几类典型随机非线性系统的辨识  

IDENTIFICATION OF SEVERAL CLASSES OF STOCHASTIC NONLINEAR SYSTEMS

作　　者：陈翰馥[1] 赵文虓[1] 

机构地区：[1]中国科学院数学与系统科学研究院系统控制重点实验室,北京100190

出　　处：《系统科学与数学》2011年第9期1019-1044,共26页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(60221301;61104052)资助课题

摘　　要：考察实际中常见的三类典型随机非线性系统(即Wiener、Hammerstein和NARX系统)的辨识,首先概述了现有的递推和非递推辨识算法,然后介绍这三类系统的一个统一辨识框架:利用系统所确定的过程的马氏性及混合型,将辨识转化为求函数零点的问题,基于扩张截尾的随机逼近算法,得到了递推、强一致的辨识结果,并给出了数值模拟验证辨识算法收敛到真值.Identification of several classes of stochastic nonlinear systems,i.e.,the Wiener system,the Hammerstein system and the nonlinear ARX system,is considered.First,existing recursive and nonrecursive algorithms for identifying these systems are briefly summarized. Then,a unified framework to recursively identify these systems is introduced.Based on the Markov chains and mixing properties connected with these systems,the identification is transformed into root searching problems.Finally,identification algorithms based on stochastic approximation with expanding truncations are introduced and strong consistency of estimates is established.The theoretical results are verified by simulation examples.

关 键 词：Wiener系统 HAMMERSTEIN系统 NARX系统 马氏链 随机逼近 递推辨识 

分 类 号：O211.6[理学—概率论与数理统计] N945.14[理学—数学]