一类非线性不确定时滞系统的多模型切换H_∞跟踪控制  

H_∞ tracking control for a class of uncertain nonlinear systems with time-delay by using multi-model switching

作　　者：钱承山[1] 吴庆宪[1] 姜长生[1] 方炜[1] 

机构地区：[1]南京航空航天大学自动化学院

出　　处：《山东大学学报（理学版）》2007年第12期49-54,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(90405011)

摘　　要：考虑了当系统存在不确定和外界干扰的情况下,一类非线性不确定时变时滞系统的多模型切换H∞跟踪控制的设计问题。利用时滞T-S模糊模型对非线性不确定时滞系统进行建模,将输入空间划分为若干个区域,在每一区域内设计局部T-S模型和控制器,这样在模糊规则数相同的情况下由于模糊论域的变小从而提高了逼近精度;在不确定性满足增益有界的条件下,得到了该类时变时滞非线性系统满足闭环稳定和H∞跟踪控制性能的充分条件,通过求解一组线性矩阵不等式(LMI),获得模糊H∞跟踪控制律,基于Lyapunov稳定性理论,证明了在此控制律下闭环系统渐进稳定;根据所选定的变量,通过多模型切换控制,将相应的区域控制器切换为全局控制器,而其他控制器不起作用,实现对整体非线性系统的逼近与控制。The design of H∞ tracking control for a class of uncertain nonlinear systems with time-delay was given using multimodel switching in the presence of uncertainty and disturbance. First, T-S models with time-delay were employed to model the uncertain nonlinear system with time-delay. The input space was divided into multiple regions. Local T-S models and controllers were designed in each region, such that the approach precision improves as the fuzzy domain decreases under constant fuzzy rides. Then, on the condition that the uncertain is gain bounded, a sufficient condition is presented for the existence of the controller, which satisfies the closed-loop stability and the performance of H∞ tracking. By solving a family of linear matrix inequalities, the H∞ tracking control law was obtained. Based on Lyapunov theory, it was proven that the closed-loop system has exponential stability. Finally, a region controller, which was chosen according to the selected variables by the multiple-model switching control, was switched to the whole controller and that other controllers did not operate. The approach and control of the entire nonlinear system was therefore established.

关 键 词：非线性不确定时滞系统 多模型切换 局部T-S模型 跟踪控制 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]