A Clustering-Based Bounded-Error Approach for Identification of PWA Hybrid Systems

A new bounded-error approach for the identification of discrete time hybrid systems in the piece-wise affine (PWA) form is introduced. The PWA identification problem involves the estimation of the number of affine submodels, the parameters of affine submodels and the partition of the PWA map from data. By imposing a bound on the identification error, we formulate the PWA identification problem as a MIN PFS problem (partition into a minimum number of feasible subsystems) and propose a greedy clustering-based method for tackling it. The proposed approach yields to better results than the greedy randomized relaxation algorithm used in previous methods. Also, it is not sensitive to the overestimation of model orders and changes in the tuning parameters and therefore finding a right combination of the tuning parameters of the algorithm to get a model with prescribed bounded prediction error is simple