DNN-state identification of 2D distributed parameter systems

I. Chairez, R. Fuentes, A. Poznyak, T. Poznyak, M. Escudero and L. Viana

International Journal of Systems Science, 2011, vol. 43, issue 2, 296-307

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.

Date: 2011
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DOI: 10.1080/00207721.2010.495187

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