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A simple scheme for semi-recursive identification of Hammerstein system nonlinearity by Haar wavelets

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Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A simple semi-recursive routine for nonlinearity recovery in Hammerstein systems is proposed. The identification scheme is based on the Haar wavelet kernel and possesses a simple and compact form. The convergence of the algorithm is established and the asymptotic rate of convergence (independent of the input density smoothness) is shown for piecewise-Lipschitz nonlinearities. The numerical stability of the algorithm is verified. Simulation experiments for a small and moderate number of input-output data are presented and discussed to illustrate the applicability of the routine.
Rocznik
Strony
507--520
Opis fizyczny
Bibliogr. 50 poz., rys., tab., wykr.
Twórcy
  • Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, Wrocław, Poland, przemyslaw.sliwinski@pwr.wroc.pl
autor
  • Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, Wrocław, Poland
autor
  • Institute of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, Wrocław, Poland
Bibliografia
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  • [6] Clancy, E.A., Liu, L., Liu, P. and Moyer, D.V.Z. (2012). Identification of constant-posture EMG-torque relationship about the elbow using nonlinear dynamic models, IEEE Transactions on Biomedical Engineering 59(1): 205–212.
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  • [10] Greblicki, W. (2002). Stochastic approximation in nonparametric identification of Hammerstein systems, IEEE Transactions on Automatic Control 47(11): 1800–1810.
  • [11] Greblicki, W. (2004). Hammerstein system identification with stochastic approximation, International Journal of Modelling and Simulation 24(2): 131–138.
  • [12] Greblicki, W. and Pawlak, M. (1986). Identification of discrete Hammerstein system using kernel regression estimates, IEEE Transactions on Automatic Control 31(1): 74–77.
  • [13] Greblicki, W. and Pawlak, M. (1987). Necessary and sufficient consistency conditions for a recursive kernel regression estimate, Journal of Multivariate Analysis 23(1): 67–76.
  • [14] Greblicki, W. and Pawlak, M. (1989). Recursive nonparametric identification of Hammerstein systems, Journal of the Franklin Institute 326(4): 461–481.
  • [15] Greblicki, W. and Pawlak, M. (2008). Nonparametric System Identification, Cambridge University Press, New York, NY.
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  • [17] Hasiewicz, Z. (1999). Hammerstein system identification by the Haar multiresolution approximation, International Journal of Adaptive Control and Signal Processing 13(8): 697–717.
  • [18] Hasiewicz, Z. (2000). Modular neural networks for non-linearity recovering by the Haar approximation, Neural Networks 13(10): 1107–1133.
  • [19] Hasiewicz, Z., Pawlak, M. and Śliwiński, P. (2005). Non-parametric identification of non-linearities in block-oriented complex systems by orthogonal wavelets with compact support, IEEE Transactions on Circuits and Systems I: Regular Papers 52(1): 427–442.
  • [20] Hasiewicz, Z. and Śliwiński, P. (2002). Identification of non-linear characteristics of a class of block-oriented non-linear systems via Daubechies wavelet-based models, International Journal of Systems Science 33(14): 1121–1144.
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  • [24] Krzyżak, A. (1993). Identification of nonlinear block-oriented systems by the recursive kernel estimate, Journal of the Franklin Institute 330(3): 605–627.
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  • [26] Kukreja, S., Kearney, R. and Galiana, H. (2005). A least-squares parameter estimation algorithm for switched Hammerstein systems with applications to the VOR, IEEE Transactions on Biomedical Engineering 52(3): 431–444.
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  • [28] Lortie, M. and Kearney, R.E. (2001). Identification of time-varying Hammerstein systems from ensemble data, Annals of Biomedical Engineering 29(2): 619–635.
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  • [41] Śliwiński, P. (2010). On-line wavelet estimation of Hammerstein system nonlinearity, International Journal of Applied Mathematics and Computer Science 20(3): 513–523, DOI: 10.2478/v10006-010-0038-y.
  • [42] Śliwiński, P. (2013). Nonlinear System Identification by Haar Wavelets, Lecture Notes in Statistics, Vol. 210, Springer-Verlag, Heidelberg.
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  • [50] Zhou, D. and De Brunner, V.E. (2007). Novel adaptive nonlinear predistorters based on the direct learning algorithm, IEEE Transactions on Signal Processing 55(1): 120–133.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-0431e8a7-03f7-48aa-875f-76c33c7dec8e
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