Clustering-based identification of MIMO piecewise affine systems

PieceWise Affine (PWA) models are used to approximate general nonlinear dynamics with an arbitrary precision. PWA model can be employed for a constrained optimal controller synthesis, whereas the complexity of the controller is in a large part determined with a complexity of the model. Among the prominent methods for a PWA system identification is the clustering-based identification, which is originally designed for identification of systems with a Multiple-Input Single-Output (MISO) structure. When applied for the Multiple-Input Multiple-Output (MIMO) system identification, previously used clustering-based approach implied independent estimation of PWA maps for each of the outputs, whereas the MIMO PWA model was constructed by merging the polyhedral partitions and parameters of each MISO model. PWA model obtained with the respective approach often contained a significant number of submodels, thus aggravating the controller design process. In this paper we propose a multivariate linear regression approach for the identification of a MIMO PWA model based on the clustering technique. The presented approach is a systematic extension and fully exploits all benefits of the clustering-based identification. The proposed approach is validated on a coupled MIMO system identification problem.