3D nonparametric neural identification

Rita Q. Fuentes, Isaac Chairez, Alexander Poznyak, Tatyana Poznyak

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

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.
Original languageAmerican English
JournalJournal of Control Science and Engineering
DOIs
StatePublished - 21 Mar 2012

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Partial differential equations
Partial differential equation
Neural Networks
Neural networks
Practical Stability
Qualitative Behavior
Applied mathematics
Differential System
Trivial
Exact Solution
Trajectories
Trajectory
Verify
Engineering
Uncertainty
Three-dimensional
Methodology
Approximation
Modeling
Model

Cite this

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title = "3D nonparametric neural identification",
abstract = "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. {\circledC} 2012 Rita Q. Fuentes et al.",
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3D nonparametric neural identification. / Fuentes, Rita Q.; Chairez, Isaac; Poznyak, Alexander; Poznyak, Tatyana.

In: Journal of Control Science and Engineering, 21.03.2012.

Research output: Contribution to journalArticle

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