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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2016, Vol. 33 ›› Issue (2): 199-205.doi: 10.3969/j.issn.1005-3085.2016.02.009

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基于输出反馈的不确定非线性系统模糊鲁棒$H_\infty$控制(英)

曲子芳1， 杜贞斌2   

  1. 1- 山东工商学院数学与信息科学学院，烟台  264005
    2- 烟台大学计算机与控制工程学院，烟台 264005
  • 收稿日期:2014-09-16 接受日期:2015-09-24 出版日期:2016-04-15 发布日期:2016-06-15
  • 基金资助:
    国家自然科学基金 (61203320)；山东省自然科学基金 (ZR2014FL023)；山东工商学院青年科学基金 (2013QN051).

Fuzzy Robust $H_\infty$ Control for Uncertain Nonlinear Systems via Output Feedback

QU Zi-fang1,   DU Zhen-bin2   

  1. 1- College of Mathematics and Information Science, Shandong Technology and Business University, Yantai 264005
    2- School of Computer and Control Engineering, Yantai University, Yantai 264005
  • Received:2014-09-16 Accepted:2015-09-24 Online:2016-04-15 Published:2016-06-15
  • Supported by:
    The National Natural Science Foundation of China (61203320); the Natural Science Foundation of Shandong Province (ZR2014FL023); the Youth Science Foundation of Shangdong Institute of Business and Technology (2013QN051).

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摘要： 本文针对一类不确定非线性系统，研究了基于输出反馈的模糊鲁棒$H_\infty$控制问题．根据模糊T-S模型表征不确定非线性系统，基于状态观测器设计模糊控制器．由线性矩阵不等式和自适应律给出了模糊控制器存在的充分性条件．基于Lyapunov稳定性理论，提出的模糊控制方案在所有闭环信号最终一致有界意义下实现了期望的$H_\infty$性能．仿真结果表明了该方案的可行性．本文所提出的模糊跟踪控制器松弛了保守性，避免了匹配条件和上界．与已有的工作相比，本文约简了线性矩阵不等式的维数．

关键词: 模糊T-S模型, 模糊逻辑系统, 不确定非线性系统, $H_\infty$控制, 输出反馈

Abstract:

This paper is concerned with a fuzzy robust $H_\infty$ control problem via output feedback for a class of uncertain nonlinear systems. The uncertain nonlinear systems are represented by fuzzy Takagi-Sugeno (T-S) model, and a fuzzy controller is designed based on the state observer. A sufficient condition for the existence of fuzzy controller is given in terms of the linear matrix inequalities (LMIs) and the adaptive law. Based on Lyapunov stability theorem, the proposed fuzzy control scheme such that the desired H∞ performance is achieved in the sense that all the closed-loop signals are uniformly ultimately bounded (UUB). Simulation results indicate the effectiveness of the developed control scheme. In this paper, a less conservative fuzzy tracking controller is proposed, where the matching condition and the upper bound are avoided. Comparing with the existing works, the dimension of the LMIs of this paper is reduced.

Key words: fuzzy T-S model, fuzzy logic systems, uncertain nonlinear systems, $H_\infty$ control, output feedback

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