We say that a control system is locally controllable if the attainable set from any state contains an open neighborhood of , 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 sont un voisinage de , 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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Ugo Boscain 1; Daniele Cannarsa 2; Valentina Franceschi 3; Mario Sigalotti 1
@article{CRMATH_2023__361_G11_1813_0, 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}, }
TY - JOUR AU - Ugo Boscain AU - Daniele Cannarsa AU - Valentina Franceschi AU - Mario Sigalotti TI - Local controllability does imply global controllability JO - Comptes Rendus. Mathématique PY - 2023 SP - 1813 EP - 1822 VL - 361 PB - Académie des sciences, Paris DO - 10.5802/crmath.538 LA - en ID - CRMATH_2023__361_G11_1813_0 ER -
%0 Journal Article %A Ugo Boscain %A Daniele Cannarsa %A Valentina Franceschi %A Mario Sigalotti %T Local controllability does imply global controllability %J Comptes Rendus. Mathématique %D 2023 %P 1813-1822 %V 361 %I Académie des sciences, Paris %R 10.5802/crmath.538 %G en %F CRMATH_2023__361_G11_1813_0
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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