PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

On-line wavelet estimation of Hammerstein system nonlinearity

Autorzy
Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A new algorithm for nonparametric wavelet estimation of Hammerstein system nonlinearity is proposed. The algorithm works in the on-line regime (viz., past measurements are not available) and offers a convenient uniform routine for nonlinearity estimation at an arbitrary point and at any moment of the identification process. The pointwise convergence of the estimate to locally bounded nonlinearities and the rate of this convergence are both established.
Rocznik
Strony
513--523
Opis fizyczny
Bibliogr. 53 poz., rys., tab., wykr.
Twórcy
  • Institute of Computer Engineering, Control and Robotics Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland, przemyslaw.sliwinski@pwr.wroc.pl
Bibliografia
  • Billings, S.A. and Fakhouri, S.Y. (1978). Theory of separable processes with application to the identification of nonlinear systems, Proceedings of IEE 125(10): 1051-1058.
  • Capobianco, E. (2002). Hammerstein system representation of financial volatility processes, The European Physical Journal B-Condensed Matter 27(2): 201-211.
  • Chen, H.-F. (2004). Pathwise convergence of recursive identification algorithms for Hammerstein systems, IEEE Transactions on Automatic Control 49(10): 1641-1649.
  • Chen, H.-F. (2005). Strong consistency of recursive identification for Hammerstein systems with discontinuous piecewise-linear memoryless block, IEEE Transactions on Automatic Control 50(10): 1612-1617.
  • Chen, S., Billings, S.A. and Luo, W. (1989). Orthogonal least squares methods and their application to non-linear system identification, International Journal of Control 50(5): 1873-1896.
  • Coca, D. and Billings, S. A. (2001). Non-linear system identification using wavelet multiresolution models, International Journal of Control 74(18): 1718-1736.
  • Daubechies, I. (1992). Ten Lectures on Wavelets, SIAM, Philadelphia, PA.
  • Donoho, D.L. (1993). Unconditional bases are optimal bases for data compression and for statistical estimation, Applied and Computational Harmonic Analysis 1(1): 100-115.
  • Donoho, D.L., Vetterli, M., DeVore, R.A. and Daubechies, I. (1998). Data compression and harmonic analysis, IEEE Transactions on Infromation Theory 44(6): 2435-2476.
  • Giannakis, G.B. and Serpedin, E. (2001). A bibliography on nonlinear system identification, Signal Processing 81(3): 533-580.
  • Greblicki, W. (1989). Nonparametric orthogonal series identification of Hammerstein systems, International Journal of Systems Science 20(12): 2355-2367.
  • Greblicki, W. (2001). Recursive identification of Wiener systems, International Journal of Applied Mathematics and Computer Science 11(4): 977-991.
  • Greblicki, W. (2002). Stochastic approximation in nonparametric identification of Hammerstein systems, IEEE Transactions on Automatic Control 47(11): 1800-1810.
  • Greblicki,W. and Pawlak,M. (1985). Fourier and Hermite series estimates of regression function, Annals of the Institute of Statistical Mathematics 37(3): 443-454.
  • Greblicki, W. and Pawlak, M. (1986). Identification of discrete Hammerstein system using kernel regression estimates, IEEE Transactions on Automatic Control 31(1): 74-77.
  • Greblicki, W. and Pawlak, M. (1989). Recursive nonparametric identification of Hammerstein systems, Journal of the Franklin Institute 326(4): 461-481.
  • Greblicki, W. and Pawlak, M. (1994). Nonparametric recovering nonlinearities in block oriented systems with the help of Laguerre polynomials, Control-Theory and Advanced Technology 10(4): 771-791.
  • Greblicki, W. and Pawlak, M. (2008). Nonparametric System Identification, Cambridge University Press, New York, NY.
  • Györfi, L., Kohler, M., Krzy˙zak, A. and Walk, H. (2002). A Distribution-Free Theory of Nonparametric Regression, Springer-Verlag, New York, NY.
  • Haber, R. and Keviczky, L. (1999). Nonlinear System Parameter Identification, Kluwer Academic Publishers, Dordrecht/Boston/London.
  • Hasiewicz, Z., Pawlak, M. and Śliwiński, P. (2005). Nonparametric identification of non-linearities in blockoriented complex systems by orthogonal wavelets with compact support, IEEE Transactions on Circuits and Systems I: Regular Papers 52(1): 427-442.
  • Hasiewicz, Z. and Śliwiński, P. (2002). Identification of nonlinear characteristics of a class of block-oriented non-linear systems via Daubechies wavelet-based models, International Journal of Systems Science 33(14): 1121-1144.
  • Hsu, K., Poolla, K. and Vincent, T.L. (2008). Identification of structured nonlinear systems, IEEE Transactions on Automatic Control 53(11): 2497-2513.
  • Jang, W. and Kim, G. (1994). Identification of loudspeaker nonlinearities using the NARMAX modelling technique, Journal of Audio Engineering Society 42(1/2): 50-59.
  • Jyothi, S. N. and Chidambaram, M. (2000). Identification of Hammerstein model for bioreactors with input multiplicities, Bioprocess Engineering 23(4): 323-326.
  • Kang, H.W., Cho, Y.S. and Youn, D. H. (1999). On compensating nonlinear distortions of an OFDM system using an efficient adaptive predistorter, IEEE Transactions on Communications 47(4): 522-526.
  • 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.
  • Lang, Z.Q. (1997). A nonparametric polynomial identification algorithm for the Hammerstein system, IEEE Transactions on Automatic Control 42(2): 1435-1441.
  • Lortie, M. and Kearney, R.E. (2001). Identification of time varying Hammerstein systems from ensemble data, Annals of Biomedical Engineering 29(2): 619-635.
  • Mallat, S.G. (1998). A Wavelet Tour of Signal Processing, Academic Press, San Diego, CA.
  • Marmarelis, V.Z. (2004). Nonlinear Dynamic Modeling of Physiological Systems, IEEE Press Series on Biomedical Engineering, Wiley IEEE Press, Piscataway, NJ.
  • Mzyk, G. (2007). Generalized kernel regression estimate for Hammerstein system identification, International Journal of Applied Mathematics and Computer Science 17(2): 101-109, DOI: 10.2478/v10006-007-0018-z.
  • Mzyk, G. (2009). Nonlinearity recovering in Hammerstein system from short measurement sequence, IEEE Signal Processing Letters 16(9): 762-765.
  • Nešić, D. and Mareels, I. M.Y. (1998). Dead-beat control of simple Hammerstein models, IEEE Transactions on Automatic Control 43(8): 1184-1188.
  • Niedźwiecki, M. (1988). Functional series modeling approach to identification of nonstationary stochastic systems, IEEE Transactions on Automatic Control 33(10): 955-961.
  • Nordsjo, A. and Zetterberg, L. (2001). Identification of certain time-varying nonlinear Wiener and Hammerstein systems, IEEE Transactions on Signal Processing 49(3): 577-592.
  • Pawlak, M. and Hasiewicz, Z. (1998). Nonlinear system identification by the Haar multiresolution analysis, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 45(9): 945-961.
  • Rutkowski, L. (1980). Sequential estimates of probability densities by orthogonal series and their application in pattern classification, IEEE Transactions on System, Man, and Cybernetics 10(12): 918-920.
  • Rutkowski, L. (1982). On-line identification of time-varying systems by nonparametric techniques, IEEE Transactions on Automatic Control 27(1): 228-230.
  • Rutkowski, L. (2004). Generalized regression neural networks in time-varying environment, IEEE Transactions on Neural Networks 15(3): 576-596.
  • Śliwiński, P. and Hasiewicz, Z. (2008). Computational algorithms for wavelet identification of nonlinearities in Hammerstein systems with random inputs, IEEE Transactions on Signal Processing 56(2): 846-851.
  • Śliwiński, P. and Hasiewicz, Z. (2009). Recursive nonparametric estimation of Hammerstein system nonlinearity by Haar wavelet series, IEEE Transactions on Automatic Control, (submitted for review).
  • Śliwiński, P., Hasiewicz, Z. and Wachel, P. (2007). On-line polynomial series estimates of Hammerstein system nonlinearities, Proceedings of the 13th IEEE IFAC International Conference on Methods and Models in Automation and Robotics MMAR 2007, Szczecin, Poland.
  • Śliwiński, P., Rozenblit, J., Marcellin, M.W. and Klempous, R. (2009). Wavelet amendment of polynomial models in nonlinear system identification, IEEE Transactions on Automatic Control 54(4): 820-825.
  • Srinivasan, R., Rengaswamy, R., Narasimhan, S. and Miller, R. (2005). Control loop performance assessment: 2. Hammerstein model approach for stiction diagnosis, Industrial & Engineering Chemistry Research 44(17): 6719-6728.
  • Stone, C.J. (1980). Optimal rates of convergence for nonparametric regression, Annals of Statistics 8(6): 1348-1360.
  • Sureshbabu, N. and Farrell, J.A. (1999). Wavelet based system identification for non-linear control, IEEE Transactions on Automatic Control 44(2): 412-417.
  • Unser, M. (1999). Splines. A perfect fit for signal and image processing, IEEE Signal Processing Magazine 16(6): 22-38.
  • Vörös, J. (2005). Identification of Hammerstein systems with time-varying piecewise-linear characteristics, IEEE Transactions on Circuits and Systems II: Express Briefs 52(12): 865-869.
  • Walter, G.G. and Shen, X. (2001). Wavelets and other orthogonal systems with applications, 2nd Edn., Chapman & Hall, Boca Raton, FL.
  • Westwick, D.T. and Kearney, R.E. (2001). Separable least squares identification of nonlinear Hammerstein models: Application to stretch reflex dynamics, Annals of Biomedical Engineering 29(8): 707-718.
  • Westwick, D.T. and Kearney, R.E. (2003). Identification of nonlinear physiological systems, IEEE Press Series on Biomedical Engineering, Wiley/IEEE Press, Piscataway, NJ.
  • Zhao,W.-X. and Chen, H.-F. (2006). Recursive identification for Hammerstein system with ARX subsystem, IEEE Transactions on Automatic Control 51(12): 1966-1974.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0057-0038
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.