Consistent identification of NARX models via regularization networks

Author

De Nicolao, G. ; Trecate, G. Ferrari

Author_Institution

Dipartimento di Inf. e Sistemistica, Pavia Univ., Italy

Volume

44

Issue

11

fYear

1999

fDate

11/1/1999 12:00:00 AM

Firstpage

2045

Lastpage

2049

Abstract

Generalization networks are nonparametric estimators obtained from the application of Tychonov regularization or Bayes estimation to the hypersurface reconstruction problem. Under symmetry assumptions, they are a particular type of radial basis function neural network. In this correspondence, it is shown that such networks guarantee consistent identification of a very general (infinite-dimensional) class of NARX models. The proofs are based on the theory of reproducing kernel Hilbert spaces and the notion of frequency of time probability, by means of which it is not necessary to assume that the input is sampled from a stochastic process

Keywords

Bayes methods; Hilbert spaces; identification; probability; radial basis function networks; stochastic processes; time series; Bayes estimation; Hilbert spaces; NARX model identification; Tychonov regularization; generalization networks; hypersurface reconstruction problem; nonparametric estimators; probability; radial basis function neural network; regularization networks; stochastic process; symmetry; time series; Bayesian methods; Computational efficiency; Frequency; Hilbert space; Kernel; Neural networks; Nonlinear systems; Radial basis function networks; Sampling methods; Stochastic processes;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.802913

Filename

802913