Zonotope parameter identification for piecewise affine system

This paper studies one identification problem for a piecewise affine system which is a special nonlinear system. As the difficulty in identifying the piecewise affine system is to determine each separated region and each unknown parameter vector simultaneously, here we propose a multi-class classification process to determine each separated region. This multi-class classification process is similar to the classical data clustering process, and the merit of our strategy is that the first-order algorithm of convex optimization can be applied to achieve this classification process. Furthermore, to relax the strict probabilistic description on external noise and identify each unknown parameter vector, a zonotope parameter identification algorithm is proposed to compute a set that contains the parameter vector, consistent with the measured output and the given bound of the noise. To guarantee our derived zonotope not growing unbounded with iterations, a sufficient condition for this requirement to hold may be formulated as one linear matrix inequality. Finally, a numerical example confirms our theoretical results.