Generalizing piecewise affine system identification to local model networks

Abstract

The problem of nonlinear system identification with local model networks (LMNs) is considered. Local model networks consist of a specific number of local models which are blended by validity functions to predict the output of the system. For this model type a novel data based parameterization is introduced. This parameterization allows to reformulate the identification problem as an optimization problem which is similar to piecewise affine (PWA) system identification. Therefore, different algorithms developed to solve the PWA identification problem can be used to solve the identification problem of local model networks. This is demonstrated for the popular parameter clustering algorithm. Due to the usage of validity functions the estimation of polyhedral validity regions, which usually requires the solution of a classification problem, is mitigated. Furthermore, for local model networks the new representation avoids reactivation effects since always the same factor is used in the exponent of the data based membership functions.