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 problem: a sufficient condition / Chittaro, F. C.; Stefani, G. - In: CONTROL AND CYBERNETICS. - ISSN 0324-8569. - 39:4(2010), pp. 1029-1068.
Singular extremals in multi-input time-optimal problem: a sufficient condition
CHITTARO F. C.;
2010-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione
