Simulation Analysis of a Nonparametric Algorithm for Identification of Discrete-Time Hammerstein System

  • Jakub Markowski
  • Maciej Popkiewicz
Conference paper
Part of the Advances in Simulation book series (ADVS.SIMULATION, volume 1)


The paper deals with the discrete-time Hammerstein system shown in Fig. 1. The system is described by the equation \({{\rm{y}}_{\rm{n}}}{\rm{ = }}\sum\nolimits_{{\rm{i = 1}}}^{\rm{n}} {{{\rm{k}}_{{\rm{n - i}}}}{\rm{m}}\left( {{{\rm{u}}_{\rm{i}}}} \right)} ,\,{\rm{i}} \in {\rm{C}}{\rm{.}}\) Greblicki and Pawlak [1,2,3] presented a new approach for identification of this system based on nonparametric estimate of regression function. For recovering the characteristic of the nonlinear subsystem the Watson-Nadaraya nonparametric kernel estimate is applied. The weighting function of the dynamical subsystem is recovered by the correlation method. In the pre-cited papers a pointwise consistency of the estimate is prooved, the rate of convergency is analised, and convergency in the global sense (mean integrated square error — MISE ) is studied.


Identification Accuracy Linear Object Global Sense Dynamical Subsystem Input White Noise 
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    Greblicki, W., Pawlak, M.: Identification of Discrete Hammerstein System Using Kernel Regression Estimates, IEEE Trans. Automat.Contr., Vol. AC-31 (1986), 1, 74–77.CrossRefGoogle Scholar
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    Greblicki, W., Pawlak, M.: IMonparametric Identification of Two-Channel Nonlinear Systems, Proc. 25th Conf. on Decision and Control, Athena (1986), 2012–2015.Google Scholar
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    Greblicki, W., Pawlak, M.: Hammerstein System Identification by Non-parametric Regression Estimation, Int. J. Control, Vol.45, (1987),1, 343–345.MathSciNetMATHCrossRefGoogle Scholar
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    Press, W.H., Flanney, B.P., Teukolsky, S.A., Vetter1ing, W.T.: Numerical Recipes, Cambridge University Press, 1986.Google Scholar

Copyright information

© Akademie-Verlag Berlin 1988

Authors and Affiliations

  • Jakub Markowski
  • Maciej Popkiewicz
    • 1
  1. 1.Institute of Engineering CyberneticsTechnical University of WrocławWrocławPoland

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