A nondegenerate maximum principle for the impulse control problem with state constraints

Abstract. In this article, a free-time impulsive control problem with state constraints and equality and inequality constraints on the trajectory endpoints is considered. A weakened maximum principle is obtained for problems with data measurable in the time variable, being the time transver-sality conditions deduced with the help of some extra convexity assumption on the state constraints. In the case of smooth problems a nondegenerate maximum principle is derived by using a penalty function method