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一类多项式非线性系统鲁棒H∞控制
引用本文:黄文超,孙洪飞,曾建平. 一类多项式非线性系统鲁棒H∞控制[J]. 控制理论与应用, 2012, 29(12): 1587-1593
作者姓名:黄文超  孙洪飞  曾建平
作者单位:厦门大学自动化系,福建厦门,361005
基金项目:国家自然科学基金资助项目(61074004); 教育部留学回国人员科研启动基金资助项目[2009].
摘    要:针对一类具有多项式向量场的仿射型不确定非线性系统,给出一种基于多项式平方和(sum of squares,SOS)技术的鲁棒H∞状态反馈控制器设计方法.该方法的优点在于控制器的设计避开了直接求解复杂的哈密尔顿-雅可比不等式(Hamilton Jacobi inequality,HJI)和构造Lyapunov函数带来的困难.将鲁棒稳定性分析和控制器设计问题转化为求解以Lyapunov函数为参数的矩阵不等式,该类不等式可利用SOS技术直接求解.此外,在前文基础上研究了基于SOS规划理论与S-procedure技术的局部稳定鲁棒H∞控制器设计方法.最后以非线性质量弹簧阻尼系统作为仿真算例验证该方法的有效性.

关 键 词:鲁棒H∞控制  非线性控制  状态反馈  多项式平方和
收稿时间:2011-09-16
修稿时间:2012-05-07

Robust H-infinity control for a class of polynomial nonlinear systems
HUANG Wen-chao,SUN Hong-fei and ZENG Jian-ping. Robust H-infinity control for a class of polynomial nonlinear systems[J]. Control Theory & Applications, 2012, 29(12): 1587-1593
Authors:HUANG Wen-chao  SUN Hong-fei  ZENG Jian-ping
Affiliation:Department of Automation, Xiamen University,Department of Automation, Xiamen University,Department of Automation, Xiamen University
Abstract:By employing the sum of squares (SOS) technique, we investigate the robust H-infinity state-feedback controller design for a class of uncertain affine nonlinear systems with polynomial vector fields. The advantage of this approach lies in its avoidance of difficulties in solving the intricate Hamilton Jacobi inequality (HJI) and constructing Lyapunov functions. By using the SOS technique, both the robust stability analysis and the controller design problems are transformed into solving the matrix inequalities with parameters of the Lyapunov function as decision variables. Besides, the robust H-infinity controller which guarantees the local stability of the closed-loop system is presented by using the SOS programming and S-procedure simultaneously. Finally, the simulation results of the nonlinear mass-spring-damper system show the effectiveness of the proposed approach.
Keywords:robust H-infinity control   nonlinear control   state feedback   sum of squares
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