非三角时滞非线性系统的齐次稳定性与控制研究

Time delay exists widely in many practical systems, such as process industry system, network transmission system, biological system and so on. Therefore, the research of stability and control problems of time-delay system has important application value. However, for time-delay nonlinear system with non-triangular structure, there still exist a large number of problems to be solved. Also, the existing control approaches do not meet demand. From the perspective of control structure and convergence performance, it is more important to find one control theory and method so that we can simplify the control and can achieve satisfac- tory convergent property. For non-triangular time-delay system with complicated nonlinear terms, this project plans to develop the existing homogeneous control theory，and will study how to design the adaptive homogeneous controller. First, within the framework of homogeneous theory, for general time-delay nonlinear systems, the project will provide some related stability definitions, and will study sufficient conditions and criterions to achieve stabilization. Based on this, using dynamic gain method and fuzzy control approach, and applying state feedback and output feedback control strategies to construct dynamic homogeneous controller for non-triangular time-delay nonlinear system. Moreover, the results will be extended to stochastic non-triangular delayed systems. At last, practical examples like flexible joint robot system with input time-delay and delayed chemical reactor system will be used to show the feasibility and effectiveness of the results.

时滞现象广泛存在于许多实际系统中，如流程工业系统、网络传输系统、生物系统等。因此，研究时滞系统的稳定性和控制问题具有重要的应用价值。然而，对于非三角结构的时滞非线性系统，仍有大量问题亟待解决。现有的控制方法也难以满足实际需求。从控制结构和系统收敛性能的角度出发，寻找一种既能简化控制结构又能实现好的收敛性的控制理论和方法具有重要意义。本项目针对带复杂非线性项的非三角时滞系统，发展现有的齐次控制理论，并探讨动态齐次控制器的设计方法。首先，在齐次理论框架下,对一般的时滞非线性系统，给出相应的稳定性定义，并研究系统稳定的充分条件和判定方法；在此基础上，对非三角结构时滞非线性系统，应用状态反馈和输出反馈策略，构造基于动态增益的齐次控制器；进一步地，将结果推广到随机非三角时滞系统上；最后，应用输入有时滞的柔性关节机器人系统和滞后化学反应系统的例子验证所得结论的可行性和有效性。

本课题考虑了非三角时滞非线性系统的齐次稳定性与控制问题。其主要研究包括：针对一类不确定高阶时滞非线性系统，利用函数增益方法及齐次占优控制方法，并结合李雅普诺夫-卡拉索夫斯基泛函技术，实现了系统的自适应状态反馈镇定；针对几类含有部分可测状态的高阶时滞非线性系统，通过构造适当的观测器并利用齐次稳定理论，解决了输出反馈跟踪控制问题。课题的实施将进一步促进非三角时滞非线性的控制理论和研究策略的发展，并为实际时滞系统控制问题的解决提供了新思路。