Geodesic
Minimum-time strong optimality of a singular arc: The multi-input non involutive case
Chittaro, Francesca1, 2  ; Stefani, Gianna3
1 Aix Marseille Université, CNRS, ENSAM, LSIS UMR 7296, 13397 Marseille, France
2 Université de Toulon, CNRS, LSIS UMR 7296, 83957 La Garde, France
3 DIMAI, via S. Marta 3−50137 Firenze, Italy
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 3, pp. 786-810

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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.

Reçu le :
DOI : 10.1051/cocv/2015026
Classification : 49J15, 49J30, 49K15, 49K30
Keywords: Control-affine systems, singular extremals, minimum-time problem, sufficient optimality conditions, second variation, Hamiltonian methods

Chittaro, Francesca 1, 2 ; Stefani, Gianna 3

1 Aix Marseille Université, CNRS, ENSAM, LSIS UMR 7296, 13397 Marseille, France
2 Université de Toulon, CNRS, LSIS UMR 7296, 83957 La Garde, France
3 DIMAI, via S. Marta 3−50137 Firenze, Italy 
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     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},
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     year = {2016},
     doi = {10.1051/cocv/2015026},
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     mrnumber = {3527944},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2015026/}
}
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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

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