Wiener and Hammerstein uncertain models identification

Abstract

Block-oriented models have proved to be useful as simple nonlinear models for a vast number of applications. They are described as a cascade of linear dynamic and nonlinear static blocks. They have emerged as an appealing proposal due to their simplicity and the property of being valid over a larger operating region than a LTI model. In the description of these models, several approaches can be found in the literature to perform the identification process. In this sense, an important improvement is to achieve robust identification of blockoriented models to cope with the presence of uncertainty. In this article, we focus at two special and widely used types of uncertain block-oriented models: Hammerstein and Wiener models. They are assumed to be represented by a parametric representation. The approach herein followed allows to describe the uncertainty as a set of parameters which is found through the solution of an optimization problem. The identification algorithms are illustrated through a set of simple examples.