Simulation Analysis of a Nonparametric Algorithm for Identification of Discrete-Time Hammerstein System

Abstract

The paper deals with the discrete-time Hammerstein system shown in Fig. 1. The system is described by the equation ${{\rm{y}}_{\rm{n}}}{\rm{ = }}\sum\nolimits_{{\rm{i = 1}}}^{\rm{n}} {{{\rm{k}}_{{\rm{n - i}}}}{\rm{m}}\left( {{{\rm{u}}_{\rm{i}}}} \right)} ,\,{\rm{i}} \in {\rm{C}}{\rm{.}}$ Greblicki and Pawlak [1,2,3] presented a new approach for identification of this system based on nonparametric estimate of regression function. For recovering the characteristic of the nonlinear subsystem the Watson-Nadaraya nonparametric kernel estimate is applied. The weighting function of the dynamical subsystem is recovered by the correlation method. In the pre-cited papers a pointwise consistency of the estimate is prooved, the rate of convergency is analised, and convergency in the global sense (mean integrated square error — MISE ) is studied.