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A state-constrained optimal control problem is considered in which the starting position is fixed and the terminal position is free. The endpoints are strictly included within the set shaped by the given state constraint which is considered scalar. For this problem formulation, the second-order necessary optimality conditions are derived including the Legendre condition over the critical cone.

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The Critical Cone and Second-Order Optimality Conditions for a State-Constrained Optimal Control Problem

  • 会议论文

  • 发表日期：

    2025年

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  • Dmitry Karamzin

摘要

A state-constrained optimal control problem is considered in which the starting position is fixed and the terminal position is free. The endpoints are strictly included within the set shaped by the given state constraint which is considered scalar. For this problem formulation, the second-order necessary optimality conditions are derived including the Legendre condition over the critical cone.