Regularity Assumptions for Second Order Conditions in Optimal Control

摘要

In this paper we unify three different notions of regularity introduced in the literature when dealing with necessary conditions for optimal control problems involving equality and inequality constraints. This approach allows us to obtain new sufficient conditions for regularity and to clearly explain some of the main difficulties encountered when deriving second order conditions on different critical directions according to different assumptions of normality usually imposed on the extremals under consideration.