离散和连续状态约束最优控制系统之间的联系：确定性情况
The connection between discrete and continuous state constraints optimal control systems: the deterministic case
摘要：
本研究考虑连续状态限制下由常微分方程驱动的最优控制问题。从操作的角度，我们引入了一个离散状态约束最优控制问题，并证明了这个离散状态约束最优控制问题是原问题的一个近似最优控制问题。此外，我们证明了近最优控制问题的最优解收敛到原问题的最优解。最后，我们用一个线性二次最优问题来验证本文的主要结果。
英文摘要：
An optimal control problem driven by an ordinary differential equation under continuous state constraints is considered in this study. From an operational point of view, we introduce a discrete state constraints optimal control problem and prove that this discrete state constraints optimal control problem is a near-optimal control problem of the original problem. Furthermore, we show that the optimal solution of the near-optimal control problem converges to the optimal solution of the original one. Finally, we use a linear quadratic optimal problem to verify the main results of this study.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
