Recursive Identification for Nonlinear ARX Systems Based on Stochastic Approximation Algorithm
Recursive Identification for Nonlinear ARX Systems Based on Stochastic Approximation Algorithm
复制标题
基于随机逼近算法的非线性ARX系统递归辨识
DOI：
10.1109/tac.2010.2042236
复制
发表时间：
2010-06-01
影响因子：
6.8
通讯作者：
Zheng, Wei Xing
中科院分区：
文献类型：
--
作者：
Zhao, Wen-Xiao;Chen, Han-Fu;Zheng, Wei Xing
The nonparametric identification for nonlinear autoregressive systems with exogenous inputs (NARX) described by y(k+1) = f(y(k),..., y(k+1-n0), u(k), u(k+1-n0)) + epsilon(k+1) is considered. First, a condition on f(.) is introduced to guarantee ergodicity and stationarity of {y(k)}. Then the kernel function based stochastic approximation algorithm with expanding truncations (SAAWET) is proposed to recursively estimate the value of f(phi*) at any given phi* (sic) [y((1)),..., y((n0)) , u((1)),..., u((n0))]tau is an element of R-2n0. It is shown that the estimate converges to the true value with probability one. In establishing the strong consistency of the estimate, the properties of the Markov chain associated with the NARX system play an important role. Numerical examples are given, which show that the simulation results are consistent with the theoretical analysis. The intention of the paper is not only to present a concrete solution to the problem under consideration but also to profile a new analysis method for nonlinear systems. The proposed method consisting in combining the Markov chain properties with stochastic approximation algorithms may be of future potential, although a restrictive condition has to be imposed on f(.), that is, the growth rate of f(x) should not be faster than linear with coefficient less than parallel to x parallel to as tends to infinity.
