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Home > Research > Methods for System Engineering > Projets institutionnels ou industriels (Dépt MIS d’Ampère) > Archive des projets Ampère «MIS» achevés ces dernières années

AIDS (2011-2013) : Approximation of Infinite-Dimensional Systems

by Laurent Krähenbühl - published on , updated on

En cours de rédaction

AIDS (Approximation of Infinite-Dimensional Systems / Approximation de Systèmes de Dimension Infinie) est un projet du programme "Jeunes Chercheuses et Jeunes Chercheurs" de l’ANR.

Programme ANR : JCJC
Projet : ANR-11-JS03-0004 - Coordonnateur : Michaël Di Loreto (INSA de Lyon)
Liens :

Projet terminé : 2011-2013 (3 ans)
Apport de l’ANR :

Partenaire : Ampère (Département Méthodes pour l’Ingénierie des Systèmes).


Résumé du projet scientifique

In this project, we address the approximation problem of distributed parameter systems, for analysis and control purposes.
We are interested in the class of distributed parameter systems governed by linear or quasi-linear partial differential equations, with appropriate boundary and initial conditions. From an input-output approach, these dynamical systems are operators with input signals and output signals, related respectively to control inputs, disturbances, and measurements or controlled variables. These input and output signals are time and space functions, and can be either localized or distributed in time and/or space domains.
To exploit a dynamical model for analysis, simulation or control purposes, the analytical representation of the distributed parameter system has to be simplified by an appropriate approximation method. Our work is based on the operator approximation, and is decomposed in two parts. The first part concerns the realization of an approximation scheme by spatial discretization using Hamiltonian formulation. The second part develops an approximation method by a class of linear time-delay operators.
We highlight additional requirements on these two approximation methods to conserve structure properties, like energy balance for the Hamiltonian approach, or weak-strong controllability for the time-delay approach. These two approaches will make use of common algebraic tools.
From these approximations, some control issues for distributed parameter systems are discussed.
With this basic research, we aim at working out new and original methods for the analysis and the control of distributed parameter systems.

Publications "Ampère" liées à AIDS

Sérine Damak, Michael Di Loreto, Warody Lombardi, Vincent Andrieu. Exponential L2-stability for a class of linear systems governed by continuous-time difference equations. Automatica, International Federation of Automatic Control, 2014, 50 (12), pp.3299-3303. <10.1016/j.automatica.2014.10.087> . hal-01092692

Sérine Damak, Michaël Di Loreto, Sabine Mondié. Network of conservation laws : Stability analysis. 2nd Workshop on Delay Systems DELSYS, Nov 2013, Toulouse, France. hal-00957359

Sérine Damak, Michaël Di Loreto, Sabine Mondié. Difference Equations in Continuous Time with Distributed Delay: Exponential Estimates. American Control Conference, Jun 2014, Portland, United States. pp.FrB14.2. hal-00957352

Sérine Damak, Ali Ferhi, Vincent Andrieu, Michaël Di Loreto, Warody Lombardi. A Bridge between Lyapunov-Krasovskii and Spectral Approaches for Stability of Difference Equations. IFAC Joint Conference, 11th Workshop on Time-Delay Systems, Feb 2013, Grenoble, France. pp.30-35, <10.3182/20130204-3-FR-4031.00166> . hal-00957324

Saïd Aoues, Damien Eberard, Wilfrid Marquis-Favre. Canonical interconnection of discrete linear port-Hamiltonian systems. CDC, Dec 2013, Firenze, Italy. pp.3166 - 3171, <10.1109/CDC.2013.6760366> . hal-00999669

Saïd Aoues, Damien Eberard, Wilfrid Marquis-Favre. Discrete IDA-PBC Design for 2D Port-Hamiltonian Systems. IFAC, Sep 2013, Toulouse, France. 9 (1), pp.134-139, <10.3182/20130904-3-FR-2041.00088> . <hal-00999667>