Uniqueness theorem for partially observed elliptic systems and application to asymptotic synchronization

Tatsien Li; Bopeng Rao

doi:10.5802/crmath.31

Contrôle Optimal

Uniqueness theorem for partially observed elliptic systems and application to asymptotic synchronization
[Théorème d’unicité de systèmes elliptiques partiellement observés et application à la synchronisation asymptotique]

Tatsien Li ¹ ; Bopeng Rao ^2,^3,⁴

¹ Shanghai Key Laboratory for Contemporary Applied Mathematics; Nonlinear Mathematical Modeling and Methods Laboratory, School of Mathematical Sciences, Fudan University, Shanghai 200433, China
² Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg, France
³ School of Mathematical Sciences, Fudan University, Shanghai 200433, China
⁴ School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Comptes Rendus. Mathématique, Volume 358 (2020) no. 3, pp. 285-295.

Résumé
Abstract

Nous montrons que sous la condition du rang de Kalman, l’observabilité d’une équation scalaire implique l’unicité de la solution d’un système d’opérateurs elliptiques. En utilisant ce résultat, nous établissons la synchronisation asymptotique par groupes de systèmes d’évolution du second ordre.

We show that under Kalman’s rank condition, the observability of a scalar equation implies the uniqueness of solution to a system of elliptic operators. Using this result, we establish the asymptotic synchronization by groups for second order evolution systems.

Reçu le : 2020-01-06
Accepté le : 2020-03-02
Publié le : 2020-07-10

DOI : 10.5802/crmath.31

Affiliations des auteurs :

Tatsien Li ¹ ; Bopeng Rao ^{2, 3, 4}

¹ Shanghai Key Laboratory for Contemporary Applied Mathematics; Nonlinear Mathematical Modeling and Methods Laboratory, School of Mathematical Sciences, Fudan University, Shanghai 200433, China
² Institut de Recherche Mathématique Avancée, Université de Strasbourg, 67084 Strasbourg, France
³ School of Mathematical Sciences, Fudan University, Shanghai 200433, China
⁴ School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Uniqueness theorem for partially observed elliptic systems and application to asymptotic synchronization},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {285--295},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {3},
     year = {2020},
     doi = {10.5802/crmath.31},
     language = {en},
}

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Tatsien Li; Bopeng Rao. Uniqueness theorem for partially observed elliptic systems and application to asymptotic synchronization. Comptes Rendus. Mathématique, Volume 358 (2020) no. 3, pp. 285-295. doi : 10.5802/crmath.31. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.31/

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