| Issue |
ESAIM: COCV
Volume 22, Number 3, July-September 2016
|
|
|---|---|---|
| Page(s) | 786 - 810 | |
| DOI | https://doi.org/10.1051/cocv/2015026 | |
| Published online | 18 May 2016 | |
Minimum-time strong optimality of a singular arc: The multi-input non involutive case∗
1
Aix Marseille Université, CNRS, ENSAM, LSIS UMR 7296,
13397
Marseille,
France
2
Université de Toulon, CNRS, LSIS UMR 7296,
83957
La Garde,
France
francesca-carlotta.chittaro@univ-tln.fr
3
DIMAI, via S. Marta 3−50137
Firenze,
Italy
gianna.stefani@unifi.it
Received: 29 April 2014
We consider the minimum-time problem for a multi-input control-affine system, where we assume that the controlled vector fields generate a non-involutive distribution of constant dimension, and where we do not assume a priori bounds for the controls. We use Hamiltonian methods to prove that the coercivity of a suitable second variation associated to a Pontryagin singular arc is sufficient to prove its strong-local optimality. We provide an application of the result to a generalization of Dubins problem.
Mathematics Subject Classification: 49J15 / 49J30 / 49K15 / 49K30
Key words: Control-affine systems / singular extremals / minimum-time problem / sufficient optimality conditions / second variation / Hamiltonian methods
© EDP Sciences, SMAI 2016
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.