A Unified Approach for the Identification of SISO/MIMO Wiener and Hammerstein Systems*

Abstract

Hammerstein and Wiener models are nonlinear representations of systems composed by the coupling of a static nonlinearity N and a linear system L in the form N-L and L-N respectively. These models can represent real processes which made them popular in the last decades. The problem of identifying the static nonlinearity and linear system is not a trivial task, and has attracted a lot of research interest. It has been studied in the available literature either for Hammerstein or Wiener systems, and either in a discrete-time or continuous-time setting. The objective of this paper is to present a unified framework for the identification of these systems that is valid for SISO and MIMO systems, discrete and continuous-time setting, and with the only a priori knowledge that the system is either Wiener or Hammerstein.

Gradient‐based recursive parameter estimation for a periodically nonuniformly sampled‐data Hammerstein–Wiener system based on the key‐term separation

“…This is the identification model of nonuniformly sample-data systems. The proposed parameter estimation algorithms in this article are based on this identification model in (10). Many identification methods are derived based on the identification models of the systems [38][39][40][41] and can be used to estimate the parameters of other linear systems and nonlinear systems [42][43][44][45][46] and can be applied to fields [47][48][49][50][51][52] such as chemical process control systems.…”

“…Nonlinear systems have attracted numerous attention of researchers owing to their simple structures and effectual reflections to nonlinear plants, [1][2][3][4] for example, the Hammerstein systems, [5][6][7] the Wiener systems, [8][9][10] the Hammerstein-Wiener (H-W) systems, 11,12 and the Wiener-Hammerstein (W-H) systems. 13,14 A Hammerstein system consists of a static input nonlinear element in series with a dynamic linear subsystem.…”