Recursive Identification for Nonlinear ARX Systems Based on Stochastic Approximation Algorithm

doi:10.1109/TAC.2010.2042236

CSpace > 系统科学研究所

	Recursive Identification for Nonlinear ARX Systems Based on Stochastic Approximation Algorithm
	Zhao, Wen-Xiao 1; Chen, Han-Fu2 ; Zheng, Wei Xing 3
	2010-06-01
发表期刊	IEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN	0018-9286
卷号	55 期号:6 页码:1287-1299
摘要	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.
关键词	Kernel function Markov chain nonlinear ARX system recursive identification stochastic approximation
DOI	10.1109/TAC.2010.2042236
语种	英语
资助项目	NSFC[60821091] ; NSFC[60874001] ; NSFC[60625305] ; NSFC[60721003] ; 973 Program[2009CB320602] ; National Laboratory of Space Intelligent Control ; Australian Research Council
WOS研究方向	Automation & Control Systems ; Engineering
WOS类目	Automation & Control Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000278532000001
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/11142
专题	系统科学研究所
通讯作者	Zhao, Wen-Xiao
作者单位	1.Tsinghua Univ, Dept Automat, Beijing 100084, Peoples R China 2.Chinese Acad Sci, AMSS, Inst Syst Sci, Key Lab Syst & Control CAS, Beijing 100190, Peoples R China 3.Univ Western Sydney, Sch Comp & Math, Sydney, NSW 1797, Australia
推荐引用方式 GB/T 7714	Zhao, Wen-Xiao,Chen, Han-Fu,Zheng, Wei Xing. Recursive Identification for Nonlinear ARX Systems Based on Stochastic Approximation Algorithm[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,2010,55(6):1287-1299.
APA	Zhao, Wen-Xiao,Chen, Han-Fu,&Zheng, Wei Xing.(2010).Recursive Identification for Nonlinear ARX Systems Based on Stochastic Approximation Algorithm.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,55(6),1287-1299.
MLA	Zhao, Wen-Xiao,et al."Recursive Identification for Nonlinear ARX Systems Based on Stochastic Approximation Algorithm".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 55.6(2010):1287-1299.