Stabilization using in-domain actuator: a numerical method for a non linear parabolic partial differential equation - Pôle Automatique et Diagnostic Accéder directement au contenu
Communication Dans Un Congrès Année : 2020

Stabilization using in-domain actuator: a numerical method for a non linear parabolic partial differential equation

Résumé

This paper deals with the problem of null controllability for an unstable nonlinear parabolic partial differential equation (PDE) system considering in-domain actuator. The main objective of this communication is to provide an efficient control law in order to stabilize the system state close to zero in a desired time whatever the initial state is. A numerical approach is developed and in order to highlight the relevance of the proposed control strategy, a realistic physical problem is investigated. Thermal evolution of a thin rod with homogeneous Dirichlet boundaries conditions is considered. Thermal state is described by the heat equation and assuming that thermal conductivity is temperature dependent, a nonlinear mathematical model has to be taken into account. Considering that all the model inputs are known, a direct problem is numerically solved (regarding a finite element method) in order to estimate the temperature at each point of the 1D geometry and at each instant. Then an inverse problem is formulated in such a way as to determine the in-domain control which ensures a final temperature close to zero. An iterative regularization method based on the conjugate gradient method (CGM) is developed for the minimization of a quadratic cost function (output error). Several numerical experimentations are provided in order to discuss the numerical approach attractiveness.
Fichier principal
Vignette du fichier
Controlo_2020.pdf (367.88 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-02973656 , version 1 (15-03-2022)

Identifiants

Citer

Thérèse Azar, Laetitia Perez, Christophe Prieur, Emmanuel Moulay, Laurent Autrique. Stabilization using in-domain actuator: a numerical method for a non linear parabolic partial differential equation. CONTROLO 2020 - 14th APCA International Conference on Automatic Control and Soft Computing, Jul 2020, Bragança, Portugal. pp.616-627, ⟨10.1007/978-3-030-58653-9_59⟩. ⟨hal-02973656⟩
103 Consultations
3174 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More