Zonotope Parameter Identification for Piecewise Affine System

Abstract

This paper studies the identification problem for piecewise affine system, which is a special nonlinear system. As the difficulty in identifying piecewise affine system is to determine each separated region and each unknown parameter vector simultaneously, 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 in identifying each unknown parameter vector, zonotope parameter identification algorithm is proposed to computes 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