Comptes Rendus
Control theory
Local controllability does imply global controllability
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 1813-1822.

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.

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.

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Accepted:
Published online:
DOI: 10.5802/crmath.538
Classification: 57R27, 34H05, 93B05

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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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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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