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.
DOI : 10.1051/cocv/2015026
Mots clés : Control-affine systems, singular extremals, minimum-time problem, sufficient optimality conditions, second variation, Hamiltonian methods
@article{COCV_2016__22_3_786_0,
author = {Chittaro, Francesca and Stefani, Gianna},
title = {Minimum-time strong optimality of a singular arc: {The} multi-input non involutive case},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {786--810},
publisher = {EDP-Sciences},
volume = {22},
number = {3},
year = {2016},
doi = {10.1051/cocv/2015026},
zbl = {1344.49034},
mrnumber = {3527944},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2015026/}
}
TY - JOUR AU - Chittaro, Francesca AU - Stefani, Gianna TI - Minimum-time strong optimality of a singular arc: The multi-input non involutive case JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 786 EP - 810 VL - 22 IS - 3 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2015026/ DO - 10.1051/cocv/2015026 LA - en ID - COCV_2016__22_3_786_0 ER -
%0 Journal Article %A Chittaro, Francesca %A Stefani, Gianna %T Minimum-time strong optimality of a singular arc: The multi-input non involutive case %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 786-810 %V 22 %N 3 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2015026/ %R 10.1051/cocv/2015026 %G en %F COCV_2016__22_3_786_0
Chittaro, Francesca; Stefani, Gianna. Minimum-time strong optimality of a singular arc: The multi-input non involutive case. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 786-810. doi : 10.1051/cocv/2015026. http://archive.numdam.org/articles/10.1051/cocv/2015026/
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