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7. Robust Fixed-Time Stability: Application to Sliding-Mode Control

Author

Vincent Léchappé, Emmanuel Bernuau, Emmanuel Moulay, Franck Plestan, Systèmes et Réseaux Intelligents (XLIM-SRI), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Ampère, Département Automatique pour l'Ingénierie des Systèmes (AIS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Paris-Saclay Food and Bioproduct Engineering (SayFood), AgroParisTech-Université Paris-Saclay-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Laboratoire des Sciences du Numérique de Nantes (LS2N), Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), and Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Sliding mode control, 020208 electrical & electronic engineering, Robust control, Scalar (physics), Fixed-time stability, 02 engineering and technology, Stability (probability), Computer Science Applications, Second order systems, Nonlinear system, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Fixed time, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, Constant (mathematics), Mathematics
Abstract

International audience; This article deals with robust fixed-time stability and stabilization. First, new global robust fixed-time stability results are proposed for scalar systems by using constant and variable exponent coefficients. Then, they are applied to global robust fixed-time stabilization of a class of uncertain nonlinear second order systems by using sliding mode control. All the results are illustrated in simulation.

Published
2022

12. Fixed-time sliding mode control with mismatched disturbances

Author

Emmanuel Moulay, Emmanuel Bernuau, Michael Defoort, Vincent Léchappé, Franck Plestan, Systèmes et Réseaux Intelligents (XLIM-SRI), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Ampère (AMPERE), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Paris-Saclay Food and Bioproduct Engineering (SayFood), AgroParisTech-Université Paris-Saclay-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201 (LAMIH), Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-INSA Institut National des Sciences Appliquées Hauts-de-France (INSA Hauts-De-France), Laboratoire des Sciences du Numérique de Nantes (LS2N), IMT Atlantique Bretagne-Pays de la Loire (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN)-École Centrale de Nantes (ECN)-Centre National de la Recherche Scientifique (CNRS), Ampère, Département Automatique pour l'Ingénierie des Systèmes (AIS), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique), Institut Mines-Télécom [Paris] (IMT)-Institut Mines-Télécom [Paris] (IMT)-École Centrale de Nantes (Nantes Univ - ECN), Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes université - UFR des Sciences et des Techniques (Nantes univ - UFR ST), Nantes Université - pôle Sciences et technologie, Nantes Université (Nantes Univ)-Nantes Université (Nantes Univ)-Nantes Université - pôle Sciences et technologie, and Nantes Université (Nantes Univ)

Subjects
fixed-time differentiator, 0209 industrial biotechnology, Sliding mode control, Computer science, 020208 electrical & electronic engineering, Mode (statistics), 02 engineering and technology, Differentiator, 020901 industrial engineering & automation, Control and Systems Engineering, Robustness (computer science), Fixed time, Control theory, fixed-time stability, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, mismatched disturbances
Abstract

International audience; The aim of this article is to develop new second-order fixed-time sliding mode controllers able to tackle mismatched disturbances. Contrary to what is done in the literature, the proposed sliding-mode control strategy does not use disturbance observers because the sliding surface possesses robustness properties. The results are applied to define a new fixed-time differentiator.

Published
2022

13. Toward a simple, generic, and rapid simulation of the drying of solid foods

Author

Emmanuel Bernuau, Hedi Romdhana, Francis Courtois, Daniel Goujot, Ingénierie, Procédés, Aliments (GENIAL), Institut National de la Recherche Agronomique (INRA)-AgroParisTech, Qualisud - Pôle de La Réunion (Qualisud Réunion), Démarche intégrée pour l'obtention d'aliments de qualité (UMR Qualisud), Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de La Réunion (UR)-Université de Montpellier (UM)-Avignon Université (AU)-Centre international d'études supérieures en sciences agronomiques (Montpellier SupAgro)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université Montpellier 1 (UM1)-Centre de Coopération Internationale en Recherche Agronomique pour le Développement (Cirad)-Institut national d’études supérieures agronomiques de Montpellier (Montpellier SupAgro), and Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de La Réunion (UR)-Université de Montpellier (UM)-Avignon Université (AU)-Centre international d'études supérieures en sciences agronomiques (Montpellier SupAgro)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université Montpellier 1 (UM1)

Subjects
General Chemical Engineering, compartment models, Finite difference, mathematical modeling, 04 agricultural and veterinary sciences, 02 engineering and technology, 040401 food science, Drying process, [SPI]Engineering Sciences [physics], 0404 agricultural biotechnology, 020401 chemical engineering, Solid food, Order (business), Simple (abstract algebra), heat and mass transfers, Applied mathematics, 0204 chemical engineering, Physical and Theoretical Chemistry, optimization, Mathematics
Abstract

International audience; In order to simulate the drying of foods, calculations based on finite differences, elements, or volumes are extremely time-consuming, particularly when embedded in an optimization procedure. Such models, involving coupled heat and mass transfers and nonlinear properties and boundaries, give rise to slow simulations. This paper proposes a new method concerning the slab, cylindrical, and spherical geometries. This method gives results equivalent to those of the finite volume method but is more rapid by an order of magnitude. The method is based on an optimized 3-compartment model whose parameters are linked to physically meaningful food properties.

Published
2019

14. Practical Consensus of Homogeneous Sampled-Data Multiagent Systems

Author

Emmanuel Bernuau, Emmanuel Moulay, Fayrouz Isfoula, Patrick Coirault, Ingénierie, Procédés, Aliments (GENIAL), Institut National de la Recherche Agronomique (INRA)-AgroParisTech, Systèmes et Réseaux Intelligents (XLIM-SRI), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique et d'Automatique pour les Systèmes (LIAS), and Université de Poitiers-ENSMA

Subjects
0209 industrial biotechnology, Emulation, Mathematical optimization, sampled-data systems, Computer science, Homogeneity (statistics), Multi-agent system, Multi-agent systems, Sampling (statistics), Graph theory, 02 engineering and technology, homogeneous systems, Computer Science Applications, Nonlinear system, 020901 industrial engineering & automation, Exponential stability, Control and Systems Engineering, Homogeneous, [INFO.INFO-MA]Computer Science [cs]/Multiagent Systems [cs.MA], practical consensus, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Electrical and Electronic Engineering
Abstract

International audience; The aim of this paper is to study the second-order practical consensus of homogeneous sampled-data multiagent systems (MASs). To do this, a new nonlinear emulation strategy based on homogeneity is developed. It is then applied to MASs under synchronously variable sampling. Finally, a comparison with the classical linear strategy is provided in the case of MASs under synchronously periodic sampling.

Published
2019

15. Stability of discontinuous homogeneous nonlinear sampled-data systems

Author

Patrick Coirault, Emmanuel Bernuau, Emmanuel Moulay, Ingénierie, Procédés, Aliments (GENIAL), Institut National de la Recherche Agronomique (INRA)-AgroParisTech, Systèmes et Réseaux Intelligents (XLIM-SRI), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique et d'Automatique pour les Systèmes (LIAS), and Université de Poitiers-ENSMA

Subjects
0209 industrial biotechnology, Computer science, 020208 electrical & electronic engineering, 02 engineering and technology, Nonlinear system, Double integrator, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Robustness (computer science), Aperiodic graph, Homogeneous, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, Sampled data systems
Abstract

International audience; The article deals with the stability of discontinuous homogeneous nonlinear systems with aperiodic sampled-data inputs. We first extend results about robustness of homogeneous nonlinear systems to the discontinuous case. Then, we prove that this framework is well suited for studying the stability of discontinuous homogeneous nonlinear sampled-data systems. The results are illustrated on the double integrator.

Published
2019

16. Practical consensus tracking of multi-agent systems with linear controllers

Author

Patrick Coirault, Qishuai Liu, Emmanuel Bernuau, Fayrouz Isfoula, Emmanuel Moulay, Qing Hui, Laboratoire d'Informatique et d'Automatique pour les Systèmes (LIAS), Université de Poitiers-ENSMA, Ingénierie, Procédés, Aliments (GENIAL), Institut National de la Recherche Agronomique (INRA)-AgroParisTech, Systèmes et Réseaux Intelligents (XLIM-SRI), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), University of Nebraska [Lincoln], and University of Nebraska System

Subjects
0209 industrial biotechnology, Computer science, Multi-agent system, 020208 electrical & electronic engineering, Control (management), Stability (learning theory), Fixed topology, Mobile robot, 02 engineering and technology, Tracking (particle physics), 020901 industrial engineering & automation, Control theory, [INFO.INFO-MA]Computer Science [cs]/Multiagent Systems [cs.MA], [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Convergence (routing), 0202 electrical engineering, electronic engineering, information engineering, Protocol (object-oriented programming), ComputingMilieux_MISCELLANEOUS
Abstract

International audience; The second-order practical consensus tracking of multi-agent systems with a fixed topology and a varying leader's velocity is obtained by using a linear control strategy and the input-to-state stability framework. Then, a new control protocol is proposed where the leader, called a perceptive leader, receives information from its followers. Finally, a study is provided in simulation and on a fleet of mobile robots showing the effectiveness of non perceptive and perceptive strategies in terms of speed of convergence, precision and connectivity maintenance.

Published
2019

17. Topological properties for compact stable attractors in ℝn

Author

Emmanuel Moulay, Emmanuel Bernuau, Patrick Coirault, Qing Hui, Ingénierie, Procédés, Aliments (GENIAL), Institut National de la Recherche Agronomique (INRA)-AgroParisTech, Systèmes et Réseaux Intelligents (XLIM-SRI), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire d'Informatique et d'Automatique pour les Systèmes (LIAS), Université de Poitiers-ENSMA, University of Nebraska [Lincoln], and University of Nebraska System

Subjects
Physics, Pure mathematics, Attractor, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], ComputingMilieux_MISCELLANEOUS
Abstract

Open access; International audience

Published
2019

18. Robustness of sampled-data homogeneous systems

Author

Emmanuel Moulay, Patrick Coirault, Emmanuel Bernuau, Florence Josse, Systèmes et Réseaux Intelligents (XLIM-SRI), XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), Paris-Saclay Food and Bioproduct Engineering (SayFood), AgroParisTech-Université Paris-Saclay-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Laboratoire d'Informatique et d'Automatique pour les Systèmes (LIAS), and Université de Poitiers-ENSMA

Subjects
Lyapunov stability, sampled-data systems, 0209 industrial biotechnology, Computer science, 020208 electrical & electronic engineering, robustness, 02 engineering and technology, homogeneous systems, Stability (probability), Set (abstract data type), 020901 industrial engineering & automation, Control and Systems Engineering, Homogeneous, Robustness (computer science), Control theory, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, 0202 electrical engineering, electronic engineering, information engineering, Electrical and Electronic Engineering, Sampled data systems
Abstract

International audience; The main goal of this article is to study the robustness of continuous homogeneous systems with sampled-data inputs subject to external disturbances. We characterize how the perturbations affect the system and we show that global asymptotic set stability is achieved.

Published
2021

19. Robustness of Homogeneous and Homogeneizable Differential Inclusions

Author

Wilfrid Perruquetti, Emmanuel Bernuau, and Denis Efimov

Subjects
Lyapunov function, symbols.namesake, Differential inclusion, Homogeneous, Robustness (computer science), Algebraic operation, symbols, Applied mathematics, Discontinuous systems, Constructive, Mathematics
Abstract

The chapter proposes constructive conditions for verifying the input-to-state stability property of discontinuous systems using geometric homogeneity. Two sets of conditions are developed for a class of homogeneous and homogenizable systems described by differential inclusions. The advantage of the proposed conditions is that they are not based on the Lyapunov function method, but more related to algebraic operations over the right-hand side of the system.

Published
2017

20. Analysis of scale invariance property applying homogeneity

Author

Emmanuel Bernuau, Wilfrid Perruquetti, and Denis Efimov

Subjects
Property (philosophy), Homogeneous, Cascade, Closeness, Scalability, Homogeneity (physics), General Medicine, Statistical physics, Scale invariance, Topology, Mathematics
Abstract

The problem of scalability of trajectories in homogeneous and locally homogeneous systems is considered. It is shown that the homogeneous systems have scalability property, and locally homogeneous systems possess this property approximately. The issue of closeness of trajectories for the system and its local homogeneous approximation is investigated. The notions of scale invariance and fold change detection are also studied. The results are illustrated by a cascade system analysis.

Published
2014

21. Verification of ISS, iISS and IOSS properties applying weighted homogeneity

Author

Wilfrid Perruquetti, Emmanuel Bernuau, Denis Efimov, Andrey Polyakov, Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS), Université de Lille, Sciences et Technologies-Centrale 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-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Systèmes Non Linéaires et à Retards (SyNeR), and Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL)

Subjects
0209 industrial biotechnology, Mathematical optimization, General Computer Science, Mechanical Engineering, Input-to-state stability, Integral input-to-state stability, 02 engineering and technology, Nonlinear system, 020901 industrial engineering & automation, Homogeneous 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, 020201 artificial intelligence & image processing, Electrical and Electronic Engineering, Mathematics
Abstract

International audience; Several conditions are proposed to check different robustness properties (ISS, iISS, IOSS and OSS) for generic nonlinear systems applying the weighted homogeneity concept (global or local). The advantages of this result are that, under some mild conditions, the system robustness can be established as a function of the degree of homogeneity.

Published
2013

22. Homogeneity of differential inclusions

Author

Andrey Polyakov, Denis Efimov, Wilfrid Perruquetti, and Emmanuel Bernuau

Subjects
Lyapunov function, 0209 industrial biotechnology, Homogeneity (statistics), Mathematical analysis, 02 engineering and technology, Discontinuous systems, Nonlinear system, symbols.namesake, 020901 industrial engineering & automation, 020401 chemical engineering, Exponential stability, Differential inclusion, Homogeneous, symbols, 0204 chemical engineering, Mathematics
Abstract

In this chapter the notion of geometric homogeneity is extended for differential inclusions. This kind of homogeneity provides the most advanced coordinate-free framework for analysis and synthesis of nonlinear discontinuous systems. The main qualitative properties of continuous homogeneous systems are extended to the discontin-uous setting: the equivalence of the global asymptotic stability and the existence of a homogeneous Lyapunov function; the link between finite-time stability and negative degree of homogeneity; the equivalence between attractivity and asymptotic stability are among the proved results.

Published
2016

23. Finite-time observation and trajectory tracking for a direct wave energy converter

Author

Alain Glumineau, Emmanuel Bernuau, Franck Plestan, and Saïd Moussaoui

Subjects
Physics, Energy converter, Control theory, Homogeneity (physics), Finite time, Simulation, Direct wave
Abstract

In this paper, we address the problem of finite-time observation and trajectory tracking for the control of a direct wave energy converter device. We first consider a simplified model of the system on which we develop an homogeneity-based finite-time observer. Then we design a control able to make the system follow a given reference trajectory in finite-time. Simulation results finally demonstrate the applicability of the method.

Published
2015

24. Scale invariance analysis for genetic networks applying homogeneity

Author

Wilfrid Perruquetti, Emmanuel Bernuau, Denis Efimov, Institut de Recherche en Communications et en Cybernétique de Nantes (IRCCyN), Mines Nantes (Mines Nantes)-École Centrale de Nantes (ECN)-Ecole Polytechnique de l'Université de Nantes (EPUN), Université de Nantes (UN)-Université de Nantes (UN)-PRES Université Nantes Angers Le Mans (UNAM)-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), 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
0209 industrial biotechnology, Mathematical optimization, Models, Genetic, Systems Biology, Applied Mathematics, Systems biology, Gene regulatory network, Mathematical Concepts, 02 engineering and technology, Scale invariance, Topology, Models, Biological, 01 natural sciences, Agricultural and Biological Sciences (miscellaneous), 010305 fluids & plasmas, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Homogeneous, Modeling and Simulation, 0103 physical sciences, Scalability, Gene Regulatory Networks, Scaling, Mathematics
Abstract

International audience; Scalability is a property describing the change of the trajectory of a dynamical system under a scaling of the input stimulus and of the initial conditions. Particular cases of scalability include the scale invariance and fold change detection (when the scaling of the input does not influence the system output). In the present paper it is shown that homogeneous systems have this scalability property while locally homogeneous systems approximately possess this property. These facts are used for detecting scale invariance or approximate scalability (far from a steady state) in several biological systems. The results are illustrated by various regulatory networks.

Published
2015

25. Homogeneous continuous finite-time observer for the triple integrator

Author

Denis Efimov, Emmanuel Bernuau, Wilfrid Perruquetti, Emmanuel Moulay, Institut de Recherche en Communications et en Cybernétique de Nantes (IRCCyN), Mines Nantes (Mines Nantes)-École Centrale de Nantes (ECN)-Ecole Polytechnique de l'Université de Nantes (EPUN), Université de Nantes (UN)-Université de Nantes (UN)-PRES Université Nantes Angers Le Mans (UNAM)-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-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), SIC (XLIM-SIC), Université de Poitiers-XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), 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-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS), and Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)

Subjects
Lyapunov function, symbols.namesake, Observer (quantum physics), Exponential stability, Homogeneous, Control theory, Integrator, symbols, Finite time, Constructive, Mathematics, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; In this paper we consider the continuous homogeneous observer defined in [1] in the case of the triple in-tegrator. In [1], convergence of the algorithm was only proved when the degree of homogeneity was sufficiently close to 0 without more tractable information. We show here that, in the case of the triple integrator, the observer presents global finite-time stability for any negative degree under constructive conditions on the gains. This is achieved with a homogeneous Lyapunov function design. Simulations of the proposed observer are also provided.

Published
2015

26. Local stabilization of switched affine systems

Author

Emmanuel Bernuau, 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), Dipartimento di Ingegneria dell'Informazione [Pisa], and University of Pisa - Università di Pisa

Subjects
Generalization, Regular polygon, State (functional analysis), Constructive, Computer Science Applications, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Nonlinear system, Control and Systems Engineering, Control theory, Affine transformation, Electrical and Electronic Engineering, Representation (mathematics), Constant (mathematics), Mathematics
Abstract

International audience; This paper considers the local stabilization problem for the class of switched affine systems. The main idea is to use an alternative representation of the switched affine system as a nonlinear system with input constraints. Switching laws can be derived by emulating locally classical controllers. It is shown that by restricting to local stabilization, the classical constraint on the existence of constant stable convex combinations may be easily avoided. The approach may be interpreted as a generalization where convex combinations defined as functions of the system state are being used. Constructive methods for deriving switching laws are proposed.

Published
2015

27. Robust finite-time output feedback stabilization of the double integrator

Author

Denis Efimov, Wilfrid Perruquetti, Emmanuel Moulay, Emmanuel Bernuau, Dipartimento di Ingegneria dell'Informazione [Pisa], University of Pisa - Università di Pisa, 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-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), SIC (XLIM-SIC), Université de Poitiers-XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), and Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)

Subjects
Output feedback, Double integrator, Discretization, Control and Systems Engineering, Homogeneous, Control theory, Robustness (computer science), [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Finite time, Integrating ADC, Closed loop, Computer Science Applications, Mathematics
Abstract

International audience; The problem of finite-time output stabilization of the double integrator is addressed applying the homogeneity approach. A homogeneous controller and a homogeneous observer are designed (for different degrees of homogeneity) ensuring the finite-time stabilization. Their combination under mild conditions is shown to stay homogeneous and finite-time stable as well. Robustness and effects of discretization on the obtained closed loop system are analyzed. The efficiency of the obtained solution is demonstrated in computer simulations.

Published
2014

28. On the robustness of homogeneous systems and a homogeneous small gain theorem

Author

Wilfrid Perruquetti, Denis Efimov, Emmanuel Bernuau, Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS), Université de Lille, Sciences et Technologies-Centrale Lille-Centre National de la Recherche Scientifique (CNRS), Dipartimento di Ingegneria dell'Informazione [Pisa], University of Pisa - Università di Pisa, 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-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centrale Lille, and Efimov, Denis

Subjects
0209 industrial biotechnology, Singular perturbation, 010102 general mathematics, Mathematical analysis, Perturbation (astronomy), 02 engineering and technology, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Small-gain theorem, [SPI.AUTO] Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Homogeneous, Stability theory, 0101 mathematics, Mathematics
Abstract

International audience; This paper is devoted to the study of the robustness properties stemming from geometric homogeneity. More precisely, we show that a continuous homogeneous system, which is asymptotically stable without perturbation, is always ISS w.r.t. a perturbation. We characterize the asymptotic gain of such a disturbed system and state a so-called homogeneous small gain theorem based on this estimation.

Published
2014

29. Robustness of homogeneous and locally homogeneous differential inclusions

Author

Denis Efimov, Wilfrid Perruquetti, Emmanuel Bernuau, Dipartimento di Ingegneria dell'Informazione [Pisa], University of Pisa - Università di Pisa, 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-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Systèmes Non Linéaires et à Retards (SyNeR), Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL), Centrale Lille, and Efimov, Denis

Subjects
Lyapunov function, 0209 industrial biotechnology, 010102 general mathematics, Mathematical analysis, 02 engineering and technology, Discontinuous systems, 01 natural sciences, Constructive, symbols.namesake, 020901 industrial engineering & automation, Differential inclusion, Robustness (computer science), Homogeneous, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Algebraic operation, symbols, 0101 mathematics, [INFO.INFO-AU] Computer Science [cs]/Automatic Control Engineering, Mathematics
Abstract

International audience; The paper proposes constructive conditions for verification of input-to-state stability property for discontinuous systems using geometric homogeneity. Two sets of conditions are developed: for a class of homogeneous and locally homogeneous systems described by differential inclusions. The advantage of the proposed conditions is that they are not based on the Lyapunov function method, but more related to algebraic operations over the right-hand side of the system.

Published
2014

30. On homogeneity and its application in sliding mode control

Author

Wilfrid Perruquetti, Denis Efimov, Andrey Polyakov, Emmanuel Bernuau, Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS), Université de Lille, Sciences et Technologies-Centrale Lille-Centre National de la Recherche Scientifique (CNRS), 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, 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
Computer Networks and Communications, Applied Mathematics, Homogeneity (statistics), Mode (statistics), Context (language use), Stability (probability), Sliding mode control, Differential inclusion, Control and Systems Engineering, Control theory, Robustness (computer science), [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Signal Processing, Algebraic number, Mathematics
Abstract

International audience; The paper is reviewing the tools to handle high-order sliding mode design and robustness. The main ingredient is homogeneity which can be checked using an algebraic test and which helps us in obtaining one of the most desired properties in sliding mode control that is finite-time stability. This paper stresses some recently obtained results about homogeneity for differential inclusions and robustness with respect to perturbations in the context of input-to-state stability. Lastly within this framework, most of the popular high-order sliding mode control schemas are analysed.

Published
2014
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31. Retraction obstruction to time-varying stabilization

Author

Wilfrid Perruquetti, Emmanuel Moulay, Emmanuel Bernuau, Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS), Université de Lille, Sciences et Technologies-Centrale 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-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Centrale Lille, SIC (XLIM-SIC), Université de Poitiers-XLIM (XLIM), Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS)-Université de Limoges (UNILIM)-Centre National de la Recherche Scientifique (CNRS), and Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centrale Lille-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Base space, Retraction obstruction, 02 engineering and technology, Space (mathematics), stabilization, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Section (fiber bundle), 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Bundle, Lyapunov stability, 0202 electrical engineering, electronic engineering, information engineering, State space, 020201 artificial intelligence & image processing, Electrical and Electronic Engineering, A fibers, Mathematics
Abstract

International audience; This paper address the problem of the global stabilization on a total space of a fiber bundle with a compact base space. We prove that, under mild assumptions (existence of a continuous section and forward unicity of solutions), no equilibrium of a continuous system defined on such a state space can be globally asymptotically uniformly stabilized using continuous time-varying feedback.

Published
2013

32. On ISS and iISS properties of homogeneous systems

Author

Emmanuel Bernuau, Wilfrid Perruquetti, Denis Efimov, Andrey Polyakov, Laboratoire d'Automatique, Génie Informatique et Signal (LAGIS), Université de Lille, Sciences et Technologies-Centrale 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-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS), Systèmes Non Linéaires et à Retards (SyNeR), and Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189 (CRIStAL)

Subjects
0209 industrial biotechnology, Degree (graph theory), Homogeneity (statistics), 02 engineering and technology, Function (mathematics), Stability (probability), [SPI.AUTO]Engineering Sciences [physics]/Automatic, Nonlinear system, 020901 industrial engineering & automation, Robustness (computer science), Homogeneous, Control theory, 0202 electrical engineering, electronic engineering, information engineering, 020201 artificial intelligence & image processing, Mathematics
Abstract

Several conditions are proposed to check input-to-state stability (ISS) and integral input-to-state stability (iISS) properties for generic nonlinear systems applying the weighted homogeneity concept (global or local). The advantages of this result is that, under some mild conditions, the system robustness can be established as a function of the degree of homogeneity.

33. Une approche du suivi de consensus pour les systèmes multi-agents

Author

Isfoula, Fayrouz, Laboratoire d'Informatique et d'Automatique pour les Systèmes (LIAS), Université de Poitiers-ENSMA, Université de Poitiers, Patrick Coirault, Emmanuel Moulay, and Emmanuel Bernuau

Subjects
Suivi par consensus, Commande échantillonnée, [INFO.INFO-MA]Computer Science [cs]/Multiagent Systems [cs.MA], Multi-Agent systems, Sampled data control, Leader perceptif, Perceptive leader, Consensus tracking, Système multi-Agents, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

An agent is an autonomous dynamics system that can coordinate with the environment as well as with other agents. A group of these autonomous agents working in coordination is called a Multi-agent system (MAS). A MAS has several advantages over single agent operation. The main objective of MAS is to achieve a complex goal which is hard to achieve by a single agent. In MAS, each agent shares its information (states) to the neighbors only to complete the task hence no centralized monitoring systems is required. We can define a multi-agent system as a network in which information is distributed. The interest of researchers in the study of distributed control and distributed coordination of autonomous agent networks is motivated by the fact that it has the ability to cope with the problems associated with centralized communication network and also allow the switching network topologies.The algorithms for distributed networks only use local information, and are robust to variations of network topology and can accommodate network with large size.One of the most studied problems in the field of MAS is the consensus, which can be defined as: for any initial conditions for all agent, what are the conditions that should hold in order that the agents agree on a common value asymptotically while only information is exchanged between neighboring agents.This thesis deals with the development of control law to achieve the consensus for fixed and switching topologies, with or without a leader (consensus tracking). It also investigates the problem of the quality of information in the network. In consensus tracking, the notion of perceptive leader is developed and a control law is proposed for a fixed and switching topology.; Un système multi-agents est composé d’un ensemble d’agents interagissant entre eux et avec leur environnement, un agent étant vu comme un système dynamique autonome. La force des SMA repose sur la capacité des agents à coopérer entre eux pour atteindre un objectif qu’un agent seul ne pourrait atteindre. Chaque agent partage ses informations avec ses voisins, ce qui permet à l’ensemble des agents de s’accorder sur un objectif commun sans qu’il y ait pour autant une centralisation de l’information et de l’objectif. En ce sens, un système multi-agents peut être vu comme un réseau dans lequel l’information est distribuée. L’intérêt croissant pour le contrôle distribué et la coordination des réseaux constitués d’agents autonomes est motivé par l’absence de centralisation de l’information et la possibilité d’avoir une topologie du réseau variable. Les algorithmes de contrôle déployés sur ces réseaux sont de nature distribuée puisqu’ils s’appuient sur des informations locales, et sont robustes vis-à-vis des variations de topologie et de taille du réseau. Le problème le plus étudié dans le cadre de ces systèmes multi-agents est celui du consensus, qui peut être résumé ainsi : étant donné des conditions initiales pour chaque agent, quelles sont les conditions pour que les agents s’accordent asymptotiquement sur une valeur commune en n’échangeant que des informations entre agents voisins. Cette thèse traite du développement de commandes permettant d’atteindre ce consensus pour des topologies fixes et variables, en présence ou non d’un leader (suivi de consensus), et sur la qualité des informations transitant dans le réseau. En suivi de consensus, la notion de leader perceptif est développée et une commande est proposée pour une topologie fixe et variable.

Published
2019

34. An appraoch of practical consensus tracking of multi agent systems

Author

Isfoula, Fayrouz, STAR, ABES, Laboratoire d'Informatique et d'Automatique pour les Systèmes (LIAS), Université de Poitiers-ENSMA, Université de Poitiers, Patrick Coirault, Emmanuel Moulay, and Emmanuel Bernuau

Subjects
Suivi par consensus, [SPI.AUTO] Engineering Sciences [physics]/Automatic, Commande échantillonnée, [INFO.INFO-MA]Computer Science [cs]/Multiagent Systems [cs.MA], Multi-Agent systems, Sampled data control, Leader perceptif, [INFO.INFO-MA] Computer Science [cs]/Multiagent Systems [cs.MA], Perceptive leader, Consensus tracking, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Système multi-Agents
Abstract

An agent is an autonomous dynamics system that can coordinate with the environment as well as with other agents. A group of these autonomous agents working in coordination is called a Multi-agent system (MAS). A MAS has several advantages over single agent operation. The main objective of MAS is to achieve a complex goal which is hard to achieve by a single agent. In MAS, each agent shares its information (states) to the neighbors only to complete the task hence no centralized monitoring systems is required. We can define a multi-agent system as a network in which information is distributed. The interest of researchers in the study of distributed control and distributed coordination of autonomous agent networks is motivated by the fact that it has the ability to cope with the problems associated with centralized communication network and also allow the switching network topologies.The algorithms for distributed networks only use local information, and are robust to variations of network topology and can accommodate network with large size.One of the most studied problems in the field of MAS is the consensus, which can be defined as: for any initial conditions for all agent, what are the conditions that should hold in order that the agents agree on a common value asymptotically while only information is exchanged between neighboring agents.This thesis deals with the development of control law to achieve the consensus for fixed and switching topologies, with or without a leader (consensus tracking). It also investigates the problem of the quality of information in the network. In consensus tracking, the notion of perceptive leader is developed and a control law is proposed for a fixed and switching topology., Un système multi-agents est composé d’un ensemble d’agents interagissant entre eux et avec leur environnement, un agent étant vu comme un système dynamique autonome. La force des SMA repose sur la capacité des agents à coopérer entre eux pour atteindre un objectif qu’un agent seul ne pourrait atteindre. Chaque agent partage ses informations avec ses voisins, ce qui permet à l’ensemble des agents de s’accorder sur un objectif commun sans qu’il y ait pour autant une centralisation de l’information et de l’objectif. En ce sens, un système multi-agents peut être vu comme un réseau dans lequel l’information est distribuée. L’intérêt croissant pour le contrôle distribué et la coordination des réseaux constitués d’agents autonomes est motivé par l’absence de centralisation de l’information et la possibilité d’avoir une topologie du réseau variable. Les algorithmes de contrôle déployés sur ces réseaux sont de nature distribuée puisqu’ils s’appuient sur des informations locales, et sont robustes vis-à-vis des variations de topologie et de taille du réseau. Le problème le plus étudié dans le cadre de ces systèmes multi-agents est celui du consensus, qui peut être résumé ainsi : étant donné des conditions initiales pour chaque agent, quelles sont les conditions pour que les agents s’accordent asymptotiquement sur une valeur commune en n’échangeant que des informations entre agents voisins. Cette thèse traite du développement de commandes permettant d’atteindre ce consensus pour des topologies fixes et variables, en présence ou non d’un leader (suivi de consensus), et sur la qualité des informations transitant dans le réseau. En suivi de consensus, la notion de leader perceptif est développée et une commande est proposée pour une topologie fixe et variable.

Published
2019

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