Title: A comparative study on global wavelet and polynomial models for non-linear regime-switching systems

Authors: Hua-Liang Wei, Stephen A. Billings

Addresses: Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK. ' Department of Automatic Control and Systems Engineering, University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK

Abstract: A comparative study of wavelet and polynomial models for non-linear Regime-Switching (RS) systems is carried out. RS systems, considered in this study, are a class of severely non-linear systems, which exhibit abrupt changes or dramatic breaks in behaviour, due to RS caused by associated events. Both wavelet and polynomial models are used to describe discontinuous dynamical systems, where it is assumed that no a priori information about the inherent model structure and the relative regime switches of the underlying dynamics is known, but only observed input-output data are available. An Orthogonal Least Squares (OLS) algorithm interfered with by an Error Reduction Ratio (ERR) index and regularised by an Approximate Minimum Description Length (AMDL) criterion, is used to construct parsimonious wavelet and polynomial models. The performance of the resultant wavelet models is compared with that of the relative polynomial models, by inspecting the predictive capability of the associated representations. It is shown from numerical results that wavelet models are superior to polynomial models, in respect of generalisation properties, for describing severely non-linear RS systems.

Keywords: NARX models; nonlinear autoregressive with exogenous; non-linear system identification; nonlinear regime-switching systems; wavelets; polynomial models.

DOI: 10.1504/IJMIC.2007.016410

International Journal of Modelling, Identification and Control, 2007 Vol.2 No.4, pp.273 - 282

Published online: 28 Dec 2007 *

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