基于交叉格莱姆矩阵的最小信息损失模型降阶方法  

Model reduction by minimizing information loss based on cross-Gramian matrix

作　　者：付金宝[1] 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,浙江杭州310027

出　　处：《浙江大学学报（工学版）》2009年第5期817-821,826,共6页Journal of Zhejiang University：Engineering Science

基　　金：国家自然科学基金资助项目(60674028;60736021;60674071);国家"863"高技术研究发展计划资助项目(2006AA04Z184)

摘　　要：运用信息论的原理和方法研究以状态空间形式描述的线性定常系统的模型降阶问题.应用线性定常系统及其对偶系统的稳态状态信息熵规范了系统能控性信息和能观性信息的定义形式.基于交叉格莱姆矩阵的系统信息属性,定义了交叉格莱姆信息.通过分析系统稳态状态信息熵的信息描述形式,揭示了交叉格莱姆信息的状态物理含义.在基于最小信息损失的模型降阶过程中以交叉格莱姆信息损失最小为目标,提出了新的模型降阶方法———CGMIL方法.理论分析和仿真结果表明,交叉格莱姆信息是包含系统能控性信息和能观性信息的综合信息描述形式,CGMIL方法与基于最小信息损失的模型降阶方法相比能够获得更好的降阶性能.The model reduction of the continuous linear time-invariant （LTI） system described by the form of state space was studied by adopting the information theoretic principle and method. The definitions of controllability information and observability information were standardized by using the information entropy of steady states of the LTI system and its dual system. Cross-Gramian information （CGI） was defined based on the information theoretic properties of the system＇s cross-Gramian matrix. By analyzing the information descriptions of system states, the physical meaning of CGI was clarified from the view of entropic points. By taking minimizing the loss of CGI as the performance index of model reduction, an improved model reduction method by minimizing the CGI loss, denoted by CGMIL, was developed. The theoretical analysis and simulation indicated that CGI is a comprehensive information description including both the controllability information and the observability information; and CGMIL algorithm is much better than the MIL algorithm in the performance of model reduction.

关 键 词：模型降阶 最小信息损失 交叉格莱姆矩阵 能控性 能观性 线性随机系统 

分 类 号：TP14[自动化与计算机技术—控制理论与控制工程]