Problems Relative to Identification of Nonlinear Systems With Cascade Structure

Abstract

The study of biological or chemical processes leads generally to a non linear model with a cascade structure and in which the same parameter can appear in different non linear parts. The number of identification method which can be used with such a class of system is very limited. The identification method proposed in this paper is based on the parametric space division. The subspaces are defined so that the parameters which belong to one subspace have the same influence at the same time on the output. This influence can be represented by the sensitivity function. A similarity coefficient of the sensitivity functions is defined and used to determine the parametric subspaces. We have to note that one parameter can belong to different subspaces. The parameter identification is obtained using the gradient method in each subspace, and one subspace after the other. The results obtained using this method are compared with those given by gradient and axis direction method. The model used for this comparison is that of a waste water biological treatment system.