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

Study on Multi-Model Soft Sensor Modeling Method and Its Model Optimization for the Fermentation Process of Pichia pastoris

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“…Based on the idea of multi-model "decomposition-synthesis", the PWA/PWL multi-model divides the sample space of the system into a finite number of sub-intervals, and each sub-interval is described by a PWA/PWL local model, which transforms the problem of solving a complex nonlinear system into the problem of solving several linear systems [20]. The advantages of the PWA multi-model are that the model structure is very simple; after all, the structure of linear systems is far less complex than that of nonlinear systems, and PWA multi-model is less time consuming than other multi-models because the time to solve a linear system is much less than that to solve a nonlinear system [21,22]. These advantages have made PWA systems a hot research topic in the field of modeling, and they are widely used in many engineering practices.…”