A Comparative Study on Global Wavelet and Polynomial Models for Nonlinear Regime-Switching Systems

A comparative study of wavelet and polynomial models for nonlinear regime-switching (RS) systems is carried out. Regime-switching systems, considered in this study, are a class of severely nonlinear systems, which exhibit abrupt changes or dramatic breaks in behaviour, due to regime switching 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 nonlinear regime-switching systems.