Near-optimal construction of wavelet networks for nonlinear system modeling

Abstract

This paper proposes a constructive modeling scheme for nonlinear systems using wavelet networks as its model structure. Taking the advantage of the multiresolution nature as well as the localized feature of wavelet networks, a multi-scale modeling strategy has been developed to capture both the global and local characteristics of the systems over different scales from coarse to fine. A shrinking technique has been developed to delete some of the wavelet nodes to make the whole wavelet network as compact a size as possible, and in this sense, we can approach a near-optimal model within prescribed error tolerance. Main convergence results are established in the paper along with the analysis backing up to the construction procedure. Simulation is used to evaluate the effectiveness of the scheme.