Identification algorithm for piecewise affine systems with bounded disturbances

Abstract

This paper presents a new identification algorithm for Piecewise Affine Autoregressive exogenous (PWARX) models in the presence of bounded disturbances. This problem includes the estimation of both parameters of the sub-models and the polyhedral partition of the regressor domain. The proposed algorithm proceeds in two stages. In the first stage, it associates each data point to the most suitable sub-model and realizes the identification of the parameters of each sub-model. This stage is based on an Outer Bounding Ellipsoid (OBE) type algorithm suitable for system identification with bounded disturbances. In the second stage, the algorithm achieves the estimation of the parameter defining the polyhedral partition. A numerical example is given so as to illustrate performance of the algorithm.