随机系统的递推辨识:从个例到一般框架

Recursive identification of stochastic systems:from individual system to a general framework

本文考察Hammerstein系统、Wiener系统和非线性带外源输入的自回归系统(autoregressive system with exogenous input,ARX)等常见的随机非线性系统的递推辨识和因特网PageRank的分布式、随机化算法.对非线性系统分别构造递推辨识算法,证明了估计的强一致性;对因特网PageRank的分布式、随机化算法,给出估计的强一致性和收敛速度;在此基础上,总结了这类问题的统一处理框架–将辨识(估计)问题转化为函数求根、进而基于随机逼近构造算法得到强一致的递推辨识;最后,通过数值例子来验证算法的有效性.

We consider the recursive identification algorithms for the stochastic nonlinear systems,such as Hammerstein system,Wiener system,and nonlinear autoregressive system with exogenous input （ARX） system and the distributed randomized PageRank algorithm （DRPA）.The strong consistency of estimates given by the identification algorithms and DRPA is established.Based on the stochastic approximation algorithm with expanding truncations,a unified framework for solving these kinds of problems is introduced.Numerical examples are given to testify the performance of the proposed algorithms.