Maximum principle for optimal control problems involving impulse controls with nonsmooth data

Abstract

This paper is concerned with the stochastic maximum principle for impulse optimal control problems of forward–backward systems, where the coefficients of the forward part are Lipschitz continuous. The domain of the regular controls is not necessarily convex. We establish a Pontryagins maximum principle for this control problem by applying Ekelands variational principle to a sequence of approximated control problems with smooth coefficients of the initial problems.