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Chapitre d'ouvrage

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

Abstract : 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.
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Contributeur : Thérèse Azar Connectez-vous pour contacter le contributeur
Soumis le : mardi 15 mars 2022 - 11:05:50
Dernière modification le : lundi 4 avril 2022 - 17:38:02


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Fichier visible le : 2022-09-15

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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. Gonçalves J.A., Braz-César M., Coelho J.P. CONTROLO 2020, vol. 695, Springer, pp.616-627, 2020, Lecture Notes in Electrical Engineering, 978-3-030-58653-9. ⟨10.1007/978-3-030-58653-9_59⟩. ⟨hal-02973656⟩



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