Necessary conditions of optimality for impulsive control problems with state constraints

This article concerns necessary conditions of optimality for impulsive control problems with dynamics given by measure driven differential inclusions or controlled differential equations and featuring both state and control constraints. We address a paradigm more general than the one usually considered in the literature since, here, the singular dynamics may depend on both the state and the control variables. One key feature of our optimality conditions consists in the fact that we consider problems which, besides the more common pointwise control and endpoint constraints, also exhibit state constraints.