一类具有时滞的脉冲微分方程的最优控制问题
Optimal Control Problems for a Class of Impulsive Differential Equations with Time-Delays
摘要: 本文考虑了一类具有脉冲效应的非线性非自治广义微分系统，通过建立时滞微分不等式，得到了脉冲系统的吸引集。通过建立一个框架来解决反馈控制问题，该问题的目标是构建一个非线性反馈控制器，使其最小化一个非线性非二次成本函数。为了避免求解哈密顿雅可比贝尔曼(HJB)方程稳态时的计算复杂性，设计了一个成本函数，该函数依赖于动态系统，李亚普诺夫函数，通过求解哈密顿雅可比贝尔曼方程的稳态来获得一个稳定的反馈控制器。最后，通过一个算例证明了所提方法的有效性。
Abstract: In this paper, a class of nonlinear nonautonomous generalized differential systems with impulsive effects is considered. The attraction set of the impulsive system is obtained by developing a time-delay differential inequality. A framework is developed to solve the feedback control problem, where the objective of the problem is to construct a nonlinear feedback controller that minimizes a nonlinear nonquadratic cost function. To avoid the computational complexity in solving the Hamil-ton-Jacobi-Bellman (HJB) equation steady state, a cost generalization function is designed which re-lies on the dynamic system, Lyapunov function, to obtain a stable feedback control law by solving the HJB equation steady state. Finally, the validity of the proposed method is demonstrated by an arithmetic example.
文章引用：周梓昕, 胡洪晓, 张洋. 一类具有时滞的脉冲微分方程的最优控制问题[J]. 应用数学进展, 2023, 12(2): 791-800. https://doi.org/10.12677/AAM.2023.122081

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