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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)

Abstract

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.

Keywords

Identification Accuracy Linear Object Global Sense Dynamical Subsystem Input White Noise 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    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
  2. [2]
    Greblicki, W., Pawlak, M.: IMonparametric Identification of Two-Channel Nonlinear Systems, Proc. 25th Conf. on Decision and Control, Athena (1986), 2012–2015.Google Scholar
  3. [3]
    Greblicki, W., Pawlak, M.: Hammerstein System Identification by Non-parametric Regression Estimation, Int. J. Control, Vol.45, (1987),1, 343–345.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    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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