Local controllability does imply global controllability

Ugo Boscain; Daniele Cannarsa; Valentina Franceschi; Mario Sigalotti

doi:10.5802/crmath.538

Théorie du contrôle

Local controllability does imply global controllability
[La contrôlabilité locale implique la contrôlabilité globale]

Ugo Boscain ¹ ; Daniele Cannarsa ² ; Valentina Franceschi ³ ; Mario Sigalotti ¹

¹ Sorbonne Université, CNRS, Inria, Laboratoire Jacques-Louis Lions (LJLL), Paris, France
² Department of Mathematics and Statistics, University of Jyväskylä, Jyväskylä, Finland
³ Dipartimento di Matematica Tullio Levi-Civita, Università di Padova, Italy

Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1813-1822.

Résumé
Abstract

Nous disons qu’un système de contrôle est localement controllable si les ensembles atteignables à partir de tout état $x$ sont un voisinage de $x$ , tandis que le système est contrôlable si les ensembles atteignables à partir de tout état coïncident avec la variété entière. Nous montrons qu’un système qui est localement controllable est contrôlable. Notre preuve est une alternative à la combinaison de deux résultats précédents par Kevin Grasse.

We say that a control system is locally controllable if the attainable set from any state $x$ contains an open neighborhood of $x$ , while it is controllable if the attainable set from any state is the entire state manifold. We show in this note that a control system satisfying local controllability is controllable. Our self-contained proof is alternative to the combination of two previous results by Kevin Grasse.

Reçu le : 2023-03-25
Révisé le : 2023-07-07
Accepté le : 2023-07-07
Publié le : 2023-12-21

DOI : 10.5802/crmath.538

Classification : 57R27, 34H05, 93B05

Affiliations des auteurs :

Ugo Boscain ¹ ; Daniele Cannarsa ² ; Valentina Franceschi ³ ; Mario Sigalotti ¹

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Ugo Boscain and Daniele Cannarsa and Valentina Franceschi and Mario Sigalotti},
     title = {Local controllability does imply global controllability},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1813--1822},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     year = {2023},
     doi = {10.5802/crmath.538},
     language = {en},
}

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Ugo Boscain; Daniele Cannarsa; Valentina Franceschi; Mario Sigalotti. Local controllability does imply global controllability. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1813-1822. doi : 10.5802/crmath.538. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.538/

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