Algebraic Identification Algorithm and Application to Dynamical Systems

Farida Benmakrouha, Christiane Hespel, Gérard Jacob and Edouard Monnier
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Farida Benmakrouha: INSA-IRISA 20 Avenue Buttes de Coësmes
Christiane Hespel: INSA-IRISA 20 Avenue Buttes de Coësmes
Gérard Jacob: LIFL (UPRESA 8022 CNRS) Université Lille I
Edouard Monnier: INSA-IRISA 20 Avenue Buttes de Coësmes

A chapter in Computer Algebra in Scientific Computing CASC 2001, 2001, pp 43-61 from Springer

Abstract: Abstract We present an algorithm for the identification of any unknown dynamical system and a partial validation of the produced model. The method consists in computing a dynamical system (B k ) whose behaviour approximates the exact system one’s, “up to order k”, when knowing only a finite set of input/output data. The approximated dynamical system provided is a bilinear system depending on some parameters. In order to preserve the generic feature of the computation, the algorithm produces a pair (bilinear system B, constraint C on parameters), where B is produced under constraint C. A computational tool is provided, in the form of Maple package DYNAMICMODEL. The model validation is a central problem in system identification [2]. It consists generally in a test that falsifies or not falsifies the model, using a validation data set. For this continuous and symbolic model, we propose an overestimation of the mistake resulting from the systems (B k ) at order k and we show the convergence towards the exact output system. We propose also a majoration, for a certain class (DP), of the gap between two consecutive outputs.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-56666-0_4

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DOI: 10.1007/978-3-642-56666-0_4

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