Set membership identification of piecewise affine models

This paper addresses the problem of identification of piecewise affine (PWA) models, which involves the joint estimation of both the parameters of the affine submodels and the partition of the PWA map from data. According to ideas from set-membership identification, the key approach is to characterize the model by its maximum allowed prediction error, which is used as a tuning knob for trading off between prediction accuracy and model complexity. At initialization, the proposed procedure for PWA identification exploits a technique for partitioning an infeasible system of linear inequalities into a (possibly minimum) number of feasible subsystems. This provides both an initial clustering of the datapoints and a guess of the number of required submodels, which therefore is not fixed a priori. A refinement procedure is then applied in order to improve both data classification and parameter estimation. The partition of the PWA map is finally estimated by considering multicategory classification techniques.