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2007 | 17 | 2 | 189-197
Tytuł artykułu

Generalized kernel regression estimatefor the identification of Hammerstein systems

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A modified version of the classical kernel nonparametric identification algorithm for nonlinearity recovering in a Hammerstein system under the existence of random noise is proposed. The assumptions imposed on the unknown characteristic are weak. The generalized kernel method proposed in the paper provides more accurate results in comparison with the classical kernel nonparametric estimate, regardless of the number of measurements. The convergence in probability of the proposed estimate to the unknown characteristic is proved and the question of the convergence rate is discussed. Illustrative simulation examples are included.
Rocznik
Tom
17
Numer
2
Strony
189-197
Opis fizyczny
Daty
wydano
2007
otrzymano
2006-11-06
poprawiono
2007-02-22
(nieznana)
2007-04-02
Twórcy
  • Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, Janiszewskiego 11/17, 50–372 Wrocław, Poland
Bibliografia
  • Bai E.W. (2003): Frequency domain identification of Hammerstein models. - IEEE Trans. Automat. Contr., Vol.48, No.4, pp.530-542.
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  • Chang F.H.I. and Luus R. (1971): A non-iterative method for identification using Hammerstein model. - IEEE Trans. Automat. Contr., Vol.AC-16, No.4, pp.464-468.
  • Chen H.F. (2005): Strong consistency of recursive identification for Hammerstein systems with discontinuous piecewise-linear memoryless block. - IEEE Trans. Automat. Contr., Vol.50, No.10, pp.1612-1617.
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  • Gomez J.C. and Basualdo M. (2000): Nonlinear model identification of batch distillation process. - Proc. Int. IFAC Symp. Advanced Control of Chemical Processes, ADCHEM, Pisa, Italy, pp.953-959.
  • Greblicki W. (1989): Nonparametric orthogonal series identification of Hammerstein systems. - Int. J. Syst. Sci., Vol.20, No.12, pp.2355-2367.
  • Greblicki W. (2001): Recursive identification of Wiener systems. - Int. J. Appl. Math. Comp. Sci., Vol.11, No.4, pp.977-991.
  • Greblicki W., Krzyżak A. and Pawlak M. (1984): Distribution-free pointwise consistency of kernel regression estimate. - Ann. Stat., Vol.12, No.4, pp.1570-1575.
  • Greblicki W. and Pawlak M. (1986): Identification of discrete Hammerstein systems using kernel regression estimates. - IEEE Trans. Automat. Contr., Vol.31, No.1, pp.74-77.
  • Greblicki W. and Pawlak M. (1989): Nonparametric identification of Hammerstein systems. - IEEE Trans. Inf. Theory, Vol.35, No.2, pp.409-418.
  • Greblicki W. and Pawlak M. (1994): Cascade non-linear system identification by a non-parametric method. - Int. J. Syst. Sci., Vol.25, No.1, pp.129-153.
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  • Haber R. and Zeirfuss P. (1988): Identification of an electrically heated heat exchanger by several nonlinear models using different structures and parameter estimation methods. - Tech. Rep., Inst. Machine and Process Automation, Technical University of Vienna, Austria.
  • Hannan E.J. and Deistler M. (1998): The Statistical Theory of Linear Systems. - New York: Wiley.
  • Hasiewicz Z. and Mzyk G. (2004a): Combined parametric-nonparametric identification of Hammerstein systems. - IEEE Trans. Automat. Contr., Vol.49, No.8, pp.1370-1376.
  • Hasiewicz Z. and Mzyk G. (2004b): Nonparametric instrumental variables for Hammerstein system identification. - Int. J. Contr., (submitted).
  • Hasiewicz Z., Pawlak M. and Śliwiński P. (2005): Nonparametric identification of nonlinearities in block-oriented systems by orthogonal wavelets with compact support. - IEEE Trans. Circ. Syst. I: Fund. Theory Applic., Vol.52, No.2, pp.427-442.
  • Härdle W. (1990): Applied Nonparametric Regression. - Cambridge: Cambridge University Press.
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  • Narendra K.S. and Gallman P.G. (1966): An iterative method for the identification of nonlinear systems using the Hammerstein model. - IEEE Trans. Automat. Contr., Vol. 11, No. 3, pp. 546-550.
  • Pawlak M. and Hasiewicz Z. (1998): Nonlinear system identification by the Haar multiresolution analysis. - IEEE Trans. Circ. Syst., Vol.45, No.9, pp.945-961.
  • Söderström T. and Stoica P. (1982): Instrumental-variable methods for identification of Hammerstein systems. - Int. J. Contr., Vol.35, No.3, pp.459-476.
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  • Vörös J. (1999): Iterative algorithm for identification of Hammerstein systems with two-segment nonlinearities. - IEEE Trans. Automat. Contr., Vol.44, No.11, pp.2145-2149.
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Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv17i2p189bwm
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