基于T-S模型的非线性系统极小极大控制  

Minimax control of nonlinear systems based on T-S model

作　　者：姜囡[1] 井元伟[1] 

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110004

出　　处：《系统工程学报》2009年第4期469-473,共5页Journal of Systems Engineering

基　　金：教育部暨辽宁省流程工业综合自动化重点实验室开放课题资助项目;国家高技术研究发展(863)计划资助项目(2004AA412030)

摘　　要：研究一类非线性系统的极小极大鲁棒控制问题.针对含有不确定项的非线性系统,构造T-S模型,引入参数不确定项,使得模糊模型能够更精确逼近原系统.利用线性矩阵不等式(LM I)处理方法和Lyapunov稳定性理论,基于模糊状态观测器,得到极小极大输出反馈控制器存在的充分条件.引入凸优化技术,求得性能指标的最小上界以及最优极小极大鲁棒控制器参数.同时保证闭环系统在干扰和不确定性最大的情形下是最终一致有界的.最后以倒立摆为例的仿真结果表明所设计的控制器具有良好的鲁棒性及较大的吸引域.This paper studies the minimax robust controls problem for uncertain nonlinear systems. Introducing parametric uncertainty terms into T-S model for nonlinear systems with uncertainty terms, the fuzzy model may approach to the original system more exactly. Existential sufficient conditions of the output feedback minimax control are derived by using Lyapunov asymptotic stability theory and formulated in the format of linear matrix inequalities （LMIs） based on fuzzy state observer. The convex optimization algorithm is used to get the minima upper bound of performance index and the parameter of optimal minimax controller. And it is guaranteed that the closed-loop system will be uniformly ultimately bounded under the condition of the worst disturbances and uncertainty. An example of inverse pendulum is given to demonstrate good robust performance and larger basin of attraction of the controller designed.

关 键 词：非线性系统 观测器 极小极大控制 T-S模型 LMI(线性矩阵不等式) 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]