Strong local optimality for generalized L1 optimal control problems

In this paper, we analyze control affine optimal control problems with a cost functional involving the absolute value of the control. The Pontrya- gin extremals associated with such systems are given by (possible) concatena- tions of bang arcs with singular arcs and with zero control arcs, that is, arcs where the control is identically zero. Here, we consider Pontryagin extremals given by a bang-zero control-bang concatenation. We establish sufficient op- timality conditions for such extremals, in terms of some regularity conditions and of the coerciveness of a suitable finite-dimensional second variation.