Zonotope parameter identification for piecewise affine systems

The problem of how to identify the piecewise affine system is studied in this paper,where this considered piecewise affine system is a special nonlinear system.The reason why it is not easy to identify this piecewise affine system is that each separated region and each unknown parameter vector are all needed to be determined simultaneously.Then,firstly,in order to achieve the identification goal,a multi-class classification process is proposed to determine each separated region.As the proposed multi-class classification process is the same with the classical data clustering strategy,the multi-class classification process can combine the first order algorithm of convex optimization,while achieving the goal of the classification process.Secondly,a zonotope parameter identification algorithm is used to construct a set,which contains the unknown parameter vector.In this zonotope parameter identification algorithm,the strict probabilistic description about the external noise is relaxed,and each unknown parameter vector is also identified.Furthermore,this constructed set is consistent with the measured output and the given bound corresponding to the noise.Thirdly,a sufficient condition about guaranteeing our derived zonotope not growing unbounded with iterations is formulated as an explicit linear matrix inequality.Finally,the effectiveness of this zonotope parameter identification algorithm is proven through a simulation example.