Three Types of Regularity for Critical Directions in Optimal Control

摘要

Two main questions related to different notions of regularity for critical directions arise when dealing with second order necessary conditions for optimal control problems involving inequality constraints in the control. One is related to the existence of different convex sets of differentially admissible variations defining the critical directions, while the other deals with the assumptions imposed on the optimal control which imply, as a necessary condition for optimality, the nonnegativity of a quadratic form in those sets. In this paper we provide new results related to both questions, based on three different notions of regularity, which are applicable to a wide range of problems in optimal control.