ABSTRACT

This paper presents an observer-based decentralized $H_{\mathrm{\infty }}$ output feedback preview tracking control method for a class of nonlinear disturbed interconnected discrete systems. The considered output tracking control problem, for the first time, is transformed into a $H_{\mathrm{\infty }}$ controller design problem of N augmented error subsystems. For each subsystem, the suggested control law is formulated by a combination of integral control action, observer-based state feedback control action and preview feedforward action of this subsystem. Based on the Lyapunov function approach, the auxiliary matrix variable approach, and some special mathematical manipulations, the controller feasibility conditions are established in linear matrix inequality (LMI) framework to guarantee the existence of the offered observer-based decentralized $H_{\mathrm{\infty }}$ preview tracking controller. And, the gain matrices of both decentralized observation and decentralized tracking control can be searched concurrently by only one-step LMI procedure. Finally, two examples are presented to verify the effectiveness and superiority of the proposed controller.

摘要

本文提出了一种基于观察者的去中心化$H_{\mathrm{\infty }}$一类非线性扰动互联离散系统的输出反馈预览跟踪控制方法。首次将所考虑的输出跟踪控制问题转化为$H_{\mathrm{\infty }}$N个增广误差子系统的控制器设计问题。对于每个子系统，建议的控制律由该子系统的积分控制动作、基于观察者的状态反馈控制动作和预览前馈动作的组合制定。基于李雅普诺夫函数法、辅助矩阵变量法和一些特殊的数学运算，在线性矩阵不等式（LMI）框架下建立了控制器的可行性条件，以保证所提供的基于观察者的分散式的存在$H_{\mathrm{\infty }}$预览跟踪控制器。并且，分散观察和分散跟踪控制的增益矩阵只需一步LMI程序即可同时搜索。最后，通过两个例子验证了所提出控制器的有效性和优越性。