Pathwise convergence of recursive identification algorithms for Hammerstein systems

Author

Chen, Han-Fu

Author_Institution

Inst. of Syst. Sci., Acad. of Math. & Syst. Sci., Beijing, China

Volume

49

Issue

10

fYear

2004

Firstpage

1641

Lastpage

1649

Abstract

This paper gives estimates for: 1) coefficients contained in the linear part of the Hammerstein system; 2) the value of the nonlinear function f(u) in the Hammerstein system at any u; 3) Ef(u_k) and Eu_kf(u_k) with u_k denoting the system input. No assumption is made on structure of f(·). The estimates given by the stochastic approximation algorithms with expanding truncations are recursive and convergent to the true values with probability one. Two numerical examples are given.

Keywords

convergence; identification; nonlinear functions; polynomial approximation; recursive estimation; stochastic processes; Hammerstein system; nonlinear function; pathwise convergence; recursive identification algorithm; stochastic approximation algorithm; Active noise reduction; Approximation algorithms; Convergence; Helium; Linear systems; Multi-layer neural network; Polynomials; Recursive estimation; Stochastic processes; Stochastic systems; Hammerstein system; nonparametric nonlinearity; recursive estimate; stochastic approximation; strong consistency;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2004.835358

Filename

1341559