Parametric Identification of Linear Systems Followed by Non-Invertible Piecewise Nonlinearities

Rimantas Pupeikis

doi:10.18052/www.scipress.com/ifsl.6.16

Abstract

The aim of the given paper is the development of an approach for parametric identification of Wiener systems with static non-invertible function, i.e., when the linear part with unknown parameters is followed by piecewise linear nonlinearity with negative slopes. It is shown here that the problem of identification of a nonlinear Wiener system could be reduced to a linear parametric estimation problem by a simple input-output data reordering and by a following data partition into three data sets. A technique based on ordinary least squares (LS) is proposed here for the separate estimation of parameters of linear and nonlinear parts of the Wiener system, including the unknown threshold of piecewise nonlinearity, by processing respective particles of input-output observations. The simulation results are given.

Highlights

A lot of physical systems are naturally described as Wiener systems, i.e., when the linear system is followed by a static nonlinearity [1 – 3]
We describe here the approach based on reconstruction of the unmeasurable internal intermediate signal, acting between both blocks of the Wiener system, without designing special and complex enough compensators [5]
The Monte Carlo simulation implies that the accuracy of parametric identification of the Wiener system with static non-invertible nonlinearity depends on the intensity of measurement noise

Summary

Introduction

A lot of physical systems are naturally described as Wiener systems, i.e., when the linear system is followed by a static nonlinearity [1 – 3]. Let us rearrange the true output data y(k), k 1, N in an ascending order of their values, assuming that measurement noise e(k) k 1, N is absent, parameters, and the threshold d of non-invertible nonlinearity (5) are known.

Results

Conclusion