STRONG LOCAL MINIMIZERS IN OPTIMAL CONTROL PROBLEMS WITH STATE CONSTRAINTS: SECOND-ORDER NECESSARY CONDITIONS

摘要

This paper is devoted to second-order necessary optimality conditions for strong local minima for a Mayer type optimal control problem with a general control constraint U subset of R-m, and state and final-point constraints described by a finite number of inequalities. We use the second-order linearization of a relaxed differential inclusion associated to the control system to find a convex subset of second-order tangents to the set of its trajectories. This leads to second-order necessary optimality conditions via a straightforward way, based on separation theorems.