摘要
This paper considers identification of the nonlinear autoregression with exogenous inputs(NARX system).The growth rate of the nonlinear function is required be not faster than linear withslope less than one.The value of f(·) at any fixed point is recursively estimated by the stochasticapproximation (SA) algorithm with the help of kernel functions.Strong consistency of the estimatesis established under reasonable conditions,which,in particular,imply stability of the system.Thenumerical simulation is consistent with the theoretical analysis.
This paper considers identification of the nonlinear autoregression with exogenous inputs （NARX system）. The growth rate of the nonlinear function is required be not faster than linear with slope less than one. The value of f（·） at any fixed point is recursively estimated by the stochastic approximation （SA） algorithm with the help of kernel functions. Strong consistency of the estimates is established under reasonable conditions, which, in particular, imply stability of the system. The numerical simulation is consistent with the theoretical analysis.
基金
supported by the National Natural Science Foundation of China under Grant Nos. 60821091and 60874001
Grant from the National Laboratory of Space Intelligent Control
Guozhi Xu Posdoctoral Research Foundation
关键词
X系统
NAR
非参数
非线性自回归
非线性函数
随机逼近
强一致性
数值模拟
α-mixing, geometrically ergodic, Markov chains, NARX, nonparametric, recursive estimate, stochastic approximation, strongly consistent.
