We consider a bang-singular normal extremal for the minimum time problem associated to a single-input control system affine in the control. We use Hamiltonian methods to prove that the coercivity of a suitable strongly-extended second variation associated to the singular arc is sufficient to prove the local optimality of the extremal in the strong topology. As a consequence we give a sufficient condition easily checkable and we apply it to three examples in R3.
Minimum time optimality for a bang-singular arc: second order sufficient conditions / L. Poggiolini;G. Stefani. - STAMPA. - (2005), pp. 1433-1438. (Intervento presentato al convegno 44th IEEE Conference on Decision and Control and European Control Conference ECC'05 tenutosi a Seville, Spain nel 12-15 December 2005) [10.1109/CDC.2005.1582360].
Minimum time optimality for a bang-singular arc: second order sufficient conditions
POGGIOLINI, LAURA;STEFANI, GIANNA
2005
Abstract
We consider a bang-singular normal extremal for the minimum time problem associated to a single-input control system affine in the control. We use Hamiltonian methods to prove that the coercivity of a suitable strongly-extended second variation associated to the singular arc is sufficient to prove the local optimality of the extremal in the strong topology. As a consequence we give a sufficient condition easily checkable and we apply it to three examples in R3.
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