基于降维动态观测器的一类多项式系统的非线性H控制

(1.厦门理工学院电气工程与自动化学院,福建 厦门 361024; 2.厦门大学信息科学与技术学院,福建 厦门 361005)

非线性H控制; 多项式系统; 动态观测器; 外部干扰

Nonlinear H Control for a Class of Polynomial Systems Based on Reduced-order Dynamic Observer
ZHOU Yanru1*,ZENG Jianping2,SHAO Zhenhua1,HUANG Chengkai1

(1.School of Electrical Engineering and Automation,Xiamen University of Technology,Xiamen 361024,China; 2.School of Information Science and Engineering,Xiamen University,Xiamen 361024,China)

nonlinear H control; polynomial systems; dynamic observer; external disturbances

DOI: 10.6043/j.issn.0438-0479.201710005

备注

针对一类存在外部扰动的多项式系统,研究了基于动态观测器的非线性H∞控制设计问题.根据该类系统的结构特征,对线性时不变系统中动态观测器形式进行推广,构造出相应的非线性降维动态观测器.借鉴变量替换法研究思路,采用Lyapunov稳定性结合多项式平方和(SOS)凸优化理论,推导出该非线性H∞控制问题的可解性条件和控制器构造方法.以质量弹簧阻尼系统为数值仿真实例,验证了所得结论的可行性和有效性.

This paper focuses on the observer-based nonlinear H∞ control problem for a class of polynomial systems with external disturbances.Structural features of such systems guarantee the extension from the dynamic observer in linear time-in-variant systems to the corresponding nonlinear reduced-order dynamic observer.Furthermore,on the basis of variable substitution simplified solution,the feasibility conditions of the nonlinear H∞ control problem and the approach of constructing the controller are obtained based on the Lyapunov stability and sum of squares(SOS)convex programming theories.Finally,simulation results of the mass-spring-damper system are given to illustrate the feasibility and effectiveness of the proposed method.