Lipschitz regularity of optimal controls

Abstract

We report on new conditions under which minimizing controls are Lipschitz continuous, for dynamic optimization problems with first order state constraints and a coercive cost function. The novelty of this research concerns both the conditions themselves and the analytic techniques used to confirm them. We replace the linear independence condition involving active state constraints, present in the earlier literature, by the condition of positive linear independence, which requires linear independence merely with respect to non-negative weighting parameters. This is achieved by studying normal extremals, rather than by means of a perturbational analysis.