Local controllability does imply global controllability
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...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-12-01
|
| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.538/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825206274848980992 |
|---|---|
| author | Boscain, Ugo Cannarsa, Daniele Franceschi, Valentina Sigalotti, Mario |
| author_facet | Boscain, Ugo Cannarsa, Daniele Franceschi, Valentina Sigalotti, Mario |
| author_sort | Boscain, Ugo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-ec41d0ccf2f644c78f76ceffd0473bd7 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-12-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-ec41d0ccf2f644c78f76ceffd0473bd72025-02-07T11:12:15ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-12-01361G111813182210.5802/crmath.53810.5802/crmath.538Local controllability does imply global controllabilityBoscain, Ugo0Cannarsa, Daniele1Franceschi, Valentina2Sigalotti, Mario3Sorbonne Université, CNRS, Inria, Laboratoire Jacques-Louis Lions (LJLL), Paris, FranceDepartment of Mathematics and Statistics, University of Jyväskylä, Jyväskylä, FinlandDipartimento di Matematica Tullio Levi-Civita, Università di Padova, ItalySorbonne Université, CNRS, Inria, Laboratoire Jacques-Louis Lions (LJLL), Paris, FranceWe 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.538/ |
| spellingShingle | Boscain, Ugo Cannarsa, Daniele Franceschi, Valentina Sigalotti, Mario Local controllability does imply global controllability Comptes Rendus. Mathématique |
| title | Local controllability does imply global controllability |
| title_full | Local controllability does imply global controllability |
| title_fullStr | Local controllability does imply global controllability |
| title_full_unstemmed | Local controllability does imply global controllability |
| title_short | Local controllability does imply global controllability |
| title_sort | local controllability does imply global controllability |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.538/ |
| work_keys_str_mv | AT boscainugo localcontrollabilitydoesimplyglobalcontrollability AT cannarsadaniele localcontrollabilitydoesimplyglobalcontrollability AT franceschivalentina localcontrollabilitydoesimplyglobalcontrollability AT sigalottimario localcontrollabilitydoesimplyglobalcontrollability |