不确定多通道奇异大系统分散鲁棒H<sub>∞</sub>控制

陈宁; 桂卫华; IKEDA Masao

引用本文:	陈宁, 桂卫华, IKEDA Masao.不确定多通道奇异大系统分散鲁棒H_∞控制[J].控制理论与应用,2007,24(2):322~328.[点击复制]
	CHEN Ning, GUI Wei-hua, IKEDA Masao.Robust decentralized H-infinity control of uncertain multi-channel descriptor systems[J].Control Theory and Technology,2007,24(2):322~328.[点击复制]

不确定多通道奇异大系统分散鲁棒H_∞控制

Robust decentralized H-infinity control of uncertain multi-channel descriptor systems

摘要点击 1577 全文点击 684 投稿时间：2005-08-08 修订日期：2006-04-18

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DOI编号 10.7641/j.issn.1000-8152.2007.2.030

2007,24(2):322-328

中文关键词分散H_∞控制奇异系统参数不确定性同伦法非线性矩阵不等式 LMI

英文关键词 decentralized H-infinity control descriptor systems parametric uncertainty homotopy method nonlinear matrix inequality LMI

基金项目国家自然科学基金重点资助项目(60634020);中国博士后科学基金资助项目(20060390883);高校博士点专项科研基金资助项目(20050533028).

作者	单位
陈宁, 桂卫华, IKEDA Masao	中南大学信息科学与工程学院, 湖南长沙 410083 大阪大学工学研究科, 日本大阪吹田 565-0871

中文摘要

研究不确定多通道奇异系统的鲁棒分散H_∞控制问题.假定不确定性是时不变、范数有界,且存在于系统和控制输入矩阵中.主要考虑分H_∞输出反馈控制问题.推导出了使不确定多通道奇异系统能鲁棒稳定且满足一定的性能指标的充分必要条件, 没有等式约束的非线性矩阵不等式条件. 采用两步同伦法迭代来求解非线性矩阵不等式(NMI).首先, 通过逐步对控制器的系数矩阵加上结构限制, 计算出当确定性不存在时的标称系统的分散H$_\infty$控制器. 然后,逐步改变标称系统分散控制器的系数,计算出不确定性参数存在时的分散鲁棒控制器. 在每一阶段, 每一次迭代过程中, 通过交替固定NMI的一个变量, 使NMI转变为线性矩阵不等式(LMI). 数值例子说明了本文提出的方法的有效性.

英文摘要

The robust decentralized H-infinity dynamic output feedback control problem for multi-channel descriptor systems is addressed in this paper. The uncertainties are assumed to be time-invariant, norm-bounded, and existing in both the system and control input matrices. Firstly, a necessary and sufficient condition for an uncertain multi-channel descriptor system to be robustly stabilizable with a specified disturbance attenuation level is derived in terms of a strict nonlinear matrix inequality (NMI). A two-stage homotopy method is then employed to solve the NMI iteratively. The decentralized H-infinity controller for the nominal descriptor system is computed by gradually imposing block-diagonal constraints on the coefficient matrices of the controller. Then, the decentralized controller is gradually modified to cope with the uncertainties. On each stage, groups of variables are alternately fixed at the iterations to reduce the NMI to linear matrix inequalities (LMIs). Finally, a given example shows the efficiency of this method.