基于动态增益的约束非线性时滞系统鲁棒控制

This project plans to study the robust control problems for two classes of constrained nonlinear time-delay systems which exist widely in practical engineering. The main contents include: .(1) For high-order nonlinear time-delay systems with full-state constraints or output constraint, by using Lyapunov-Krasovskii stability theory and the dynamic gain method, the robust tracking controller will be designed. For systems with the input constraint, the state feedback controller and the output feedback controller will be designed respectively by combining the homogeneous dominance idea, the dynamic gain method and the observer construction method. .(2) For high-order stochastic nonlinear time-delay systems, the application scope of the changing rate of time-delay will be further broadened. We will consider two cases, i.e., the system model is known and the system contains unknown factors. The Lyapunov-Razumikhin stability theory of nonlinear time-delay systems will be generalized. By employing the adding a power integral method, the dynamic gain method and the homogeneous domination theory, robust stabilization controllers will be designed to guarantee the closed-loop systems global stability in probability..(3) The effectiveness of the proposed methods are to be verified by examples of the chemical reaction system and the mechanical system..The implementation of this project will not only enrich the theory of nonlinear time-delay systems, but also provide ideas for solving some new problems.

本项目拟研究广泛存在于实际工程中的两类约束非线性时滞系统的鲁棒控制问题。主要内容包括：(1)对于高阶非线性时滞系统，在全状态约束或输出约束条件下，利用Lyapunov-Krasovskii稳定理论和动态增益方法，设计鲁棒跟踪控制器。结合齐次占优思想、动态增益方法和观测器构造方法，分别设计输入约束系统的状态反馈控制器和输出反馈控制器，实现对给定信号的跟踪控制。(2)对高阶随机非线性时滞系统，放宽时滞变化率的适用范围，分别研究系统已知和未知的情形，推广现有非线性时滞系统的Lyapunov-Razumikhin稳定理论，并基于增加幂次积分方法、动态增益方法和齐次占优理论，设计鲁棒镇定控制器，实现系统依概率大范围稳定。(3)应用化学反应系统和机械系统的例子验证所提方法的有效性。本项目的实施不仅丰富非线性时滞系统的控制理论，还为一些新问题的解决提供思路。

在实际工程中，许多系统可以建模为非线性系统。这些系统常常包含时滞和多种不确定性因素，且受到不同约束条件的限制。本项目针对几类约束非线性时滞系统，研究系统的鲁棒控制问题。具体包括：对于两类高阶不确定非线性时滞系统，基于动态增益控制方法、自适应技术和齐次占优方法，解决了系统的鲁棒跟踪和镇定控制问题；对于具有输入约束的非线性时滞系统，采用动态增益技术、模糊控制方法、反推控制等策略研究了系统的鲁棒控制问题，并设计了新的控制器；对于高阶随机非线性时滞系统，基于动态增益方法和齐次占优技术，设计了鲁棒镇定控制器，并利用李雅普诺夫-克拉索夫斯基稳定性理论分析了系统的稳定性。课题的实施不仅丰富了非线性时滞系统的控制理论和方法，也为解决实际系统的控制问题提供新的思路。