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弹箭与制导学报 >

2014 , Vol. 34 >Issue 5: 37 - 40,50

DOI: https://doi.org/10.15892/j.cnki.djzdxb.2014.05.010

导弹与制导技术

基于迭代平方和优化的多项式非线性系统H∞静态输出反馈控制器设计

  • 蔡宗平 ,
  • 曹创锋 ,
  • 马清亮 ,
  • 邓会选
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  • 第二炮兵工程大学,西安 710025

蔡宗平(1964-),男,陕西岐山人,教授,硕士生导师,研究方向:导航制导与控制。

收稿日期: 2013-09-09

  网络出版日期: 2025-05-30

基金资助

国家自然科学基金(61104223)

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Nonlinear H∞ Static Output Feedback Controller Design for Polynomial Systems: An Iterative Sum of Squares Approach

  • CAI Zongping ,
  • CAO Chuangfeng ,
  • MA Qingliang ,
  • DENG Huixuan
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  • The Second Artillery Engineering University, Xi'an 710025, China

Received date: 2013-09-09

  Online published: 2025-05-30

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摘要

针对一类范数有界的不确定多项式非线性系统的H∞静态输出反馈控制器设计问题,以双线性矩阵不等式(bilinearmatrixinequalities,BMIs)形式给出了此类控制器存在的充要条件。由于BMIs问题是非凸的,因此引入一种迭代平方和优化(iterativesumofsquares,ISOS)算法。该算法能够有效的求解BMIs问题,并进一步得到H∞静态输出反馈控制器。最后,仿真算例证明了该方法的有效性。

关键词： 不确定多项式系统; 静态输出反馈; 多项式平方和; 双线性矩阵不等式

本文引用格式

蔡宗平 , 曹创锋 , 马清亮 , 邓会选 . 基于迭代平方和优化的多项式非线性系统H∞静态输出反馈控制器设计[J]. 弹箭与制导学报, 2014 , 34(5) : 37 -40,50 . DOI: 10.15892/j.cnki.djzdxb.2014.05.010

Abstract

In view of design of a nonlinear H∞ static output feedback controller for polynomial systems, the derivation of the controller was given in terms of solvability conditions of state-dependent bilinear matrix inequalities (BMIs). An iterative algorithm based on the SOS decomposition was proposed to solve these state-dependent BMIs. Finally, numerical examples were provided to demonstrate the validity of the proposed design approach.

Key words： polynomial system; static output feedback; sum of squares; bilinear matrix inequalities

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