Strong local optimality for generalized L1 optimal control problems

Francesca C Chittaro (1) , Laura Poggiolini (2)

1 LSIS - Laboratoire des Sciences de l'Information et des Systèmes
2 DMA - Dipartimento di Matematica Applicata [Firenze]

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

Domaines: Optimisation et contrôle [math.OC]

Francesca C Chittaro, Laura Poggiolini. Strong local optimality for generalized L1 optimal control problems. Journal of Optimization Theory and Applications, In press. ⟨hal-01585634v1⟩