowledge on the structure (regular/singular) of the solution. The optimal control problem is then reformulated as a constraints optimization problem over the Hamiltonian systems and solved via a direct method. In addition, state path constraints are included. Numerical simulations for boost, buck-boost and Flying Capacitor converters, both in continuous and discontinuous conduction mode, illustrate the effectiveness of the proposed methodology.

Published
2012
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10. Sampled control design for switched affine systems: robust stabilization

Author

Pierre Riedinger, Claude Iung, Pascal Hauroigne, 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, European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Riedinger, Pierre, and Highly-complex and networked control systems - HYCON2 - - EC:FP7:ICT2010-09-01 - 2014-11-30 - 257462 - VALID

Subjects
Lyapunov function, 0209 industrial biotechnology, Steady state (electronics), Attracting set, Input-to-state stability, 020208 electrical & electronic engineering, 02 engineering and technology, Distinctive feature, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Switching time, symbols.namesake, [SPI.AUTO] Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Control theory, Control Lyapunov function, Hybrid system, 0202 electrical engineering, electronic engineering, information engineering, symbols, Switched affine system, Affine transformation, Robust control, Control-Lyapunov function, Mathematics
Abstract

International audience; This paper deals with sampled feedback strategies applied on the class of switched affine systems without common equilibria. A distinctive feature of these systems is a cyclical behavior in steady state. From the existence of a Control Lyapunov Function for a relaxed control problem, a novel procedure enabling to compute global attracting sets for the whole system trajectories is exhibited. This procedure is extended to the case of parameter and/or switching time uncertainties leading to Input-to-State Stability results. An application on a flying capacitor converter is used as an illustrative example.

Published
2011
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11. Stabilization of sampled-data Lur’e systems with nonuniform sampling

Author

Louis, Julien, Jungers, Marc, Daafouz, Jamal, Centre de Recherche en Automatique de Nancy (CRAN), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Région Lorraine, ANR-13-BS03-0004,COMPACS,Computation Aware Control Systems(2013), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Jungers, Marc, Blanc 2013 - Computation Aware Control Systems - - COMPACS2013 - ANR-13-BS03-0004 - Blanc 2013 - VALID, Highly-complex and networked control systems - HYCON2 - - EC:FP7:ICT2010-09-01 - 2014-11-30 - 257462 - VALID, and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

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

International audience; The paper addresses the problem of Lur’e sampled-data control design with non uniform sampling. It is shown that this problem can be treated using a methodology based on Euler approximate discrete time models associated to a formulation of the problem in the switched systems framework. Given a finite set of sampling periods, the problem is formulated as a stabilization problem for discrete-time switched Lur’e systems with norm bounded uncertainty. A quadratic criterion is used to take into account possible penalties on the sampling periods. Sufficient conditions are provided to compute both the controller gains and the active sampling period. The approach takes into account the inter-sample behaviour and provides stability guarantees for the exact Lur’e sampled-data system.

Published
2015

12. Robustness of stochastic discrete-time switched linear systems with application to control with shared resources

Author

Luca Greco, Antoine Chaillet, Elena Panteley, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), and European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010)

Subjects
Stochastic Jump Linear Systems, Markov chain, Stochastic process, Variable-order Markov model, Linear system, Markov process, Markov model, Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, Discrete time and continuous time, Control and Systems Engineering, Control theory, Robustness (computer science), symbols, Input to state stability, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Electrical and Electronic Engineering, Mathematics
Abstract

International audience; Motivated by control applications relying on shared resources (such as computation time or bandwidth), we analyze the stability and robustness of discrete-time switched linear systems with stochastic commutations. We show that a wide class of shared resources control strategies can be modeled by a stochastic jump linear system involving two stochastic processes. The class of systems we study encompasses Markov chains and independent and identically distributed switching processes. For these systems, we recall existing definitions of stability and robustness, by relying on the input-to-state stability (ISS) property. We show that, for the class of systems under concern, δ-moment stability is equivalent to δ-moment ISS and that they both imply almost sure ISS. Several sufficient conditions are provided to guarantee these properties. Anytime control design for a Translational Oscillator/Rotational Actuator (TORA) system is used to illustrate all these concepts.

Published
2015
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13. L2 -induced gain for discrete-time switched Lur'e systems via a suitable Lyapunov function

Author

Louis, Julien, Jungers, Marc, Daafouz, Jamal, Castelan, Eugênio, Centre de Recherche en Automatique de Nancy (CRAN), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Departamento de Automação e Sistemas (DAS), Federal University of Santa Catarina, CAPES/COFECUB n° 701/11, Région Lorraine, CNPq Brazil., ANR-13-BS03-0004,COMPACS,Computation Aware Control Systems(2013), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Jungers, Marc, Blanc 2013 - Computation Aware Control Systems - - COMPACS2013 - ANR-13-BS03-0004 - Blanc 2013 - VALID, and Highly-complex and networked control systems - HYCON2 - - EC:FP7:ICT2010-09-01 - 2014-11-30 - 257462 - VALID

Subjects
[SPI.AUTO] Engineering Sciences [physics]/Automatic, L2 -induced gain, Lur'e type Lyapunov functions, Switched systems, Lur'e type systems, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; This paper deals with discrete-time switched Lur'e systems including an additional saturated input and a bounded energy disturbance. Two control design issues are investigated related to the L2-induced gain and the rejection of disturbance. An common optimization problem under LMI conditions and differing from the cost function to optimize, is provided to offer a solution to the both problems. The main approach is to upper bound a criterion with a suitable Lur'e type Lyapunov function. Numerical examples are given to underline the efficiency of our approach and to allow a discussion with the literature.

Published
2015

14. Sufficient LMI stability conditions for Lur'e type systems governed by a control law designed on their Euler approximate model

Author

Jamal Daafouz, Marc Jungers, Julien Louis, Centre de Recherche en Automatique de Nancy (CRAN), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), ANR-13-BS03-0004,COMPACS,Computation Aware Control Systems(2013), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Lyapunov function, 0209 industrial biotechnology, Quantitative Biology::Molecular Networks, Lur'e type Lyapunov functions, 020208 electrical & electronic engineering, Structure (category theory), Linear matrix inequality, 02 engineering and technology, Type (model theory), Stability (probability), Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, Stability conditions, 020901 industrial engineering & automation, Euler discretization, Control and Systems Engineering, Control theory, Law, Stability theory, Lur'e systems, 0202 electrical engineering, electronic engineering, information engineering, symbols, Euler's formula, Mathematics
Abstract

International audience; In this paper, the stability issue of Lur'e systems governed by a control law stabilizing their forward Euler approximate model is investigated. More specifically the considered control law is obtained by exploiting the advantages of a new Lur'e type Lyapunov function with disconnected level sets. This Lyapunov function is adapted to the discrete-time Lur'e systems and to the structure of the forward Euler approximate model. The main result consists of LMI conditions allowing to guarantee that the continuous time Lur'e system associated with the proposed piecewise constant control law is globally asymptotically stable. The relevance of this approach is illustrated using a numerical example.

Published
2015
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15. Uniform ultimate boundedness analysis and synthesis for linear systems with dead-zone in the actuators

Author

Dilda, Vanessa, Jungers, Marc, Castelan, Eugênio, Departamento de Automação e Sistemas (DAS), Federal University of Santa Catarina, Centre de Recherche en Automatique de Nancy (CRAN), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), CAPES-COFECUB n° 701/11, European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
parametrized piecewise affine bounds, uniform ultimate boundedness, dead-zone nonlinearity, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; The presence of the dead-zone nonlinearity is common in many physical systems and in general degrades the control systems performance or stability. This note considers an interconnection between a continuous time multiple-input linear system and a dead-zone nonlinearity associated with a state feedback. The issue of analyzing the property of uniform ultimate boundedness (UUB) of a system and the issue of designing a control under UUB constraint are studied. Firstly, the dead-zone is replaced via a linear transformation introducing the saturation. Secondly, we improve the size of the UUB area that can be found in the literature, by expressing the saturation in terms of parametrized piecewise affine bounds. This allows also a link between standard approaches such ones using piecewise affine models or ones considering global cone bounded sector conditions. In the framework of analysis and synthesis, sufficient conditions are obtained by linear matrix inequalities. Illustrative examples are given to spotlight the efficiency of our approach.

Published
2015
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16. Consistance des systèmes de Lur'e commutés : application à la synthèse de commande numérique avec un échantillonnage non uniforme

Author

Marc Jungers, Jamal Daafouz, Julien Louis, Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Région Lorraine, ANR-13-BS03-0004,COMPACS,Computation Aware Control Systems(2013), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), Jungers, Marc, Blanc 2013 - Computation Aware Control Systems - - COMPACS2013 - ANR-13-BS03-0004 - Blanc 2013 - VALID, and Highly-complex and networked control systems - HYCON2 - - EC:FP7:ICT2010-09-01 - 2014-11-30 - 257462 - VALID

Subjects
Système non linéaire de type Lur'e, 0209 industrial biotechnology, 02 engineering and technology, Consistance des systèmes commutés, Industrial and Manufacturing Engineering, Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, [SPI.AUTO] Engineering Sciences [physics]/Automatic, Commande à données échantillonnées, Control and Systems Engineering, 0202 electrical engineering, electronic engineering, information engineering, système non linéaire de type Lur’e, 020201 artificial intelligence & image processing, Electrical and Electronic Engineering, échantillonnage non uniforme, Echantillonnage non uniforme
Abstract

International audience; Dans cet article, à partir d’une relecture de la consistance des systèmes commutés linéaires, la propriété de consistance pour les systèmes non-linéaires de type Lur’e commutés à temps discret est étudiée. Une discussion montre qu’il faut considérer le plus petit majorant quadratique possible de la performance au lieu de la valeur optimale elle-même (qui coïncident dans le cadre linéaire) pour permettre l’extension. Un problème d’optimisation sous contraintes LMI est proposé pour obtenir une stratégie de type min-switching satisfaisant la consistance en non-linéaire. Dans un second temps, cette contribution est utilisée pour la synthèse d’un contrôleur à données échantillonnées avec un échantillonnage non uniforme. Un exemple numérique est alors proposé pour mettre en évidence les apports de ces résultats.

Published
2015
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17. Variable Structure Control with Generalized Relays: A Simple Convex Optimization Approach

Author

Thierry Floquet, Emilia Fridman, Laurentiu Hetel, Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS), Université de Lille, Sciences et Technologies-Centrale Lille-Centre National de la Recherche Scientifique (CNRS), Department of Electrical Engineering, Tel Aviv University [Tel Aviv], Non-Asymptotic estimation for online systems (NON-A), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Interreg IV A 2 Mers Seas Zeeen program SYSIASS, European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Tel Aviv University (TAU), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), and Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)

Subjects
Ellipsoid method, Linear system, Linear matrix inequality, Proper convex function, Subderivative, Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Control and Systems Engineering, Control theory, Convex optimization, Convex combination, Electrical and Electronic Engineering, Convex function, Mathematics
Abstract

International audience; The article proposes a convex optimization approach for the design of relay feedback controllers. The case of linear systems is studied in the presence of matched perturbations. The system input is a generalized relay that may take values in a finite set of constant vectors. A simple design method is proposed using Linear Matrix Inequalities (LMIs). Furthermore, the approach is used in the sampled-data case in order to guarantee (locally) the practical stabilization to a bounded ellipsoid of the order of the sampling interval. Time-varying uncertainties (in the state matrix and the sampling interval) can be easily included in the analysis.

Published
2015
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18. On stabilizability conditions for discrete-time switched linear systems

Author

Mirko Fiacchini, Antoine Girard, Marc Jungers, GIPSA - Systèmes non linéaires et complexité (GIPSA-SYSCO), Département Automatique (GIPSA-DA), Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Calculs Algébriques et Systèmes Dynamiques (CASYS), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), ANR-11-LABX-0025,PERSYVAL-lab,Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011), ANR-13-BS03-0004,COMPACS,Computation Aware Control Systems(2013), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), 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 (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-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 (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-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 (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-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 (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Centre National de la Recherche Scientifique (CNRS)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Joseph Fourier - Grenoble 1 (UJF)-Université Pierre Mendès France - Grenoble 2 (UPMF)

Subjects
0209 industrial biotechnology, Generality, Property (philosophy), Linear system, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, Conservatism, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Discrete time and continuous time, Control theory, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Mathematics
Abstract

International audience; In this paper we consider the stabilizability property for discrete-time switched linear systems. Novel conditions, in LMI form, are presented that permit to combine generality with computational affordability. The relations and implications between different conditions, new ones and taken from literature, for stabilizability are analyzed to infer and compare their conservatism and their complexity.

Published
2014
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19. Hybrid control of a three-agent network cluster

Author

Carolina Albea, Luca Zaccarian, Alexandre Seuret, Équipe Services et Architectures pour Réseaux Avancés (LAAS-SARA), 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), ANR-12-BS03-0005,LimICoS,Synthèse et analyse des systèmes avec informations limitées(2012), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), 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
Hybrid systems, Computer science, Multi-agent system, Distributed computing, Multi-agent systems, Load balancing (computing), Load Balancing, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Computer Science::Performance, Computer Science::Multiagent Systems, Hybrid system, Server, Computer Science::Operating Systems, Queue, Efficient energy use
Abstract

International audience; We consider the management problem for a cluster of three identical servers treating an external request. We assume that each agent has a constant computational speed and we build a deterministic hybrid dynamical model of the overall system. Then, inspired by consensus theory, we propose a centralized control law distributing the computational load among the agents and deciding when to turn on or off each agent, for energy effciency, while ensuring that the queues of each agent asymptotically converge to a desirable level. We prove the properties of the proposed law and highlight some interesting peculiarities in terms of non-uniform convergence.

Published
2014

20. A switching observer for systems with linearizable error dynamics via singular time-scaling

Author

Hoang, Trong-Bien, Pasillas-Lépine, William, Respondek, Witold, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Mathématiques de l'INSA de Rouen Normandie (LMI), Institut national des sciences appliquées Rouen Normandie (INSA Rouen Normandie), Institut National des Sciences Appliquées (INSA)-Normandie Université (NU)-Institut National des Sciences Appliquées (INSA)-Normandie Université (NU), and European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010)

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

International audience; In this paper, we propose a new observer design for nonlinear systems that can be linearized using a change of coordinates and a singular time re-scaling. Our observer is a switched system and the observer error dynamics are described, after time re-scaling, by a switched linear system that is uniformly exponentially stable. We also give necessary and sufficient conditions for linearizability via a change of coordinates and a singular time re-scaling. Our methods are illustrated by an example coming from the ABS literature.

Published
2014

21. Tutorial on arbitrary and state-dependent sampling

Author

Hassan Omran, Christophe Fiter, Laurentiu Hetel, Jean-Pierre Richard, Systèmes Non Linéaires et à Retards (SyNeR), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centrale Lille, Non-Asymptotic estimation for online systems (NON-A), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), European Project: 06-020-FR,SYSIASS, Inria Lille - Nord Europe, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL)

Subjects
Theoretical computer science, Computer science, Stability (learning theory), Sampling (statistics), Control engineering, self-triggering, event-triggering, Self triggering, Domain (software engineering), dynamic sampling, State dependent, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Focus (optics), networked control systems, Sampled data systems, time-varying sam-pling
Abstract

International audience; This tutorial, presents basic concepts and recent research directions about sampled-data systems. We focus mainly on the stability of systems with time-varying sampling intervals. Without being exhaustive, which would be neither possible nor useful, we try to give a structural survey of what we think to be the main results and issues in this domain.

Published
2014
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22. Robustness under saturated feedback: Strong iISS for a class of nonlinear systems

Author

Luca Greco, Remi Azouit, Antoine Chaillet, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), iCODE, and European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010)

Subjects
Nonlinear system, Spacecraft, Exponential stability, business.industry, Robustness (computer science), Control theory, Angular velocity, Lyapunov redesign, business, Actuator, Control-Lyapunov function, Mathematics, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; This note proposes sufficient conditions under which a nonlinear system can be made Strongly iISS in the presence of actuator saturation. This property, recently proposed as a compromise between the strength of ISS and the generality of iISS, ensures boundedness of all solutions provided that the disturbance magnitude is below a certain threshold. We also show that, under a growth rate condition, the bounded feedback law proposed by Lin and Sontag for the stabilization of the disturbance-free system based on the knowledge of a control Lyapunov function, ensures Strong iISS in the presence of perturbations. We illustrate our findings on the angular velocity control of a spacecraft with limited-power thrusters.

Published
2014
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23. A switched LQ regulator design in continuous time

Author

Pierre Riedinger, Centre de Recherche en Automatique de Nancy (CRAN), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), Hycon2, European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Lyapunov function, Linear system, Lyapunov optimization, Optimal control, Linear-quadratic-Gaussian control, Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, Control and Systems Engineering, Control theory, symbols, Lyapunov equation, switched systems, Electrical and Electronic Engineering, Lyapunov redesign, LQ regulator, Mathematics, Control-Lyapunov function
Abstract

International audience; In this paper, the design of a LQ regulator for linear switched systems in continuous time is investigated. From a relaxation of the optimal control problem, a Lyapunov based switching law is provided. Even if the subsystems are all unstable, the state feedback switching law can be applied subject to a positiveness condition. In any cases, the real cost is always upper bounded by the Lyapunov function value. The optimality of the switching law is also discussed and we prove that the switching conditions are optimal in some generic cases. This point explains why the obtained results over examples approach finely the optimal solutions. Finally, a design strategy is also given that extends the results to the cases where the subsystems are controlled linear systems.

Published
2014
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24. 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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25. Non-Asymptotic estimation for on-line systems: Finite-time algorithms and applications

Author

Richard, Jean-Pierre, Perruquetti, Wilfrid, Non-Asymptotic estimation for online systems (NON-A), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS), Université de Lille, Sciences et Technologies-Centrale Lille-Centre National de la Recherche Scientifique (CNRS), ANR-11-BS03-0007,ChaSliM,Vers une commande par modes glissants performante: réduction du chattering, rejet de perturbations, et boite à outils.(2011), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), European Project: 06-020-FR,SYSIASS, Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), and Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)

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

International audience; Finite-time estimation is a way to perform real-time control and achieve specified time performance. The Inria project-team Non-A is focusing on designing such "non-asymptotic" algorithms: there, mathematics (algebra, homogeneity) are combined with real-time applications (robotics, energy, environment)… For engineers, a wide variety of information is not directly obtained through measurement. Some parameters (constants of an electrical actuator, time delay in communication, etc.) or internal variables (torques applied to a robot arm, posture and localization of a mobile, detection of impact of angles in biped walk, etc.) are unknown or are not measured. Similarly, more often than not, signals from sensors are distorted and tainted by measurement noises. To control such processes, and to extract information conveyed by the signals, one often has to estimate parameters or variables. Estimation can concern parameters (identification), states (observation), derivatives (differentiation), inputs (left inversion) or noisy data (filtering). It means a nearly infinite number of results have already been produced in this area, concerning either control or signal processing… However, unlike traditional methods, the majority of which pertain to asymptotic statistics, the particularity of Non-A is to develop algorithms which converge after a finite-time. This is summarized in the project's name: "Non-Asymptotic estimation for online systems".

Published
2014

26. Stability analysis of bilinear systems under aperiodic sampled-data control

Author

Jean-Pierre Richard, Hassan Omran, Françoise Lamnabhi-Lagarrigue, Laurentiu Hetel, Systèmes Non Linéaires et à Retards (SyNeR), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), and European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010)

Subjects
Bilinear systems, 0209 industrial biotechnology, 020208 electrical & electronic engineering, 02 engineering and technology, Ellipsoid, [SPI]Engineering Sciences [physics], 020901 industrial engineering & automation, Exponential stability, Control and Systems Engineering, Aperiodic graph, Control theory, Data control, Bounded function, 0202 electrical engineering, electronic engineering, information engineering, Applied mathematics, Electrical and Electronic Engineering, Invariant (mathematics), Linear state feedback, Mathematics
Abstract

International audience; This note considers the problem of local stability of bilinear systems with aperiodic sampled-data linear state feedback control. The sampling intervals are time-varying and upper bounded. It is shown that the feasibility of some linear matrix inequalities (LMIs), implies the local asymptotic stability of the sampled-data system in an ellipsoidal region containing the equilibrium. The method is based on the analysis of contractive invariant sets, and it is inspired by the dissipativity theory. The results are illustrated by means of numerical examples.

Published
2014
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27. A novel control design for delayed teleoperation based on delay-scheduled Lyapunov-Krasovskii functionals

Author

Jean-Pierre Richard, Alexandre Kruszewski, Bo Zhang, Systèmes Non Linéaires et à Retards (SyNeR), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centrale Lille, Non-Asymptotic estimation for online systems (NON-A), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Inria Lille - Nord Europe, and Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL)

Subjects
Scheme (programming language), 0209 industrial biotechnology, Stability criterion, Control (management), position/force tracking, Stability (learning theory), teleoperation system, 02 engineering and technology, Synchronization, delay-scheduled Lyapunov-Krasovskii functionals, [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI], 020901 industrial engineering & automation, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, [INFO.INFO-RB]Computer Science [cs]/Robotics [cs.RO], Hinf control, Mathematics, computer.programming_language, asymmetric time-varying delays, 020208 electrical & electronic engineering, Linear matrix inequality, Control engineering, Computer Science Applications, Control and Systems Engineering, Teleoperation, Linear Matrix Inequality, computer
Abstract

International audience; This paper addresses the controller design problem for bilateral teleoperation over unreliable networks. The stability and tracking performance analysis are presented for a novel force-reflecting emulator control scheme. The performance (stability, synchronization, transparency) is guaranteed by Hinf control theory and delay-scheduled Lyapunov-Krasovskii functionals (LKF), which could improve the existing stability criterion. The design is achieved by using Linear Matrix Inequality (LMI) optimization. For the simulation, firstly, numerical examples are given to demonstrate the effectiveness and benefits of the delay-scheduled LKF-based stability results; secondly, the proposed controller design solution is illustrated by various simulations and compared with other recent approaches under different working conditions, e.g. abrupt tracking motion and wall contact.

Published
2014
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28. Feedback strategies for discrete-time linear-quadratic two-player descriptor games

Author

Marc Jungers, Centre de Recherche en Automatique de Nancy (CRAN), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Mathematical optimization, Computer Science::Computer Science and Game Theory, 0211 other engineering and technologies, 02 engineering and technology, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Matrix (mathematics), 020901 industrial engineering & automation, Stackelberg competition, Discrete Mathematics and Combinatorics, Uniqueness, Game theory, Mathematics, Numerical Analysis, 021103 operations research, Algebra and Number Theory, Feedback information structure, Descriptor games, Information structure, Nash strategy, Stackelberg strategy, Dynamic programming, Discrete time and continuous time, Best response, Geometry and Topology, Matrix block formulation
Abstract

International audience; This paper deals with discrete-time linear-quadratic descriptor two-player games. The two frameworks of Nash and Stackelberg strategies with feedback information structure are considered. The aim is to provide sufficient conditions ensuring, for any initial state, the existence and the uniqueness of a tri-trajectory, gathering the state and the controls of the two players, which reaches the equilibrium. The provided results are mainly based on a discrete-time matrix block formulation. The provided algorithms consist in an iterative backward in time procedure, issued from Dynamic Programming. Numerical examples illustrate this approach and the particular case of explicit systems is recovered for both kinds of strategies.

Published
2014
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29. A numerical framework for optimal control of switched input affine nonlinear systems subject to path constraint

Author

Irinel-Constantin Morrescu, Pierre Riedinger, Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Contrat de Projet État-Région 2007-2013, Région Lorraine, European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), and Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)

Subjects
0209 industrial biotechnology, Mathematical optimization, General Computer Science, 0211 other engineering and technologies, 02 engineering and technology, Numerical method, Theoretical Computer Science, Hamiltonian system, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Singular solution, Control theory, Complementarity systems, Switched systems, Mathematics, Numerical Analysis, 021103 operations research, Applied Mathematics, Numerical analysis, Singular optimal control, Optimal control, Slack variable, Constraint (information theory), Modeling and Simulation, Path (graph theory), A priori and a posteriori
Abstract

International audience; In this paper, we address the problem of numerical implementation of optimal control for switched input affine nonlinear systems subject to path constraint. In order to properly solve the problem, a relaxed system is introduced and the connection between the solution of this system and the solution of the initial one is established. One of the main difficulties is then related to the fact that the optimal solution can be singular. We show that, using slack variables, a set of complementarity constraints can be used to take into account the singular nature of the solution. The optimal control problem is then reformulated as a constraint optimization problem over the Hamiltonian systems and solved via a direct method. This formulation does not require a priori knowledge on the structure (regular/singular) of the solution. In addition, state path constraints are included. Numerical simulations for boost, buck-boost and flying capacitor converters, both in continuous and discontinuous conduction mode, illustrate the effectiveness of the proposed methodology.

Published
2014
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30. A Razumikhin approach for the incremental stability of delayed nonlinear systems

Author

Alexander Yu. Pogromsky, Björn S. Rüffer, Antoine Chaillet, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Department of Mechanical Engineering [Eindhoven], Eindhoven University of Technology [Eindhoven] (TU/e)-Technische Universiteit Eindhoven (TU/e), Signal and System Theory Group, University of Paderborn, and European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010)

Subjects
0209 industrial biotechnology, Perturbation (astronomy), 02 engineering and technology, incremental stability, Razumikhin approach, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 03 medical and health sciences, Nonlinear system, 020901 industrial engineering & automation, 0302 clinical medicine, Exponential stability, Control theory, Bounded function, 030217 neurology & neurosurgery, time-delay systems, Mathematics
Abstract

International audience; This paper provides sufficient conditions for the incremental stability of time-delayed nonlinear systems. It relies on the Razumikhin-Lyapunov approach, which consists in invoking small-gain arguments by treating the delayed state as a feedback perturbation. The results are valid for multiple delays, as well as bounded time-varying delays. We provide conditions under which the limit solution of a time-delayed nonlinear system in response to a periodic (resp. constant) input is itself periodic and of the same period (resp. constant). As an illustration, a specific focus is given on a class of delayed Lur'e systems.

Published
2013
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31. Packet-based dynamic control for nonlinear networked systems

Author

Luca Greco, Antoine Chaillet, Massimiliano Gamba, Stefano Falasca, Antonio Bicchi, Centro di ricerca E. Piaggio, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Interdep. Research Center 'E. Piaggio', University of Pisa - Università di Pisa, Istituto Italiano di Tecnologia (IIT), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), and Centro di Ricerca Enrico Piaggio

Subjects
030213 general clinical medicine, 0209 industrial biotechnology, Signal processing, Computer science, Network packet, Node (networking), Real-time computing, packet-based control, 02 engineering and technology, Networked control system, Telecommunications network, Synchronization, stabilization, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Scheduling (computing), 03 medical and health sciences, Nonlinear system, 020901 industrial engineering & automation, 0302 clinical medicine, Distributed parameter system, network controlled systems
Abstract

International audience; The possibility to remotely control a plant through a communication network offers strong advantages in terms of installation, flexibility, and maintenance. These advantages come at the price of specific challenges due to the format of the transmitted data, the network nodes scheduling, and the inherent delays. To address these obstacles, we have recently developed a control methodology that exploits the packetized nature of the transmitted data by relying on a model-based prediction of the control signal to be applied. However, this methodology was limited to static controllers. Dynamic control laws indeed require a more careful synchronization between the plant and its remote model. This paper aims at filling this gap by exploiting the transmission of the measurements history, rather than their instantaneous value only.

Published
2013
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32. Sampled-data control of LTI systems with relays: a convex optimization approach

Author

Hetel, Laurentiu, Fridman, Emilia, Floquet, Thierry, Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS), Université de Lille, Sciences et Technologies-Centrale Lille-Centre National de la Recherche Scientifique (CNRS), Department of Electrical Engineering, Tel Aviv University [Tel Aviv], Non-Asymptotic estimation for online systems (NON-A), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Tel Aviv University (TAU), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Hetel, Laurentiu, and Highly-complex and networked control systems - HYCON2 - - EC:FP7:ICT2010-09-01 - 2014-11-30 - 257462 - VALID

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

International audience; We consider a generalized class of relay controllers where the system input may take values in a finite set of constant vectors. A simple continuous-time design method is proposed for linear time invariant (LTI) systems. Furthermore, it is used in the sampled-data case in order to guarantee (locally) the practical stabilization to a bounded ellipsoid containing the origin. The sampling intervals may be unknown and time-varying in a given interval. Simple linear matrix inequalities (LMIs) conditions are proposed for checking (local) practical stability.

Published
2013

33. Discrétisation et analyse de stabilité des systèmes de type Lur'e

Author

Louis, Julien, Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), Louis, Julien, and Highly-complex and networked control systems - HYCON2 - - EC:FP7:ICT2010-09-01 - 2014-11-30 - 257462 - VALID

Subjects
[SPI.AUTO] Engineering Sciences [physics]/Automatic, Discrétisation par la méthode d'Euler, Fonction de Lyapunov, LMI, Stabilité, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

National audience; La stabilité des systèmes de type Lur'e à temps continu et discret a généré un nombre important de publications. Récemment un nouveau résultat a été proposé sur la stabilité de ces systèmes à temps discret à l'aide d'une nouvelle fonction de Lyapunov. Cette fonction est composée d'un terme quadratique en l'état et d'un terme croisé entre l'état et la non-linéarité. Elle peut mener à des lignes de niveaux non-convexes et non-connexes, adaptées à la stabilité des systèmes non-linéaires à temps discret. L'objectif de cet article est d'étudier la stabilité d'un système de Lur'e à temps continu à partir de sa discrétisation et de ce nouveau résultat. Un aspect important est que les conditions suffisantes de stabilité globale, données sous forme d'inégalités matricielles linéaires, ne feront intervenir que la condition de secteur de la non-linéarité, sans contrainte sur ses variations. Un exemple académique sera présenté pour illustrer notre approche.

Published
2013

34. Basal ganglia oscillations: The role of delays and external excitatory nuclei

Author

Antoine Chaillet, Ihab Haidar, William Pasillas-Lépine, Elena Panteley, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), and European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010)

Subjects
Physics, 0303 health sciences, Quantitative Biology::Neurons and Cognition, basal ganglia oscillations, Neurophysiology, Motor symptoms, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 03 medical and health sciences, 0302 clinical medicine, stability of MIMO delayed systems, Basal ganglia, Excitatory postsynaptic potential, [SDV.NEU]Life Sciences [q-bio]/Neurons and Cognition [q-bio.NC], Neuroscience, 030217 neurology & neurosurgery, 030304 developmental biology, Pedunculopontine nucleus
Abstract

Basal ganglia are interconnected deep brain structures involved in movement generation. Their beta-band oscillations (13-30Hz) are known to be linked to Parkinson's disease motor symptoms. In this paper, we provide conditions under which these oscillations may occur, by explicitly considering the role of the pedunculopontine nucleus (PPN). We analyze the existence of equilibria in the associated firing-rate dynamics and study their stability by relying on a delayed MIMO frequency analysis. These results are illustrated with simulations that confirm numerically the analytic predictions of our two main theorems.

Published
2013
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35. Guaranteed cost certification for discrete-time linear switched system with a dwell time

Author

Jamal Daafouz, Marc Jungers, Centre de Recherche en Automatique de Nancy (CRAN), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Lyapunov function, 0209 industrial biotechnology, Mathematical optimization, Computation, Linear system, periodic Lyapunov equations, 02 engineering and technology, Upper and lower bounds, Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Dwell time, symbols.namesake, 020901 industrial engineering & automation, Discrete time and continuous time, Control and Systems Engineering, Control theory, 0202 electrical engineering, electronic engineering, information engineering, symbols, 020201 artificial intelligence & image processing, Lyapunov equation, Quadratic programming, performance certification, Electrical and Electronic Engineering, Switched systems, Mathematics
Abstract

International audience; This paper studies the guaranteed cost of a quadratic criterion associated with a linear discrete-time switched system for all the set of admissible switching laws. The admissible switching laws are here the ones exhibiting a dwell time. The approach provided here is to design an upper bound and a parametrized family of lower bounds of the guaranteed cost as close as possible in order to obtain a certification of the guaranteed cost. The upper bound is determined via a switched Lyapunov function and the lower bounds are obtained via the numerical computation of the cost induced by particular periodic switching laws. The features of the proposed approach are illustrated by a numerical example.

Published
2013
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36. Strong iISS: combination of iISS and ISS with respect to small inputs

Author

Hiroshi Ito, Antoine Chaillet, David Angeli, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Department of Electrical and Electronic Engineering [London] (DEEE), Imperial College London, Kyushu Institute of Technology (Kyutech), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Kyushu Institute of Technology, Chaillet, Antoine, and Highly-complex and networked control systems - HYCON2 - - EC:FP7:ICT2010-09-01 - 2014-11-30 - 257462 - VALID

Subjects
Lyapunov function, 0209 industrial biotechnology, 010102 general mathematics, 02 engineering and technology, State (functional analysis), 01 natural sciences, Stability (probability), [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, [SPI.AUTO] Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Exponential stability, Robustness (computer science), Control theory, Stability theory, Bounded function, symbols, 0101 mathematics, Robust control, Mathematics
Abstract

International audience; This paper studies the notion of Strong iISS, which imposes both integral input-to-state stability (iISS) and input-to-state stability (ISS) with respect to small inputs. This combination characterizes the robustness property, exhibited by many practical systems, that the state remains bounded as long as the magnitude of exogenous inputs is reasonably small but may diverge for stronger disturbances. We provide three Lyapunov-type sufficient conditions for Strong iISS. One is based on iISS Lyapunov functions admitting a radially non- vanishing (class K) dissipation rate. However we show that it is not a necessary condition for Strong iISS. Two less conservative conditions are then provided, which are used to demonstrate that asymptotically stable bilinear systems are Strongly iISS. Finally, we discuss cascade and feedback interconnections of Strong iISS systems.

Published
2012

37. Validity of the phase approximation for coupled nonlinear oscillators: a case study

Author

Alessio Franci, Antoine Chaillet, William Pasillas-Lépine, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Neurosynch, European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Pasillas-Lépine, William, and Highly-complex and networked control systems - HYCON2 - - EC:FP7:ICT2010-09-01 - 2014-11-30 - 257462 - VALID

Subjects
0209 industrial biotechnology, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Phase (waves), [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], Proportional control, 02 engineering and technology, Synchronization, 01 natural sciences, Phase locking, Phase-models, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Nonlinear oscillators, Structural stability, 020901 industrial engineering & automation, Control theory, 0103 physical sciences, Statistical physics, Small coupling, 010306 general physics, Mathematics, Kuramoto model, Normal hyperbolicity, [SPI.AUTO] Engineering Sciences [physics]/Automatic, Phase dynamics, Phase-locking
Abstract

International audience; Motivated by neuroscience applications, we rigorously derive the phase dynamics of an ensemble of interconnected nonlinear oscillators under the effect of a proportional feedback. We individuate the critical parameters determining the validity of the phase approximation and derive bounds on the accuracy of the latter in reproducing the behavior of the original system. We use these results to study the existence of oscillating phase-locked solutions in the original oscillator model.

Published
2012

38. Source localization using Poisson integrals

Author

Antoine Rousseau, Pierre Rouchon, Ruggero Fabbiano, Federica Garin, Carlos Canudas de Wit, Networked Controlled Systems (NECS), 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), 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 (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-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 (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-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 (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-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 (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), 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 (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Centre Automatique et Systèmes (CAS), Mines Paris - PSL (École nationale supérieure des mines de Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Modelling, Observations, Identification for Environmental Sciences (MOISE), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Université Stendhal - Grenoble 3-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), and MINES ParisTech - École nationale supérieure des mines de Paris

Subjects
Pointwise, Hessian matrix, 0209 industrial biotechnology, Computation, Isotropy, Mathematical analysis, Source seeking, 02 engineering and technology, Poisson distribution, symbols.namesake, 020901 industrial engineering & automation, Diffusion process, sensor networks, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, symbols, Torque, 020201 artificial intelligence & image processing, multi-agent systems, Laplace operator, Mathematics
Abstract

International audience; This paper deals with the problem of source localization in diffusion processes via several sensor devices providing pointwise concentration measures; sensors are assumed to be arranged in circular arrays, they can be fixed along the array or they can turn along a circular path defined by the array. The originality of the proposed source localization solution lies in the computation of the gradient and of higher-order derivatives (i. e., the Hessian) from Poisson integrals; in opposition to other solutions published in the literature, this computation does neither require specific knowledge of the solution of the difiusion process, nor the use of probing signals, but only exploits properties of the PDE. The Laplacian of the measured value is null on the studied domain; such an assumption is justified for isotropic diffusive sources in steady-state. The paper also presents some simulation results of a source-seeking torque control law for mobile non-holonomic robots looking for a heat source in a room, where the source is modeled as a small circular region.

Published
2012
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39. Stability analysis of discrete-time Lur'e systems

Author

Carlos Alberto Cavichioli Gonzaga, Marc Jungers, Jamal Daafouz, Centre de Recherche en Automatique de Nancy (CRAN), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Lyapunov function, 0209 industrial biotechnology, 02 engineering and technology, Bounded sector nonlinearity, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Control theory, Lur'e systems, 0202 electrical engineering, electronic engineering, information engineering, Lyapunov equation, Basin of attraction estimate, Electrical and Electronic Engineering, Lyapunov redesign, Mathematics, Control-Lyapunov function, Absolute stability, Linear system, Function (mathematics), Saturation, Control and Systems Engineering, Bounded function, Convex optimization, symbols, 020201 artificial intelligence & image processing
Abstract

International audience; A class of Lyapunov functions is proposed for discrete-time linear systems interconnected with a cone bounded nonlinearity. Using these functions, we propose sufficient conditions for the global stability analysis, in terms of linear matrix inequalities (LMI), only taking the bounded sector condition into account. Unlike frameworks based on the Lur'e-type function, the additional assumptions about the derivative or discrete variation of the nonlinearity are not necessary. Hence, a wider range of cone bounded nonlinearities can be covered. We also show that there is a link between global stability LMI conditions based on this new Lyapunov function and a transfer function of an auxiliary system being strictly positive real. In addition, the novel function is considered in the local stability analysis problem of discrete-time Lur'e systems subject to a saturating feedback. A convex optimization problem based on sufficient LMI conditions is formulated to maximize an estimate of the basin of attraction. Another specificity of this new Lyapunov function is the fact that the estimate is composed of disconnected sets. Numerical examples reveal the effectiveness of this new Lyapunov function in providing a less conservative estimate with respect to the quadratic function.

Published
2012
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40. A State Dependent Sampling for Linear State Feedback

Author

Wilfrid Perruquetti, Jean-Pierre Richard, Laurentiu Hetel, Christophe Fiter, Systèmes Non Linéaires et à Retards (SyNeR), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Non-Asymptotic estimation for online systems (NON-A), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille, Ce travail a été soutenu financièrement par le Ministère de l'Éducation Supérieure et de la Recherche, Le Conseil de la Région Nord-Pas de Calais et FEDER, au moyen du 'Contrat de Projets État Région (CPER) 2007-2013'. La recherche menant à ces résultats a reçu des fonds du 7ème Programme de Travail de la Communauté Européenne (FP7/2007-2013) sous l'accord n°257462 : HYCON2 Network of Excellence 'Highly-Complex and Networked Control Systems'. La recherche menant à ces résultats a reçu des fonds du programme INTERREG IV A 2 Mers Seas Zeen Cross-border Cooperation Program 2007-2013, par le projet SYSIASS 6-20., and European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010)

Subjects
state dependent sampling, 0209 industrial biotechnology, exponential stability, networked/embedded control systems, Polytope, 02 engineering and technology, Stability (probability), [SPI.AUTO]Engineering Sciences [physics]/Automatic, LTI system theory, 020901 industrial engineering & automation, Exponential stability, Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Lyapunov-Razumikhin, Electrical and Electronic Engineering, Mathematics, 020208 electrical & electronic engineering, Linear matrix inequality, Sampling (statistics), Exponential function, Stability conditions, self-triggered control, Control and Systems Engineering, convex polytope, linear matrix inequality
Abstract

International audience; In this work, a new state-dependent sampling control enlarges the sampling intervals of state feedback control. We consider the case of linear time invariant systems and guarantee the exponential stability of the system origin for a chosen decay rate. The approach is based on LMIs obtained thanks to sufficient Lyapunov-Razumikhin stability conditions and follows two steps. In the first step, we compute a Lyapunov-Razumikhin function that guarantees exponential stability for all time-varying sampling intervals up to some given bound. This value can be used as a lower-bound of the state-dependent sampling function. In a second step, an off-line computation provides a mapping from the state-space into the set of sampling intervals: the state is divided into a finite number of regions, and to each of these regions is associated an allowable upper-bound of the sampling intervals that will guarantee the global (exponential or asymptotic) stability of the system. The results are based on sufficient conditions obtained using convex polytopes. Therefore, they involve some conservatism with respect to necessary and sufficient conditions. However, at each of the two steps, an optimization on the sampling upper-bounds is proposed. The approach is illustrated with numerical examples from the literature for which the number of actuations is shown to be reduced with respect to the periodic sampling case.

Published
2012
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41. Equilibrium and stability of Wilson and Cowan's time coarse graining model

Author

Pasillas-Lépine, William, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Pasillas-Lépine, William, and Highly-complex and networked control systems - HYCON2 - - EC:FP7:ICT2010-09-01 - 2014-11-30 - 257462 - VALID

Subjects
Time-delay systems, [SPI.AUTO] Engineering Sciences [physics]/Automatic, Quantitative Biology::Neurons and Cognition, Equilibrium, Parkinson's disease, Neurosciences, Stability, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; The model proposed by Wilson and Cowan describes the dynamics of two interacting subpopulations of excitatory and inhibitory neurons. It can be used to model neural structures like the olfactory bulb, whisker barrels and the subthalamo-pallidal loop. In the paper, a new necessary and sufficient condition for the existence of multiple equilibria is derived for this model. Then, local asymptotic stability is characterized and related to the existence of multiple equilibria. A sufficient condition for global stability is also proposed. Finally, the case of loop delays is investigated, using a frequency-response analysis. The results obtained in the paper can be used for the stability analysis of the subthalamo-pallidal loop, a deep brain structure involved in Parkinson's disease.

Published
2012

42. Sampled data control of switched affine systems: a continuous-time approach

Author

Laurentiu Hetel, Emilia Fridman, Systèmes Non Linéaires et à Retards (SyNeR), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Department of Electrical Engineering, Tel Aviv University (TAU), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Tel Aviv University [Tel Aviv], Hetel, Laurentiu, and Highly-complex and networked control systems - HYCON2 - - EC:FP7:ICT2010-09-01 - 2014-11-30 - 257462 - VALID

Subjects
0209 industrial biotechnology, 020208 electrical & electronic engineering, Sampling (statistics), 02 engineering and technology, General Medicine, Function (mathematics), State (functional analysis), Linear matrix, [SPI.AUTO]Engineering Sciences [physics]/Automatic, [SPI.AUTO] Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Control theory, Data control, 0202 electrical engineering, electronic engineering, information engineering, Point (geometry), Affine transformation, Sampling interval, Mathematics
Abstract

International audience; This paper considers the stabilization problem for switched affine systems with a sampled-data switching law. The switching law is assumed to be a function of the system state at sampling instants and the sampling interval may be subject to variations or uncertainty. The main idea is to provide a robust switching law design criterion that takes into account the sampled-data implementation. The problem is addressed from the continuous-time point of view using Linear Matrix Inequalities (LMIs). The method is illustrated by a numerical example.

Published
2012
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43. The EECI-HYCON Graduate School on Control: Back on ten years of doctoral training

Author

Elena Panteley, Eugenie Gonçalves, Antoine Chaillet, Françoise Lamnabhi-Lagarrigue, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Chaillet, Antoine, and Highly-complex and networked control systems - HYCON2 - - EC:FP7:ICT2010-09-01 - 2014-11-30 - 257462 - VALID

Subjects
0209 industrial biotechnology, Engineering, Medical education, Event (computing), business.industry, media_common.quotation_subject, Control (management), 02 engineering and technology, General Medicine, Wide field, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, [SPI.AUTO] Engineering Sciences [physics]/Automatic, Excellence, Mathematics education, business, media_common
Abstract

International audience; This year the EECI-HYCON Graduate School on Control celebrates its 10th anniversary. This note aims at analyzing the evolution of this yearly event. We start by giving a historical perspective of the Graduate School since its creation and by recalling the major scientific areas covered by the lecturers. We then provide a detailed description of the organization of this event, including financial issues. As the Graduate School is part of a larger European initiative that aims at reinforcing European excellence in the wide field of the control of complex networked systems, we also present related activities.

Published
2012

44. Min-switching stabilization for discrete-time switching systems win non-linear modes

Author

Jungers, Marc, Cavichioli Gonzaga, Carlos, Daafouz, Jamal, Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL), Jungers, Marc, and Highly-complex and networked control systems - HYCON2 - - EC:FP7:ICT2010-09-01 - 2014-11-30 - 257462 - VALID

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

International audience; This paper studies the stabilization of discrete-time switched systems, with nonlinear modes via switching law as the control input. The modal nonlinearities are assumed to satisfy their own cone bounded sector condition. The min-switching strategy is applied with Lur'e-like Lyapunov functions to design the stabilizing switching law. Sufficient conditions to stabilize the considered system are given by suitable Lyapunov-Metzler inequalities. An academic example is presented to illustrate the validity of our main result.

Published
2012

45. Stability analysis and stabilisation of switched nonlinear systems

Author

Jamal Daafouz, Carlos Alberto Cavichioli Gonzaga, Marc Jungers, Centre de Recherche en Automatique de Nancy (CRAN), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), and Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)

Subjects
Lyapunov function, local stability and stabilisation, 0209 industrial biotechnology, input saturation, Active mode, 02 engineering and technology, Stability (probability), [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Control theory, 0202 electrical engineering, electronic engineering, information engineering, cone-bounded nonlinearity, basin of attraction estimate, Mathematics, LMIs, Linear matrix inequality, Function (mathematics), Computer Science Applications, Constraint (information theory), Nonlinear system, Control and Systems Engineering, symbols, 020201 artificial intelligence & image processing, Actuator
Abstract

International audience; A class of switched non-quadratic Lyapunov functions is considered in this article. The function is associated with discrete-time switched systems subject to mode-dependent cone-bounded nonlinearities and saturation actuator. These Lyapunov functions depend on the switched nonlinearities and on the active mode, instead of the time-invariant Lur'e-type function. The only assumption considered here is the mode-dependent sector condition, without constraint related to the slope of the nonlinearities. The stability analysis and control design problems lead to linear matrix inequality conditions. Optimisation problems are provided to cope with both issues in order to maximise the size of the basin of attraction estimate, which may be composed of disconnected sets. Numerical examples illustrate via comparisons that we improve the results of the literature.

Published
2012
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46. A proportional mean-field feedback for the desynchronization and inhibition of Kuramoto oscillators

Author

Franci, Alessio, Chaillet, Antoine, Pasillas-Lépine, William, Panteley, Elena, Lamnabhi-Lagarrigue, Françoise, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), CNRS PEPS project TREMBATIC., and European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010)

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

International audience; In this paper we summarize recent advances in the controlled alteration of synchronization in networks of in- terconnected Kuramoto oscillators. Motivated by neuroscience applications, and in particular by the deep brain stimulation treatment for Parkinson's disease, we show that a scalar signal, proportional to the mean behaviour of the oscillators population, may either desynchronize or inhibit the resulting oscillations.

Published
2012

47. Exploiting Packet Size in Uncertain Nonlinear Networked Control Systems

Author

Antonio Bicchi, Antoine Chaillet, Luca Greco, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), Interdep. Research Center 'E. Piaggio', University of Pisa - Università di Pisa, Istituto Italiano di Tecnologia (IIT), HYCON2 NoE contract number FP7-ICT- 257462, European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), and Centro di Ricerca Enrico Piaggio

Subjects
packet-switching networks, 0209 industrial biotechnology, Transmission delay, Computer science, Network packet, model-based control, Node (networking), Distributed computing, 020208 electrical & electronic engineering, Real-time computing, Bandwidth (signal processing), time-varying delays, 02 engineering and technology, Networked control system, Networked control systems, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Model predictive control, 020901 industrial engineering & automation, Transmission (telecommunications), Control and Systems Engineering, 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, Data transmission
Abstract

12; International audience; This paper addresses the problem of stabilizing uncertain nonlinear plants over a shared limited-bandwidth packet-switching network. While conventional control loops are designed to work with circuit-switching networks, where dedicated communication channels provide almost constant bit rate and delay, many networks, such as Ethernet, organize data transmission in packets, carrying larger amount of information at less predictable rates. To avoid the bandwidth waste due to the relatively large overhead inherent to packet transmission, we exploit the packet payload to carry longer control sequences. To this aim we adopt a model-based approach to remotely compute a predictive control signal on a suitable time horizon, which leads to effectively reducing the bandwidth required to guarantee stability. We consider networks for which both the time between consecutive accesses to each node (MATI) and the transmission and processing delays (MAD) for measurements and control packets are bounded. Communications are assumed to be ruled by a rather general protocol model, which encompasses many protocols used in practice. As a distinct improvement over the state of the art, our result is shown to be robust with respect to sector-bounded uncertainties in the plant model. Namely, an explicit bound on the combined effects of MATI and MAD is provided as a function of the basin of attraction and the model accuracy. A case study is presented to appreciate the improvements induced by the packet-based control strategy over existing methods.

Published
2012

48. Desynchronization of coupled phase oscillators, with application to the Kuramoto system under mean-field feedback

Author

Elena Panteley, Antoine Chaillet, Alessio Franci, Françoise Lamnabhi-Lagarrigue, Laboratoire des signaux et systèmes (L2S), Université Paris-Sud - Paris 11 (UP11)-CentraleSupélec-Centre National de la Recherche Scientifique (CNRS), PEPS CNRS project 'TREMBATIC', and European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010)

Subjects
0209 industrial biotechnology, mean-field, desynchronization, Phase (waves), 02 engineering and technology, Topology, 01 natural sciences, Instability, Synchronization, Time–frequency analysis, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Mean field theory, Matrix algebra, Control theory, 0103 physical sciences, Euclidean geometry, 010306 general physics, Kuramoto oscillators, Variable (mathematics), Mathematics
Abstract

International audience; This note introduces two notions of desynchronization for interconnected phase oscillators by requiring that phases drift away from one another either at all times or in average. It provides a characterization of each of these two notions based on the grounded variable associated to the system, and relates them to a classical notion of instability valid in Euclidean spaces. An illustration is provided through the Kuramoto system, which is shown to be desynchronizable by proportional mean-field feedback.

Published
2011

49. Échantillonnage dépendant de l'état pour les systèmes avec perturbations et retards

Author

Christophe Fiter, Jean-Pierre Richard, Laurentiu Hetel, Wilfrid Perruquetti, Systèmes Non Linéaires et à Retards (SyNeR), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Non-Asymptotic estimation for online systems (NON-A), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille, Ce travail a été soutenu financièrement par le Ministère de l'Éducation Supérieure et de la Recherche, Le Conseil de la Région Nord-Pas de Calais et FEDER, au moyen du 'Contrat de Projets État Région (CPER) 2007-2013'. La recherche menant à ces résultats a reçu des fonds du 7ème Programme de Travail de la Communauté Européenne (FP7/2007-2013) sous l'accord n°257462 : HYCON2 Network of Excellence 'Highly-Complex and Networked Control Systems'., and European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010)

Subjects
Physics, Système embarqué/commandé par réseau, 0209 industrial biotechnology, 020208 electrical & electronic engineering, Lyapunov krasovskii, échantillonnage dépendant de l'état, 02 engineering and technology, Lyapunov-Krasovskii, stabilité L2, Feedback regulation, Industrial and Manufacturing Engineering, Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Combinatorics, 020901 industrial engineering & automation, Control and Systems Engineering, Interval matrix, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, système à retard, 0202 electrical engineering, electronic engineering, information engineering, inégalité matricielle linéaire, State dependence, Electrical and Electronic Engineering, Delay time
Abstract

Distinction du "meilleur article jeune chercheur"; National audience; Dans ce travail, nous présentons un contrôle dynamique de l'échantillonnage qui permet d'élargir le pas d'échantillonnage de commande par retour d'état. Nous nous intéressons au cas de systèmes échantillonnés linéaires sujets à des perturbations et des retards, et assurons leur stabilité L2. L'approche est basée sur une nouvelle classe de fonctionnelles de Lyapunov-Krasovskii dont les matrices dépendent de l'état. Grâce aux LMIs obtenues, une cartographie de l'espace d'état est réalisée hors-ligne: elle donne pour chaque point de l'espace d'état le pas d'échantillonnage maximal admissible, ce qui permet de réduire le nombre de mises à jour de l'actionneur pendant le contrôle du système en temps-réel.

Published
2011
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50. Switched affine systems using sampled-data controllers: robust and guaranteed stabilization

Author

Claude Iung, Pascal Hauroigne, Pierre Riedinger, 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), ANR ArHyCo,ANR ArHyCo, European Project: 257462,EC:FP7:ICT,FP7-ICT-2009-5,HYCON2(2010), and ANR-08-SEGI-0004,ArHyCo,Architectures Hybrides et Contraintes(2008)

Subjects
0209 industrial biotechnology, Mathematical optimization, Optimization problem, 020208 electrical & electronic engineering, Nonuniform sampling, 02 engineering and technology, Computer Science Applications, Whole systems, input-to-state stability, 020901 industrial engineering & automation, switched affine systems, stabilization of hybrid systems, Control and Systems Engineering, Robustness (computer science), Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Affine transformation, Electrical and Electronic Engineering, Robust control, robust control, Control-Lyapunov function, Sampled data systems, Mathematics
Abstract

International audience; The problem of robust and guaranteed stabilization is addressed for switched affine systems using sampled state feedback controllers. Based on the existence of a control Lyapunov function for a relaxed system, we propose three sampled-data controls. Global attracting sets, computed by solving a sequence of optimization problems, guarantee practical and global asymptotic stabilization for the whole system trajectories. In addition, robust margins with respect to parameters uncertainties and non uniform sampling are provided using input-to-state stability. Finally, a buck-boost converter is considered to illustrate the effectiveness of the proposed approaches.

Published
2011
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