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Dynamical Neural Networks that Ensure Exponential Identification Error Convergence.

Petros A. Ioannou1, Manolis A. Christodoulou, Elias B. Kosmatopoulos

  • 1University of Southern California, Greece

Neural Networks : the Official Journal of the International Neural Network Society
|March 1, 1997
PubMed
Summary

New adaptive learning laws for recurrent high order neural networks (RHONN) guarantee zero identification error convergence. This overcomes limitations of classical adaptive schemes in nonlinear system identification.

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Correction on 'Dynamical neural networks that ensure exponential identification error convergence'

Neural networks : the official journal of the International Neural Network Society·2003
See all related articles

Area of Science:

  • Control Systems Engineering
  • Artificial Intelligence
  • Computational Neuroscience

Background:

  • Classical adaptive and robust adaptive schemes struggle with modeling errors, leading to bounded, not zero, identification errors in nonlinear system identification.
  • Existing methods for 'black-box' identification of nonlinear systems often result in suboptimal performance due to inherent limitations in error convergence.

Purpose of the Study:

  • To introduce novel adaptive learning laws for Recurrent High Order Neural Networks (RHONN).
  • To demonstrate exponential convergence of the identification error to zero, even under modeling uncertainties.
  • To analyze the parameter convergence properties and compare them with existing adaptive schemes.

Main Methods:

  • Development of new adaptive learning laws specifically designed for RHONN.

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  • Theoretical analysis to prove exponential convergence of the identification error.
  • Examination of parameter convergence capabilities to an optimal neural network model.

    • Main Results:

    • The proposed learning laws ensure the identification error converges exponentially fast to zero.
    • If the initial identification error is zero, it remains zero throughout the process.
    • Parameter convergence properties are comparable to classical adaptive and parameter estimation schemes.

    Conclusions:

    • The novel adaptive learning laws offer a significant improvement for nonlinear system identification using RHONN.
    • These laws achieve precise identification by ensuring zero error convergence, a feat not possible with traditional methods.
    • A limitation is the non-local implementability of the proposed learning laws due to their reliance on global signal and parameter knowledge.