Identification of MIMO Hammerstein Models in the Presence of Piecewise Polynomial Disturbances using Kaczmarz Algorithm

Abstract

The Kaczmarz algorithm, originally, is an iterative projection algorithm for solving a linear system of equations. After the publications of the result, it was observed that it is possible to design simple recursive algorithm for parameters estimation. Because of its simplicity algorithm found different applications including tomography, distributed computation, computer vision and medicine (scanners) to name a few. In this paper, we try to expand the area of applications. Namely, we consider the problem of Hammerstein model identification. It is supposed that system has MIMO (multi-input multioutput) structure. The nonlinear part of Hammerstein model has general structure and disturbance has piecewise polynomial form. The algorithm is novel and the key ingredient of the algorithm is the Shannon – Kulebakin operator.