线性多变量控制系统的干扰抑制性能极限:信息论方法  

Performance limits of disturbance rejection in linear multivariable control systems: information theoretic approaches

作　　者：章辉[1] 孙优贤[1] 

机构地区：[1]浙江大学工业控制技术国家重点实验室浙江大学控制科学与工程系现代控制工程研究所,浙江杭州310027

出　　处：《控制理论与应用》2004年第3期357-361,共5页Control Theory & Applications

基　　金：国家973项目(2002CB312200).

摘　　要：考察了受随机干扰的线性离散多变量时不变反馈控制系统中的不确定性和信息传输,从信息论的角度阐述了系统干扰抑制的性能极限.讨论中采用熵率和信息率作为系统干扰抑制的性能函数.针对调节问题,利用Bode积分定理将控制系统中的熵率和系统开环不稳定极点结合起来,修正了"变异度守恒定律";针对跟踪问题,研究高斯系统中干扰与输出间的互信息率和系统闭环传递函数H∞熵的关系,并在此基础上得出了系统干扰抑制的性能上界.By investigating the transmission of uncertainty and information in linear time invariant multivariable control systems disturbed by stationary stochastic processes,performance limits of disturbance rejection were studied within the framework of information theory.Two measures of information and uncertainty,entropy rate and mutual information rate,were employed as performance functions of linear regulation system and linear tracking system,respectively.For linear regulation problem,the entropy rate of system output was computed by using Bode integral formula,then the performance limit of disturbance rejection was formulated in terms of unstable poles of open-loop transfer function,and the'conservation law of variety' was revised.For linear tracking problem,a relation between H∞ entropy of system closed-loop transfer function and mutual information rate of the pair of disturbance and output was deduced by using frequency calculation method of mutual information rate,and an upper bound of disturbance rejection performance in Gaussian systems was derived based on this relation.

关 键 词：信息率 Bode积分 H∞熵 性能极限 线性多变量系统 随机干扰 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]