| Issue |
ESAIM: COCV
Volume 30, 2024
|
|
|---|---|---|
| Article Number | 4 | |
| Number of page(s) | 37 | |
| DOI | https://doi.org/10.1051/cocv/2023073 | |
| Published online | 22 January 2024 | |
Necessary conditions for local controllability of a particular class of systems with two scalar controls
1
Université côte d’Azur, Inria, CNRS, LJAD,
France
2
CEREMADE, Université Paris-Dauphine & CNRS UMR 7534, Université PSL,
75016
Paris, France
3
RIMS, Kyoto University,
Japan
* Corresponding author: cmoreau@kurims.kyoto-u.ac.jp
Received:
10
July
2019
Accepted:
12
October
2023
We consider control-afflne systems with two scalar controls, such that one control vector field vanishes at an equilibrium state. We state two necessary conditions for local controllability around this equilibrium, involving the iterated Lie brackets of the system vector fields, with controls that are either bounded, small in L∞ or small in W1,∞. These results are illustrated with several examples.
Mathematics Subject Classification: 34H05 / 57R27 / 93B05
Key words: Controllability / control theory
© The authors. Published by EDP Sciences, SMAI 2024
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