Local controllability does imply global controllability
Abstract
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.
Main Authors
Format
Articles
Research article
Published
2023
Series
Subjects
Publication in research information system
Publisher
Academie des Sciences
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202401121239Käytä tätä linkitykseen.
Review status
Peer reviewed
ISSN
1631-073X
DOI
https://doi.org/10.5802/crmath.538
Language
English
Published in
Comptes Rendus Mathematique
Citation
- Boscain, U., Cannarsa, D., Franceschi, V., & Sigalotti, M. (2023). Local controllability does imply global controllability. Comptes Rendus Mathematique, 361, 1813-1822. https://doi.org/10.5802/crmath.538
License
Funder(s)
Research Council of Finland
Funding program(s)
Academy Project, AoF
Akatemiahanke, SA
Additional information about funding
This work was partially supported by the ANR-DFG project ANR-22-CE92-0077-01 CoRoMo. The second author is supported by the Academy of Finland (grant 322898 ‘Sub-Riemannian Geometry via Metricgeometry and Lie-group Theory’). This project has received financial support from the CNRS through the MITI interdisciplinary programs.
Copyright© 2023 the Authors