Algebraic Identification Algorithm and Application to Dynamical Systems

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.