Minimum-time strong optimality of a singular arc: the multi-input non involutive case

Francesca Chittaro (1) , Gianna Stefani (2)

1 LSIS - Laboratoire des Sciences de l'Information et des Systèmes
2 DIMAI - Dipartimento di Matematica e Informatica "Ulisse Dini"

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.

Mots clés: singular extremals; sufficient optimality conditions; Hamiltonian methods for optimality conditions

Domaines: Optimisation et contrôle [math.OC]

Francesca Chittaro, Gianna Stefani. Minimum-time strong optimality of a singular arc: the multi-input non involutive case. ESAIM: Control, Optimisation and Calculus of Variations, 2016, 22 (3), pp.786--810 ⟨10.1051/cocv/2015026⟩. ⟨hal-00984986v2⟩