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Parametric identification of robotic systems with stable time-varying Hopfield networks

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Abstract

In this work, a novel method for on-line identification of non-linear systems is proposed based upon the optimisation methodology with Hopfield neural networks. The original Hopfield model is adapted so that the weights of the resulting network are time-varying. A rigorous analytical study proves that, under mild assumptions, the estimations provided by the method converge to the actual parameter values in the case of constant parameters, or to a bounded neighbourhood of the parameters when these are time-varying. Time-varying parameters, often appearing in mechanical systems, are dealt with by the neural estimator in a more natural way than by least squares techniques. Both sudden and slow continuous variations are considered. Besides, in contrast to the gradient method, the neural estimator does not critically depend on the adjustment of the gain. The proposed method is applied to the identification of a robotic system with a flexible link. A reduced output prediction error and an accurate estimation of parameters are observed in simulation results.

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Abbreviations

ODE :

Ordinary differential equation

LIP :

Linear in the parameters (system)

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Acknowledgements

This work has been partially supported by project no. TIC2001-1758, funded by the Spanish Ministerio de Ciencia y Tecnología (MCYT) and FEDER funds. The comments of the anonymous reviewers are gratefully acknowledged.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, E.T.S.I.Telecomunicación, Complejo Politécnico, Universidad de Málaga, Campus de Teatinos, s/n, 29071, Málaga, Spain

    Miguel Atencia

  2. Departamento de Tecnología Electrónica, E.T.S.I.Telecomunicación, Complejo Politécnico, Universidad de Málaga, Campus de Teatinos, s/n, 29071, Málaga, Spain

    Gonzalo Joya & Francisco Sandoval

Authors
  1. Miguel Atencia
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  2. Gonzalo Joya
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  3. Francisco Sandoval
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Corresponding author

Correspondence to Miguel Atencia.

Additional information

This is a considerably extended version of a paper presented at the conference on Engineering Applications of Neural Networks (EANN), held in September 2003 at Málaga, Spain.

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Atencia, M., Joya, G. & Sandoval, F. Parametric identification of robotic systems with stable time-varying Hopfield networks. Neural Comput & Applic 13, 270–280 (2004). https://doi.org/10.1007/s00521-004-0421-4

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  • DOI: https://doi.org/10.1007/s00521-004-0421-4

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