Identification of Hybrid Systems Using a Class of Unified Wavelet-NARX models

A novel approach is proposed for the identification of hybrid systems based on a unified wavelet-based modelling framework, where the system input-output relationship is connected using mixed multi-resolution wavelet decompositions with respect to different types of wavelet and associated scaling functions. No a priori information on the system dynamics is required to estimate a wavelet-NARX model but only a given input-output data set with assumption that the system input and the output are bounded in a finite interval. Several examples, which involve precise affine (PWA) systems, open-loop threshold autoregressive systems (TARSO), piecewise rational systems and hinging hyperplane ARX (HHARX) systems, are provided to demonstrate the effectiveness and applicability of the new identification procedures.