New Approaches to Identification of PWARX Systems

Abstract

We consider the clustering-based procedures for the identification of discrete-time hybrid systems in the piecewise affine (PWA) form. These methods exploit three main techniques which are clustering, linear identification, and pattern recognition. The clustering method based on thek-means algorithm is treated in this paper. It consists in estimating both the parameter vector of each submodel and the coefficients of each partition while knowing the model ordersnaandnband the number of submodelss. The performance of this approach can be threatened by the presence of outliers and poor initializations. To overcome these problems, we propose new techniques for data classification. The proposed techniques exploit Chiu’s clustering technique and the self-artificial Kohonen neural network approach in order to improve the performance of both the clustering and the final linear regression procedure. Simulation results are presented to illustrate the performance of the proposed method.