Normality of the maximum principle for non convex constrained Bolza problems

Abstract

In this paper we consider a Bolza optimal control problem under state constraints and provide a sufficient condition for any Lipschitz trajectory satisfying the maximum principle to be a normal extremal. In the difference with the previous works we allow the initial condition to be fixed and consider less regular state constraints. To prove normality we use J.Yorke type linearization of control systems and show the existence of solution to a linearized control system satisfying new state constraints defined, in turn, by linearization of the original set of constraints along the extremal trajectory.