Markov chain approach to identifying Wiener systems  

作　　者：ZHAO WenXiao CHEN HanFu 

机构地区：[1]Key Laboratory of Systems and Control,Institute of Systems Science,AMSS,Chinese Academy of Sciences,Beijing 100190,China [2]National Center for Mathematics and Interdisciplinary Sciences,Chinese Academy of Sciences,Beijing 100190,China

出　　处：《Science China(Information Sciences)》2012年第5期1201-1217,共17页中国科学（信息科学）（英文版）

基　　金：supported by National Nature Science Foundation of China (Grant Nos. 61120106011,61134013,61104052,91130008)

摘　　要：Identification of the Wiener system composed of an infinite impulse response （IIR） linear subsystem followed by a static nonlinearity is considered. The recursive estimates for unknown coefficients of the linear subsystem and for the values of the nonlinear function at any fixed points are given by the stochastic approx- imation algorithms with expanding truncations （SAA^VET）. With the help of properties of the Markov chain connected with the linear subsystem, all estimates derived in the paper are proved to be strongly consistent. In comparison with the existing results on the topic, the method presented in the paper simplifies the convergence analysis and requires weaker conditions. A numerical example is given, and the simulation results are consistent with the theoretical analysis.Identification of the Wiener system composed of an infinite impulse response （IIR） linear subsystem followed by a static nonlinearity is considered. The recursive estimates for unknown coefficients of the linear subsystem and for the values of the nonlinear function at any fixed points are given by the stochastic approx- imation algorithms with expanding truncations （SAA^VET）. With the help of properties of the Markov chain connected with the linear subsystem, all estimates derived in the paper are proved to be strongly consistent. In comparison with the existing results on the topic, the method presented in the paper simplifies the convergence analysis and requires weaker conditions. A numerical example is given, and the simulation results are consistent with the theoretical analysis.

关 键 词：Wiener system recursive identification stochastic approximation Markov chain strong consis-tency 

分 类 号：O211.62[理学—概率论与数理统计] TU855[理学—数学]