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

作　　者：陈宁[1] 桂卫华[1] IKEDA Masao 

机构地区：[1]中南大学 信息科学与工程学院,湖南长沙410083 [2]大阪大学 工学研究科

出　　处：《控制理论与应用》2007年第2期322-328,共7页Control Theory & Applications

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

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．主要考虑分散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_∞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．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.

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 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]