We consider the minimum time problem for a multi-input control-affine system. We assume that the Lie algebra generated by the controlled vector fields is two-step bracket-generating. 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 and dodgem car problems.
Minimum-Time Strong Optimality of a Singular Arc : Extended Dubins problem / Francesca C. Chittaro; Gianna Stefani. - (2013), pp. 1-6. (Intervento presentato al convegno 52nd IEEE Conference on Decision and Control tenutosi a Firenze nel 10-13 December 2013).
Minimum-Time Strong Optimality of a Singular Arc : Extended Dubins problem
CHITTARO, FRANCESCA CARLOTTA;STEFANI, GIANNA
2013
Abstract
We consider the minimum time problem for a multi-input control-affine system. We assume that the Lie algebra generated by the controlled vector fields is two-step bracket-generating. 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 and dodgem car problems.
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