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

Abstract : 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.
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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, EDP Sciences, 2016, 22 (3), pp.786--810 ⟨10.1051/cocv/2015026 ⟩. ⟨hal-00984986v2⟩

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