Optimal Feedback Control for a Class of Nonlinear Time-Delay Systems

• 成果类型: Article
• 署名作者: Hu, Hongxiao; Zhou, Zixin; Xu, Liguang; Ding, Zhengtao
• 署名单位: University of Shanghai for Science & Technology; University of Shanghai for Science & Technology; University of Manchester
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3552022
• 发表日期: 2025
• 页码: 5568-5575
• 关键词: Feedback control; mathematical models; Numerical stability; Adaptive control; asymptotic stability; steady-state; Nonlinear systems; infinite horizon; Delay effects; vectors; Coinvariantly differentiable; functional Hamilton-Jacobi-Bellman (HJB) equation; optimal feedback control; uniformly asymptotically stable (UAS)

摘要

This article addresses the problem of optimal nonlinear feedback control for a class of nonlinear time-delay systems over an infinite horizon, involving a nonlinear-nonquadratic performance functional. To this end, we propose a framework for analyzing and designing nonlinear feedback controllers that minimize such cost functionals for these systems. By applying the Lyapunov functional method, the stability of a class of nonlinear time-delay systems is determined over an infinite horizon. This Lyapunov functional is shown to be the solution to a functional Hamilton-Jacobi-Bellman (HJB) equation. Sufficient conditions for optimality are then provided in the form of a steady-state version of the functional HJB equation, thereby guaranteeing both stability and optimality. In addition, the corresponding results of optimal feedback control problem for a class of nonlinear delay-free systems are further developed. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed methods.