Wavelet amendment of polynomial models in hammerstein systems identification

Przemysław Śliwiński; Jerzy Rozenblit; Michael W. Marcellin; Ryszard Klempous

doi:10.1109/TAC.2008.2009620

Wavelet amendment of polynomial models in hammerstein systems identification

Przemysław Śliwiński, Jerzy Rozenblit, Michael W. Marcellin, Ryszard Klempous

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

A new wavelet algorithm for on-line improvement of an existing polynomial model of nonlinearity in a Hammerstein system is proposed and its properties are examined. The algorithm employs wavelet bases on interval. Convergence of the resulting assembly, comprising the parametric polynomial model and a nonparametric wavelet add-on, to the system nonlinearity is shown. Rates of convergence for uniformly smooth and piecewise smooth nonlinearities with discontinuities are both established.

Original language	English (US)
Pages (from-to)	820-825
Number of pages	6
Journal	IEEE Transactions on Automatic Control
Volume	54
Issue number	4
DOIs	https://doi.org/10.1109/TAC.2008.2009620
State	Published - 2009

Keywords

Hammerstein system
Nonlinear system identification
Order statistics
Polynomial models
Semiparametric approach
Wavelet bypass
Wavelet regression estimate

ASJC Scopus subject areas

Control and Systems Engineering
Computer Science Applications
Electrical and Electronic Engineering

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10.1109/TAC.2008.2009620

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title = "Wavelet amendment of polynomial models in hammerstein systems identification",

abstract = "A new wavelet algorithm for on-line improvement of an existing polynomial model of nonlinearity in a Hammerstein system is proposed and its properties are examined. The algorithm employs wavelet bases on interval. Convergence of the resulting assembly, comprising the parametric polynomial model and a nonparametric wavelet add-on, to the system nonlinearity is shown. Rates of convergence for uniformly smooth and piecewise smooth nonlinearities with discontinuities are both established.",

keywords = "Hammerstein system, Nonlinear system identification, Order statistics, Polynomial models, Semiparametric approach, Wavelet bypass, Wavelet regression estimate",

author = "Przemys{\l}aw {\'S}liwi{\'n}ski and Jerzy Rozenblit and Marcellin, {Michael W.} and Ryszard Klempous",

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AU - Śliwiński, Przemysław

AU - Rozenblit, Jerzy

AU - Marcellin, Michael W.

AU - Klempous, Ryszard

PY - 2009

Y1 - 2009

N2 - A new wavelet algorithm for on-line improvement of an existing polynomial model of nonlinearity in a Hammerstein system is proposed and its properties are examined. The algorithm employs wavelet bases on interval. Convergence of the resulting assembly, comprising the parametric polynomial model and a nonparametric wavelet add-on, to the system nonlinearity is shown. Rates of convergence for uniformly smooth and piecewise smooth nonlinearities with discontinuities are both established.

AB - A new wavelet algorithm for on-line improvement of an existing polynomial model of nonlinearity in a Hammerstein system is proposed and its properties are examined. The algorithm employs wavelet bases on interval. Convergence of the resulting assembly, comprising the parametric polynomial model and a nonparametric wavelet add-on, to the system nonlinearity is shown. Rates of convergence for uniformly smooth and piecewise smooth nonlinearities with discontinuities are both established.

KW - Hammerstein system

KW - Nonlinear system identification

KW - Order statistics

KW - Polynomial models

KW - Semiparametric approach

KW - Wavelet bypass

KW - Wavelet regression estimate

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DO - 10.1109/TAC.2008.2009620

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SP - 820

EP - 825

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 4

ER -

Wavelet amendment of polynomial models in hammerstein systems identification

Abstract

Keywords

ASJC Scopus subject areas

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