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Recursive Identification for Nonlinear ARX Systems Based on Stochastic Approximation Algorithm
Zhao, Wen-Xiao1; Chen, Han-Fu2; Zheng, Wei Xing3
2010-06-01
Source PublicationIEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN0018-9286
Volume55Issue:6Pages:1287-1299
AbstractThe 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.
KeywordKernel function Markov chain nonlinear ARX system recursive identification stochastic approximation
DOI10.1109/TAC.2010.2042236
Language英语
Funding ProjectNSFC[60821091] ; NSFC[60874001] ; NSFC[60625305] ; NSFC[60721003] ; 973 Program[2009CB320602] ; National Laboratory of Space Intelligent Control ; Australian Research Council
WOS Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000278532000001
PublisherIEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Citation statistics
Cited Times:35[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/11142
Collection系统科学研究所
Affiliation1.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
Recommended Citation
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.
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