A simple scheme for semi-recursive identification of Hammerstein system nonlinearity by Haar wavelets

Abstract

A simple semi-recursive routine for nonlinearity recovery in Hammerstein systems is proposed. The identification scheme is based on the Haar wavelet kernel and possesses a simple and compact form. The convergence of the algorithm is established and the asymptotic rate of convergence (independent of the input density smoothness) is shown for piecewiseLipschitz nonlinearities. The numerical stability of the algorithm is verified. Simulation experiments for a small and moderate number of input-output data are presented and discussed to illustrate the applicability of the routine.