3D Nonparametric Neural Identification
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 disadvantag...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
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| Series: | Journal of Control Science and Engineering |
| Online Access: | http://dx.doi.org/10.1155/2012/618403 |
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| _version_ | 1849398729802514432 |
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| author | Rita Q. Fuentes Isaac Chairez Alexander Poznyak Tatyana Poznyak |
| author_facet | Rita Q. Fuentes Isaac Chairez Alexander Poznyak Tatyana Poznyak |
| author_sort | Rita Q. Fuentes |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a5bc352a9a2d417ca61913c062972a4d |
| institution | Kabale University |
| issn | 1687-5249 1687-5257 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Control Science and Engineering |
| spelling | doaj-art-a5bc352a9a2d417ca61913c062972a4d2025-08-20T03:38:31ZengWileyJournal of Control Science and Engineering1687-52491687-52572012-01-01201210.1155/2012/6184036184033D Nonparametric Neural IdentificationRita Q. Fuentes0Isaac Chairez1Alexander Poznyak2Tatyana Poznyak3Automatic Control Department, CINVESTAV-IPN, 07360 México, DF, MexicoBioprocess Department, UPIBI-IPN, 07360 México, DF, MexicoAutomatic Control Department, CINVESTAV-IPN, 07360 México, DF, MexicoSEPI, ESIQIE-IPN, 07738 México, DF, MexicoThis 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.http://dx.doi.org/10.1155/2012/618403 |
| spellingShingle | Rita Q. Fuentes Isaac Chairez Alexander Poznyak Tatyana Poznyak 3D Nonparametric Neural Identification Journal of Control Science and Engineering |
| title | 3D Nonparametric Neural Identification |
| title_full | 3D Nonparametric Neural Identification |
| title_fullStr | 3D Nonparametric Neural Identification |
| title_full_unstemmed | 3D Nonparametric Neural Identification |
| title_short | 3D Nonparametric Neural Identification |
| title_sort | 3d nonparametric neural identification |
| url | http://dx.doi.org/10.1155/2012/618403 |
| work_keys_str_mv | AT ritaqfuentes 3dnonparametricneuralidentification AT isaacchairez 3dnonparametricneuralidentification AT alexanderpoznyak 3dnonparametricneuralidentification AT tatyanapoznyak 3dnonparametricneuralidentification |