### Abstract

Original language | American English |
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Journal | Journal of Control Science and Engineering |

DOIs | |

State | Published - 21 Mar 2012 |

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### Cite this

*Journal of Control Science and Engineering*. https://doi.org/10.1155/2012/618403

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*Journal of Control Science and Engineering*. https://doi.org/10.1155/2012/618403

**3D nonparametric neural identification.** / Fuentes, Rita Q.; Chairez, Isaac; Poznyak, Alexander; Poznyak, Tatyana.

Research output: Contribution to journal › Article

TY - JOUR

T1 - 3D nonparametric neural identification

AU - Fuentes, Rita Q.

AU - Chairez, Isaac

AU - Poznyak, Alexander

AU - Poznyak, Tatyana

PY - 2012/3/21

Y1 - 2012/3/21

N2 - 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. © 2012 Rita Q. Fuentes et al.

AB - 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. © 2012 Rita Q. Fuentes et al.

U2 - 10.1155/2012/618403

DO - 10.1155/2012/618403

M3 - Article

JO - Journal of Control Science and Engineering

JF - Journal of Control Science and Engineering

SN - 1687-5249

ER -