A unified approach for the parametric 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 settings, and with the only a priori knowledge that the system belongs to the set including Wiener and Hammerstein models.