Recursive Identification of MIMO Wiener Systems

Author

Bi-Qiang Mu ; Han-Fu Chen

Author_Institution

Key Lab. of Syst. & Control, Acad. of Math. & Syst. Sci., Beijing, China

Volume

58

Issue

3

fYear

2013

fDate

Mar-13

Firstpage

802

Lastpage

808

Abstract

Stochastic approximation (SA) algorithms are proposed to identify a multi-input and multi-output (MIMO) Wiener system, in which the system input is taken to be a sequence of independent and identically distributed (i.i.d.) Gaussian random vectors uk ∈ N(0,I). The algorithm for identifying the nonlinear part is designed with multi-variable kernel functions. Under suitable conditions, we show that the estimates of the coefficients of the linear subsystem and of the values of the nonlinear function converge to the respective true values with probability one.

Keywords

Gaussian processes; MIMO systems; approximation theory; convergence of numerical methods; linear systems; nonlinear functions; random processes; recursive estimation; set theory; vectors; Gaussian random vectors; MIMO Wiener systems; SA algorithm; independent and identically distributed Gaussian random vectors; linear subsystem; multiinput and multioutput Wiener system; multivariable kernel functions; nonlinear function convergence; probability; recursive identification; stochastic approximation algorithm; Approximation algorithms; Approximation methods; Convergence; Estimation; Kernel; MIMO; Vectors; $alpha$ -mixing; MIMO Wiener system; stochastic approximation; strong consistency;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2012.2215539

Filename

6286990