In this paper we study second order sufficient conditions for the strong-local optimality of singular Pontryagin extremals. In particular, we focus on the minimum-time problem for a control-affine system with vector inputs. We use Hamiltonian methods to prove that the coercivity of a suitably-defined second variation - plus an involutivity assumption on the distribution of the controlled fields - is a sufficient condition for the strong optimality of a candidate extremal.
SINGULAR EXTREMALS IN MULTI-INPUT TIME-OPTIMAL PROBLEMS: ASUFFICIENT CONDITION / F. C. CHITTARO ; G . STEFANI. - In: CONTROL AND CYBERNETICS. - ISSN 0324-8569. - STAMPA. - vol.39 n.4:(2010), pp. 1029-1068.
SINGULAR EXTREMALS IN MULTI-INPUT TIME-OPTIMAL PROBLEMS: ASUFFICIENT CONDITION
STEFANI, GIANNA
2010
Abstract
In this paper we study second order sufficient conditions for the strong-local optimality of singular Pontryagin extremals. In particular, we focus on the minimum-time problem for a control-affine system with vector inputs. We use Hamiltonian methods to prove that the coercivity of a suitably-defined second variation - plus an involutivity assumption on the distribution of the controlled fields - is a sufficient condition for the strong optimality of a candidate extremal.
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