Robust Control Synthesis of Polynomial Nonlinear Systems Using Sum of Squares Technique  

作　　者：HUANG Wen-Chao SUN Hong-Fei ZENG Jian-Ping 

机构地区：[1]Department of Automation, Xiamen University, Xiamen 361005 China

出　　处：《自动化学报》2013年第6期799-805,共7页Acta Automatica Sinica

基　　金：Supported by National Natural Science Foundation of China（61074004）

摘　　要：在这篇论文，广场(求救) 加技术被用来与多项式向量领域为不明确的仿射的非线性的系统的一个类分析柔韧的州的反馈合成问题。没有或与保证费用或 Hperformance 目的，足够的条件被给获得答案到上述控制问题。而且，如此的可解决的条件能以能被 SOS 技术直接处理的州的依赖线性矩阵不平等(LMI ) 作为求救编程问题被提出。而且，一个想法被提供由介绍一些额外的多项式描述多项式或甚至合理的矩阵的逆。一个数字例子被举说明途径的有效性。In this paper, sum of squares （SOS） technique is used to analyze the robust state feedback synthesis problem for a class of uncertain affine nonlinear systems with polynomial vector fields. Sufficient conditions are given to obtain the solutions to the above control problem either without or with guaranteed cost or H∞ performance objectives. Moreover, such solvable conditions can be formulated as SOS programming problems in terms of state dependent linear matrix inequalities （LMIs） which can be dealt with by the SOS technique directly. Besides, an idea is provided to describe the inverse of polynomial or even rational matrices by introducing some extra polynomials. A numerical example is presented to illustrate the effectiveness of the approach.

关 键 词：多项式向量场 仿射非线性系统 合成技术 鲁棒控制 平方和 线性矩阵不等式 状态反馈 SOS 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] O175.1[自动化与计算机技术—控制科学与工程]