出版社：SISSA, Scuola Internazionale Superiore di Studi Avanzati
摘要：We consider a bang–singular normal extremal for a Mayer problem associated to a single–input
control system affine in the control. We give sufficient conditions for the extremal to be a strong
local minimizer. The conditions include the coercivity of the extended second variation associated
to the problem restricted to the singular arc and regularity conditions on the bang arc. Remark that
the non-negativity of the extended second variation is a necessary condition, when the normalized
adjoint covector is unique, and its coercivity is sufficient to ensure that the singular arc is a local
minimizer for the restricted problem. The paper is an attempt to give second order sufficient
conditions for an extremal including a finite number of both bang and singular arcs.
