LIPSCHITZ SOLUTIONS OF OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS OF ARBITRARY ORDER

In this paper we generalize to an arbitrary order, under minimalhypotheses, some suffient conditions for Lipschitz continuity of theoptimal control. The proof combines the approach by Hager in 1979for dealing with first-order state constraints, and the high-order alternative formulation of the optimality conditions. It takes into account the restrictive sign conditions taken into account in some recent papers.