Abstract
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 $U \subset {\mathbb R}^m$, 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.
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