Robustness of the "hopfield estimator" for identification of dynamical systems

Authors:
Miguel Atencia;Gonzalo Joya;Francisco Sandoval
Affiliations:
Departamento de Matemática Aplicada, Universidad de Málaga, Málaga, Spain;Departamento de Tecnología Electrónica, Universidad de Málaga, Málaga, Spain;Departamento de Tecnología Electrónica, Universidad de Málaga, Málaga, Spain
Venue:
IWANN'11 Proceedings of the 11th international conference on Artificial neural networks conference on Advances in computational intelligence - Volume Part II
Year:
2011

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Abstract

In previous work, a method for estimating the parameters of dynamical systems was proposed, based upon the stability properties of Hopfield networks. The resulting estimation is a dynamical system itself, and the analysis of its properties showed, under mild conditions, the convergence of the estimates towards the actual values of parameters. Also, it was proved that in the presence of noise in the measured signals, the estimation error remains asymptotically bounded. In this work, we aim at advancing in this robustness analysis, by considering deterministic disturbances, which do not fulfill the usual statistical hypothesis such as normality and uncorrelatedness. Simulations show that the estimation error asymptotically vanishes when the disturbances are additive. Thus the form of the perturbation affects critically the dynamical behaviour and magnitude of the estimation, which is a significant finding. The results suggest a promising robustness of the proposed method, in comparison to conventional techniques.