Asymptotic Behaviour of Gradient Learning Algorithms in Neural Network Models for the Identification of Nonlinear Systems

Valerii N. Azarskov; Dmytro P. Kucherov; Sergii A. Nikolaienko; Leonid S. Zhiteckii

doi:doi:10.11648/j.ajnna.20150101.11

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Asymptotic Behaviour of Gradient Learning Algorithms in Neural Network Models for the Identification of Nonlinear Systems

Valerii N. Azarskov, Dmytro P. Kucherov, Sergii A. Nikolaienko, Leonid S. Zhiteckii

Published in American Journal of Neural Networks and Applications (Volume 1, Issue 1)

Received: 14 June 2015 Accepted: 28 July 2015 Published: 29 July 2015

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Abstract

This paper deals with studying the asymptotical properties of multilayer neural networks models used for the adaptive identification of wide class of nonlinearly parameterized systems in stochastic environment. To adjust the neural network’s weights, the standard online gradient type learning algorithms are employed. The learning set is assumed to be infinite but bounded. The Lyapunov-like tool is utilized to analyze the ultimate behaviour of learning processes in the presence of stochastic input variables. New sufficient conditions guaranteeing the global convergence of these algorithms in the stochastic frameworks are derived. The main their feature is that they need no a penalty term to achieve the boundedness of weight sequence. To demonstrate asymptotic behaviour of the learning algorithms and support the theoretical studies, some simulation examples are also given

Published in	American Journal of Neural Networks and Applications (Volume 1, Issue 1)
DOI	10.11648/j.ajnna.20150101.11
Page(s)	1-10
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Neural Network, Nonlinear Model, Gradient Learning Algorithm, Stochastic Environment, Convergence

References

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APA Style

Valerii N. Azarskov, Dmytro P. Kucherov, Sergii A. Nikolaienko, Leonid S. Zhiteckii. (2015). Asymptotic Behaviour of Gradient Learning Algorithms in Neural Network Models for the Identification of Nonlinear Systems. American Journal of Neural Networks and Applications, 1(1), 1-10. https://doi.org/10.11648/j.ajnna.20150101.11

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ACS Style

Valerii N. Azarskov; Dmytro P. Kucherov; Sergii A. Nikolaienko; Leonid S. Zhiteckii. Asymptotic Behaviour of Gradient Learning Algorithms in Neural Network Models for the Identification of Nonlinear Systems. Am. J. Neural Netw. Appl. 2015, 1(1), 1-10. doi: 10.11648/j.ajnna.20150101.11

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AMA Style

Valerii N. Azarskov, Dmytro P. Kucherov, Sergii A. Nikolaienko, Leonid S. Zhiteckii. Asymptotic Behaviour of Gradient Learning Algorithms in Neural Network Models for the Identification of Nonlinear Systems. Am J Neural Netw Appl. 2015;1(1):1-10. doi: 10.11648/j.ajnna.20150101.11

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@article{10.11648/j.ajnna.20150101.11,
  author = {Valerii N. Azarskov and Dmytro P. Kucherov and Sergii A. Nikolaienko and Leonid S. Zhiteckii},
  title = {Asymptotic Behaviour of Gradient Learning Algorithms in Neural Network Models for the Identification of Nonlinear Systems},
  journal = {American Journal of Neural Networks and Applications},
  volume = {1},
  number = {1},
  pages = {1-10},
  doi = {10.11648/j.ajnna.20150101.11},
  url = {https://doi.org/10.11648/j.ajnna.20150101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajnna.20150101.11},
  abstract = {This paper deals with studying the asymptotical properties of multilayer neural networks models used for the adaptive identification of wide class of nonlinearly parameterized systems in stochastic environment. To adjust the neural network’s weights, the standard online gradient type learning algorithms are employed. The learning set is assumed to be infinite but bounded. The Lyapunov-like tool is utilized to analyze the ultimate behaviour of learning processes in the presence of stochastic input variables. New sufficient conditions guaranteeing the global convergence of these algorithms in the stochastic frameworks are derived. The main their feature is that they need no a penalty term to achieve the boundedness of weight sequence. To demonstrate asymptotic behaviour of the learning algorithms and support the theoretical studies, some simulation examples are also given},
 year = {2015}
}

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TY - JOUR
T1 - Asymptotic Behaviour of Gradient Learning Algorithms in Neural Network Models for the Identification of Nonlinear Systems
AU - Valerii N. Azarskov
AU - Dmytro P. Kucherov
AU - Sergii A. Nikolaienko
AU - Leonid S. Zhiteckii
Y1 - 2015/07/29
PY - 2015
N1 - https://doi.org/10.11648/j.ajnna.20150101.11
DO - 10.11648/j.ajnna.20150101.11
T2 - American Journal of Neural Networks and Applications
JF - American Journal of Neural Networks and Applications
JO - American Journal of Neural Networks and Applications
SP - 1
EP - 10
PB - Science Publishing Group
SN - 2469-7419
UR - https://doi.org/10.11648/j.ajnna.20150101.11
AB - This paper deals with studying the asymptotical properties of multilayer neural networks models used for the adaptive identification of wide class of nonlinearly parameterized systems in stochastic environment. To adjust the neural network’s weights, the standard online gradient type learning algorithms are employed. The learning set is assumed to be infinite but bounded. The Lyapunov-like tool is utilized to analyze the ultimate behaviour of learning processes in the presence of stochastic input variables. New sufficient conditions guaranteeing the global convergence of these algorithms in the stochastic frameworks are derived. The main their feature is that they need no a penalty term to achieve the boundedness of weight sequence. To demonstrate asymptotic behaviour of the learning algorithms and support the theoretical studies, some simulation examples are also given
VL - 1
IS - 1
ER -

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Author Information

Valerii N. Azarskov

Faculty of Computer Science, National Aviation University, Kiev, Ukraine
Dmytro P. Kucherov

Faculty of Computer Science, National Aviation University, Kiev, Ukraine
Sergii A. Nikolaienko

Cybernetics Centre, Dept. of Automated Data Processing Systems, Kiev, Ukraine
Leonid S. Zhiteckii

Cybernetics Centre, Dept. of Automated Data Processing Systems, Kiev, Ukraine

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APA Style

Valerii N. Azarskov, Dmytro P. Kucherov, Sergii A. Nikolaienko, Leonid S. Zhiteckii. (2015). Asymptotic Behaviour of Gradient Learning Algorithms in Neural Network Models for the Identification of Nonlinear Systems. American Journal of Neural Networks and Applications, 1(1), 1-10. https://doi.org/10.11648/j.ajnna.20150101.11

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ACS Style

Valerii N. Azarskov; Dmytro P. Kucherov; Sergii A. Nikolaienko; Leonid S. Zhiteckii. Asymptotic Behaviour of Gradient Learning Algorithms in Neural Network Models for the Identification of Nonlinear Systems. Am. J. Neural Netw. Appl. 2015, 1(1), 1-10. doi: 10.11648/j.ajnna.20150101.11

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AMA Style

Valerii N. Azarskov, Dmytro P. Kucherov, Sergii A. Nikolaienko, Leonid S. Zhiteckii. Asymptotic Behaviour of Gradient Learning Algorithms in Neural Network Models for the Identification of Nonlinear Systems. Am J Neural Netw Appl. 2015;1(1):1-10. doi: 10.11648/j.ajnna.20150101.11

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@article{10.11648/j.ajnna.20150101.11,
  author = {Valerii N. Azarskov and Dmytro P. Kucherov and Sergii A. Nikolaienko and Leonid S. Zhiteckii},
  title = {Asymptotic Behaviour of Gradient Learning Algorithms in Neural Network Models for the Identification of Nonlinear Systems},
  journal = {American Journal of Neural Networks and Applications},
  volume = {1},
  number = {1},
  pages = {1-10},
  doi = {10.11648/j.ajnna.20150101.11},
  url = {https://doi.org/10.11648/j.ajnna.20150101.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajnna.20150101.11},
  abstract = {This paper deals with studying the asymptotical properties of multilayer neural networks models used for the adaptive identification of wide class of nonlinearly parameterized systems in stochastic environment. To adjust the neural network’s weights, the standard online gradient type learning algorithms are employed. The learning set is assumed to be infinite but bounded. The Lyapunov-like tool is utilized to analyze the ultimate behaviour of learning processes in the presence of stochastic input variables. New sufficient conditions guaranteeing the global convergence of these algorithms in the stochastic frameworks are derived. The main their feature is that they need no a penalty term to achieve the boundedness of weight sequence. To demonstrate asymptotic behaviour of the learning algorithms and support the theoretical studies, some simulation examples are also given},
 year = {2015}
}

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