Neural network identication of uncertain 2d partial differential equations

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

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Scopus citations

Abstract

There are many examples in science and engineering which are reduced to a set of partial differential equations (PDE's) through a process of mathematical modeling. Nevertheless there exist many sources of uncertainties around the aforementioned mathematical representation. 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 paper a strategy based on DNN for the non parametric identification of a mathematical model described by a class of two dimensional (2D) partial differential equations 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 behavior of the suggested methodology, here a non parametric modeling problem for a distributed parameter plant is analyzed.

Original languageEnglish
Title of host publication2009 6th International Conference on Electrical Engineering, Computing Science and Automatic Control, CCE 2009
DOIs
StatePublished - 2009
Event2009 6th International Conference on Electrical Engineering, Computing Science and Automatic Control, CCE 2009 - Toluca, Mexico
Duration: 10 Nov 200913 Nov 2009

Publication series

Name2009 6th International Conference on Electrical Engineering, Computing Science and Automatic Control, CCE 2009

Conference

Conference2009 6th International Conference on Electrical Engineering, Computing Science and Automatic Control, CCE 2009
Country/TerritoryMexico
CityToluca
Period10/11/0913/11/09

Keywords

  • Adaptive identification
  • Distributed parameter systems
  • Neural networks
  • Partial differential equations and practical stability

Fingerprint

Dive into the research topics of 'Neural network identication of uncertain 2d partial differential equations'. Together they form a unique fingerprint.

Cite this