DNN-state identification of 2D distributed parameter systems |
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Authors: | I. Chairez R. Fuentes A. Poznyak T. Poznyak M. Escudero L. Viana |
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Affiliation: | 1. Department of Bioelectronics , UPIBI-IPN , México D.F., Méxicoisaac_chairez@yahoo.com;3. Department of Automatic Control , CINVESTAV-IPN , México D.F., México;4. SEPI , ESIQIE-IPN , México D.F., México;5. Department of Bioelectronics , UPIBI-IPN , México D.F., México |
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Abstract: | There are many examples in science and engineering which are reduced to a set of partial differential equations (PDEs) through a process of mathematical modelling. Nevertheless there exist many sources of uncertainties around the aforementioned mathematical representation. Moreover, to find exact solutions of those PDEs is not a trivial task especially if the PDE is described in two or more dimensions. It is well known that neural networks can approximate a large set of continuous functions defined on a compact set to an arbitrary accuracy. In this article, a strategy based on the differential neural network (DNN) for the non-parametric identification of a mathematical model described by a class of two-dimensional (2D) PDEs is proposed. The adaptive laws for weights ensure the ‘practical stability’ of the DNN-trajectories to the parabolic 2D-PDE states. To verify the qualitative behaviour of the suggested methodology, here a non-parametric modelling problem for a distributed parameter plant is analysed. |
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Keywords: | neural networks adaptive identification distributed parameter systems partial differential equations practical stability |
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