Identification of piecewise affine systems based on statistical clustering technique

This paper is concerned with the identification of a class of piecewise affine systems called a piecewise affine autoregressive exogenous (PWARX) model. The PWARX model is composed of ARX sub-models each of which corresponds to a polyhedral region of the regression space. Under the temporary assumption that the number of sub-models is known a priori, the input-output data are collected into several clusters by using a statistical clustering algorithm. We utilize support vector classifiers to estimate the boundary hyperplane between two adjacent regions in the regression space. In each cluster, the parameter vector of the sub-model is obtained by the least squares method. It turns out that the present statistical clustering approach enables us to estimate the number of sub-models based on the information criteria such as CAIC and MDL. The estimate of the number of sub-models is performed by applying the identification procedure several times to the same data set, after having fixed the number of sub-models to different values. Finally, we verify the applicability of the present identification method through a numerical example of a Hammerstein model.