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.
This work has been partially supported by the Spanish Ministerio de Ciencia e Innovación (project no. TIN2008-04985), the Junta de Andalucía (project no. P08-TIC-04026), and the Agencia Española de Cooperación Internacional para el Desarrollo (project no. D/030223/10).
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References
Abe, S.: Theories on the Hopfield Neural Networks. In: Proc. IEE International Joint Conference on Neural Networks, vol. I, pp. 557–564 (1989)
Alonso, H., Mendonça, T., Rocha, P.: Hopfield neural networks for on-line parameter estimation. Neural Networks 22(4), 450–462 (2009)
Atencia, M., Joya, G., Sandoval, F.: Modelling the HIV-AIDS Cuban Epidemics with Hopfield Neural Networks. In: Mira, J., Álvarez, J. (eds.) IWANN 2003. LNCS, vol. 2687, pp. 1053–1053. Springer, Heidelberg (2003)
Atencia, M., Joya, G., Sandoval, F.: Dynamical Analysis of Continuous Higher Order Hopfield Networks for Combinatorial Optimization. Neural Computation 17(8), 1802–1819 (2005)
Atencia, M., Joya, G., Sandoval, F.: Hopfield Neural Networks for Parametric Identification of Dynamical Systems. Neural Processing Letters 21(2), 143–152 (2005)
Atencia, M.A., Joya, G., García-Garaluz, E., de Arazoza, H., Sandoval, F.: Estimation of the Rate of Detection of Infected Individuals in an Epidemiological Model. In: Sandoval, F., Prieto, A.G., Cabestany, J., Graña, M. (eds.) IWANN 2007. LNCS, vol. 4507, pp. 948–955. Springer, Heidelberg (2007)
Ghogho, M.: Maximum likelihood estimation of amplitude-modulated time series. Signal Processing 75(2), 99–116 (1999)
Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences of the United States of America 79(8), 2554–2558 (1982)
Hopfield, J.J.: Neurons with graded response have collective computational properties like those of two-state neurons. Proceedings of the National Academy of Sciences of the United States of America 81(10), 3088–3092 (1984)
Hopfield, J.J., Tank, D.W.: “Neural” computation of decisions in optimization problems. Biological Cybernetics 52, 141–152 (1985)
Khalil, H.: Nonlinear systems, 2nd edn. Prentice Hall, Upper Saddle River (1996)
Ljung, L.: System identification: theory for the user. Prentice-Hall, Englewood Cliffs (1999)
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Atencia, M., Joya, G., Sandoval, F. (2011). Robustness of the “Hopfield Estimator” for Identification of Dynamical Systems. In: Cabestany, J., Rojas, I., Joya, G. (eds) Advances in Computational Intelligence. IWANN 2011. Lecture Notes in Computer Science, vol 6692. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21498-1_65
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DOI: https://doi.org/10.1007/978-3-642-21498-1_65
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