Volume 22, Number 3, July-September 2016
|Page(s)||786 - 810|
|Published online||18 May 2016|
Minimum-time strong optimality of a singular arc: The multi-input non involutive case∗
Aix Marseille Université, CNRS, ENSAM, LSIS UMR 7296,
2 Université de Toulon, CNRS, LSIS UMR 7296, 83957 La Garde, France
3 DIMAI, via S. Marta 3−50137 Firenze, Italy
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
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