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.

Abstract (VO)
Résumé

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.

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.

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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     author = {Tatsien Li and Bopeng Rao},
     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/

Bibliographie
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Tatsien Li; Bopeng Rao Asymptotic synchronization of a coupled system of wave equations on a rectangular domain with reflecting sides, Asymptotic Analysis, Volume 128 (2022) no. 1, pp. 85-102 | DOI:10.3233/asy-211699 | Zbl:1507.35270
Tatsien Li; Bopeng Rao Uniform synchronization of an abstract linear second order evolution system, SIAM Journal on Control and Optimization, Volume 59 (2021) no. 4, pp. 2740-2755 | DOI:10.1137/20m1375310 | Zbl:1470.93071
Tatsien Li; Bopeng Rao Uniqueness of solution to systems of elliptic operators and application to asymptotic synchronization of linear dissipative systems, European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations, Volume 26 (2020), p. 26 (Id/No 117) | DOI:10.1051/cocv/2020062 | Zbl:1461.93416

Cité par 3 documents. Sources : zbMATH

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