Strong local optimality for generalized L1 optimal control problems

TL;DR

This paper establishes sufficient optimality conditions for a class of control problems involving absolute value costs, focusing on extremals with specific bang-inactive-bang structures, using regularity and second variation coercivity.

Contribution

It introduces new sufficient optimality conditions for generalized L1 optimal control problems with specific extremal structures, expanding theoretical understanding.

Findings

Sufficient conditions for optimality of bang-inactive-bang extremals.

Regularity and coercivity conditions ensure local optimality.

Analysis applies to control problems with absolute value cost function.

Abstract

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.