网络稳定性与控制的小增益原理:回顾与近期进展

小增益定理是现代控制理论中极为重要的基本工具之一,它在关联系统和不确定系统的鲁棒稳定性分析以及鲁棒控制器设计的许多工作中都发挥着极大的作用.基于输入到状态稳定性的概念,笔者于1994年首次提出了广义非线性小增益定理.与之前的小增益定理不同,这一结果为同时刻画关联系统的内部稳定性和外部稳定性提供了一个统一的框架.从镇定与鲁棒自适应控制到分散式或分布式控制以及输出调节(抗干扰渐近跟踪),基于非线性小增益定理已经发展出一系列的鲁棒非线性控制器设计新工具.在过去10年间,复杂非线性大系统已成为研究热点,驱动着小增益定理向更加完备的网络小增益定理方向发展,以期解决网络稳定性与控制中的新问题.对此,针对非线性小增益理论的一些最新研究进展及其在通讯和计算约束下的网络化控制和事件驱动控制应用结果进行综述,并对该理论的未来研究方向给出一些建议.

A small-gain principle for network stability and control: An overview and recent results

The small-gain theorem is one of the fundamentally important and systematic tools in modern control theory.Its power in testing robustness of stability and designing robust controllers for interconnected and uncertain systems has clearly been demonstrated in the work of many others.Taking explicit advantage of input-to-state stability(ISS), the first generalized nonlinear ISS small-gain theorem was proposed by one of the authors in 1994.The nonlinear ISS small-gain theorem distinguishes itself from earlier small-gain theorems by providing a unified framework for internal stability and external stability of interconnected systems.Applications to a variety of control problems ranging from stabilization and robust adaptive control to decentralized or distributed control and output regulation (asymptotic tracking with disturbance rejection) have generated several novel tools for the design of robust nonlinear controllers.In the past ten years, renewed interest in large-scale nonlinear systems has motivated the further development of small-gain theorems toward a complete network small-gain theory for network stability and control.This paper provides a survey of some recent developments of the nonlinear small-gain theory and its applications in networked control systems and event-based control subject to communications and computation constraints, and gives some suggestions on this theory and future research direction.