离散随机模型降阶的最小条件信息损失方法  

Minimum conditional information loss approach to discrete stochastic model reduction

作　　者：章辉[1] 孙优贤[1] 

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

出　　处：《控制理论与应用》2005年第6期919-924,共6页Control Theory & Applications

基　　金：国家973计划资助项目(2002CB312200)

摘　　要：针对随机系统的模型降阶问题,从分析离散线性随机状态方程模型中的条件信息描述机制入手,讨论了模型状态集聚过程中系统的平均条件信息损失.运用在模式识别领域中获得成功应用的最小信息损失准则得出了一种新的模型降阶信息论方法———基于状态集聚的最小条件信息损失方法,并讨论了降阶模型阶次的选择.分析表明,当原系统是渐近稳定时,由该方法得出的降阶模型也是渐近稳定的.该方法运用简单,仿真研究也表明由该方法得出的降阶模型具有良好的近似性能.Aiming at the problem of stochastic model reduction, the average conditional information loss of the state aggregation is discussed by analyzing the conditional information description of discrete linear state space model. A new information theoretic method for linear stochastic model reduction, the minimum conditional information loss approach based on state aggregation, is deduced by the principle of minimum information loss which was applied successfully in the field of pattern recognition .The selection of the order of reduced-order model is also discussed. It is proved that the derived reduced-order model is asymptotically stable when the full-order model is asymptotically stable. Simulation results show that, this method is easily applicable and the reduced-order models derived by it have good approximation performance.

关 键 词：模型降阶 状态集聚 最小信息损失 熵 离散线性随机系统 

分 类 号：O231.3[理学—运筹学与控制论]