Critères du type de Kálmán pour la contrôlabilité approchée et la synchronisation approchée d'un système couplé d'équations des ondes

Tatsien Li; Bopeng Rao

doi:10.1016/j.crma.2014.10.023

Contrôle optimal

Critères du type de Kálmán pour la contrôlabilité approchée et la synchronisation approchée d'un système couplé d'équations des ondes
[Criteria of Kálmán's type for the approximate controllability and the approximate synchronization of a coupled system of wave equations]

Presented by: Philippe G. Ciarlet

Tatsien Li ^1,²; Bopeng Rao ³

¹ School of Mathematical Sciences, Fudan University, Shanghai 200433, China
² Shanghai Key Laboratory for Contemporary Applied Mathematics, Nonlinear Mathematical Modeling and Methods Laboratory, China
³ Institut de recherche mathématique avancée, Université de Strasbourg, 67084 Strasbourg, France

Comptes Rendus. Mathématique, Volume 353 (2015) no. 1, pp. 63-68.

Abstract
Résumé

In this Note, we obtain necessary conditions, formulated as criteria of Kálmán's type, for the approximate null controllability and the approximate synchronization by groups of a coupled system of wave equations with Dirichlet boundary controls. We also establish the sufficiency of these conditions for some systems, in particular for systems in one space dimension.

Dans cette Note, nous obtenons des conditions nécessaires, exprimées sous la forme de critères du type de Kálmán, pour la contrôlabilité nulle approchée et la synchronisation approchée par groupes d'un système couplé d'équations des ondes avec des contrôles frontières de Dirichlet. De plus, nous établissons la suffisance de ces conditions pour certains systèmes, en particulier pour des systèmes en dimension d'espace un.

Received: 2014-10-14
Accepted: 2014-10-23
Published online: 2014-11-22

DOI: 10.1016/j.crma.2014.10.023

Author's affiliations:

Tatsien Li ^{1, 2}; Bopeng Rao ³

¹ School of Mathematical Sciences, Fudan University, Shanghai 200433, China
² Shanghai Key Laboratory for Contemporary Applied Mathematics, Nonlinear Mathematical Modeling and Methods Laboratory, China
³ Institut de recherche mathématique avancée, Université de Strasbourg, 67084 Strasbourg, France

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     author = {Tatsien Li and Bopeng Rao},
     title = {Crit\`eres du type de {K\'alm\'an} pour la contr\^olabilit\'e approch\'ee et la synchronisation approch\'ee d'un syst\`eme coupl\'e d'\'equations des ondes},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {63--68},
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Tatsien Li; Bopeng Rao. Critères du type de Kálmán pour la contrôlabilité approchée et la synchronisation approchée d'un système couplé d'équations des ondes. Comptes Rendus. Mathématique, Volume 353 (2015) no. 1, pp. 63-68. doi : 10.1016/j.crma.2014.10.023. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.10.023/

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