Multimodeling vs PieceWise Affine modeling for the identification of open channel systems

The modeling of open-channel systems is a major research problem, particularly because the management of the water resource is getting critical. These systems belong to the general class of nonlinear diffusive systems. In this paper, we present a comparison between a multimodeling approach and a piecewise affine modeling approach for the identification of open channel systems. Both approaches are developed to approximate the behavior of non linear dynamical systems. Based on an a priori physical knowledge, the multimodeling method consists in the determination of a finite number of linear models along with appropriate weighting functions. Unlike the multimodeling, the piecewise affine modeling is a black-box identification approach. Given input-output data from the true system, this approach consists in (i) clustering the data according to their submodels, (ii) estimating the minimum number of submodels, (iii) estimating the parameter vector of each submodel and finally (iv) determining the regions of the regressor space where each of the submodels is valid.