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Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2016

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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Dates and versions

hal-00984986 , version 1 (29-04-2014)
hal-00984986 , version 2 (29-04-2014)

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