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Journal of Control Science and Engineering
Volume 2012, Article ID 618403, 10 pages
Research Article

3D Nonparametric Neural Identification

1Automatic Control Department, CINVESTAV-IPN, 07360 México, DF, Mexico
2Bioprocess Department, UPIBI-IPN, 07360 México, DF, Mexico
3SEPI, ESIQIE-IPN, 07738 México, DF, Mexico

Received 23 August 2011; Accepted 2 October 2011

Academic Editor: Haibo He

Copyright © 2012 Rita Q. Fuentes et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper presents the state identification study of 3D partial differential equations (PDEs) using the differential neural networks (DNNs) approximation. There are so many physical situations in applied mathematics and engineering that can be described by PDEs; these models possess the disadvantage of having many sources of uncertainties around their mathematical representation. Moreover, to find the exact solutions of those uncertain PDEs is not a trivial task especially if the PDE is described in two or more dimensions. Given the continuous nature and the temporal evolution of these systems, differential neural networks are an attractive option as nonparametric identifiers capable of estimating a 3D distributed model. The adaptive laws for weights ensure the “practical stability” of the DNN trajectories to the parabolic three-dimensional (3D) PDE states. To verify the qualitative behavior of the suggested methodology, here a nonparametric modeling problem for a distributed parameter plant is analyzed.