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.
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References
Greblicki, W., Pawlak, M.: Identification of Discrete Hammerstein System Using Kernel Regression Estimates, IEEE Trans. Automat.Contr., Vol. AC-31 (1986), 1, 74–77.
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© 1988 Akademie-Verlag Berlin
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Markowski, J., Popkiewicz, M. (1988). Simulation Analysis of a Nonparametric Algorithm for Identification of Discrete-Time Hammerstein System. In: Sydow, A., Tzafestas, S.G., Vichnevetsky, R. (eds) Systems Analysis and Simulation I. Advances in Simulation, vol 1. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-6389-7_36
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DOI: https://doi.org/10.1007/978-1-4684-6389-7_36
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97091-2
Online ISBN: 978-1-4684-6389-7
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