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

Capobianco, E. (2002). Hammerstein system representation of financial volatility processes, The European Physical JournalB: Condensed Matter 27(2): 201-211.10.1140/epjb/e20020154Search in Google Scholar

Chen, H.-F. (2004). Pathwise convergence of recursive identification algorithms for Hammerstein systems, IEEETransactions on Automatic Control 49(10): 1641-1649.10.1109/TAC.2004.835358Search in Google Scholar

Chen, H.-F. (2010). Recursive identification for stochastic Hammerstein systems, in F. Giri and E.W. Bai (Eds.), Block-oriented Nonlinear System Identification, Lecture Notes in Control and Information Sciences, Vol. 404, Springer-Verlag, Berlin/Heidelberg, pp. 69-87.10.1007/978-1-84996-513-2_6Search in Google Scholar

Chen, S., Billings, S.A. and Luo, W. (1989). Orthogonal least squares methods and their application to non-linear system identification, International Journal of Control50(5): 1873-1896.10.1080/00207178908953472Search in Google Scholar

Chen, W., Khan, A.Q., Abid, M. and Ding, S.X. (2011). Integrated design of observer based fault detection for a class of uncertain nonlinear systems, InternationalJournal of Applied Mathematics and Computer Science21(3): 423-430, DOI: 10.2478/v10006-011-0031-0.10.2478/v10006-011-0031-0Search in Google Scholar

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, IEEETransactions on Biomedical Engineering 59(1): 205-212.10.1109/TBME.2011.217042321968709Search in Google Scholar

Coca, D. and Billings, S.A. (2001). Non-linear system identification using wavelet multiresolution models, InternationalJournal of Control 74(18): 1718-1736.10.1080/00207170110089743Search in Google Scholar

Gallman, P. (1975). An iterative method for the identification of nonlinear systems using a Uryson model, IEEE Transactionson Automatic Control 20(6): 771-775.10.1109/TAC.1975.1101087Search in Google Scholar

Gomes, S.M. and Cortina, E. (1995). Some results on the convergence of sampling series based on convolution integrals, SIAM Journal on Mathematical Analysis26(5): 1386-1402.10.1137/S1052623493255096Search in Google Scholar

Greblicki, W. (2002). Stochastic approximation in nonparametric identification of Hammerstein systems, IEEE Transactions on Automatic Control47(11): 1800-1810.10.1109/TAC.2002.804483Search in Google Scholar

Greblicki, W. (2004). Hammerstein system identification with stochastic approximation, International Journal of Modellingand Simulation 24(2): 131-138.10.1080/02286203.2004.11442297Search in Google Scholar

Greblicki, W. and Pawlak, M. (1986). Identification of discrete Hammerstein system using kernel regression estimates, IEEE Transactions on Automatic Control 31(1): 74-77.10.1109/TAC.1986.1104096Search in Google Scholar

Greblicki, W. and Pawlak, M. (1987). Necessary and sufficient consistency conditions for a recursive kernel regression estimate, Journal of Multivariate Analysis 23(1): 67-76.10.1016/0047-259X(87)90178-3Search in Google Scholar

Greblicki, W. and Pawlak, M. (1989). Recursive nonparametric identification of Hammerstein systems, Journal of theFranklin Institute 326(4): 461-481.10.1016/0016-0032(89)90045-8Search in Google Scholar

Greblicki, W. and Pawlak, M. (2008). Nonparametric SystemIdentification, Cambridge University Press, New York, NY.10.1017/CBO9780511536687Search in Google Scholar

Györfi, L., Kohler, M., Krzyżak, A. and Walk, H. (2002). A Distribution-Free Theory of Nonparametric Regression, Springer-Verlag, New York, NY.10.1007/b97848Search in Google Scholar

Hasiewicz, Z. (1999). Hammerstein system identification by the Haar multiresolution approximation, International Journalof Adaptive Control and Signal Processing 13(8): 697-717.10.1002/(SICI)1099-1115(199912)13:8<691::AID-ACS591>3.0.CO;2-7Search in Google Scholar

Hasiewicz, Z. (2000). Modular neural networks for non-linearity recovering by the Haar approximation, Neural Networks13(10): 1107-1133.10.1016/S0893-6080(00)00055-1Search in Google Scholar

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 andSystems I: Regular Papers 52(1): 427-442.10.1109/TCSI.2004.840288Search in Google Scholar

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 Science33(14): 1121-1144.10.1080/0020772021000064171Search in Google Scholar

Jyothi, S.N. and Chidambaram, M. (2000). Identification of Hammerstein model for bioreactors with input multiplicities, Bioprocess Engineering 23(4): 323-326.10.1007/s004499900141Search in Google Scholar

Krzyżak, A. (1986). The rates of convergence of kernel regression estimates and classification rules, IEEE Transactionson Information Theory 32(5): 668-679.10.1109/TIT.1986.1057226Search in Google Scholar

Krzyżak, A. (1992). Global convergence of the recursive kernel regression estimates with applications in classification and nonlinear system estimation, IEEE Transactions on InformationTheory 38(4): 1323-1338.10.1109/18.144711Search in Google Scholar

Krzyżak, A. (1993). Identification of nonlinear block-oriented systems by the recursive kernel estimate, Journal of theFranklin Institute 330(3): 605-627.10.1016/0016-0032(93)90101-YSearch in Google Scholar

Krzyżak, A. and Pawlak, M. (1984). Distribution-free consistency of a nonparametric kernel regression estimate and classification, IEEE Transactions on Information Theory30(1): 78-81.10.1109/TIT.1984.1056842Search in Google Scholar

Kukreja, S., Kearney, R. and Galiana, H. (2005). A least-squares parameter estimation algorithm for switched Hammerstein systems with applications to the VOR, IEEE Transactionson Biomedical Engineering 52(3): 431-444.10.1109/TBME.2004.84328615759573Search in Google Scholar

Kushner, H.J. and Yin, G.G. (2003). Stochastic Approximationand Recursive Algorithms and Applications, 2nd Edn., Stochastic Modelling and Applied Probability, Springer, New York, NY.Search in Google Scholar

Lortie, M. and Kearney, R.E. (2001). Identification of time-varying Hammerstein systems from ensemble data, Annals of Biomedical Engineering 29(2): 619-635.10.1114/1.138042111501626Search in Google Scholar

Mallat, S.G. (1998). A Wavelet Tour of Signal Processing, Academic Press, San Diego, CA.10.1016/B978-012466606-1/50008-8Search in Google Scholar

Marmarelis, V.Z. (2004). Nonlinear Dynamic Modeling ofPhysiological Systems, IEEE Press Series on Biomedical Engineering, Wiley-IEEE Press, Piscataway, NJ.10.1002/9780471679370Search in Google Scholar

Nordsjo, A. and Zetterberg, L. (2001). Identification of certain time-varying nonlinear Wiener and Hammerstein systems, IEEE Transactions on Signal Processing 49(3): 577-592.10.1109/78.905884Search in Google Scholar

Patan, K. and Korbicz, J. (2012). Nonlinear model predictive control of a boiler unit: A fault tolerant control study, International Journal of Applied Mathematicsand Computer Science 22(1): 225-237, DOI: 10.2478/v10006-012-0017-6.10.2478/v10006-012-0017-6Search in Google Scholar

Pawlak, M. and Hasiewicz, Z. (1998). Nonlinear system identification by the Haar multiresolution analysis, IEEETransactions on Circuits and Systems I: Fundamental Theoryand Applications 45(9): 945-961.10.1109/81.721260Search in Google Scholar

Pawlak, M., Rafajłowicz, E. and Krzyżak, A. (2003). Postfiltering versus prefiltering for signal recovery from noisy samples, IEEE Transactions on Information Theory49(12): 3195-3212.10.1109/TIT.2003.820013Search in Google Scholar

Rutkowski, L. (1984). On nonparametric identification with prediction of time-varying systems, IEEE Transactions onAutomatic Control 29(1): 58-60.10.1109/TAC.1984.1103377Search in Google Scholar

Rutkowski, L. (2004). Generalized regression neural networks in time-varying environment, IEEE Transactions on NeuralNetworks 15(3): 576 - 596.10.1109/TNN.2004.82612715384547Search in Google Scholar

Saeedi, H., Mollahasani, N., Moghadam, M.M. and Chuev, G.N. (2011). An operational Haar wavelet method for solving fractional Volterra integral equations, InternationalJournal of Applied Mathematics and Computer Science21(3): 535-547, DOI: 10.2478/v10006-011-0042-x.10.2478/v10006-011-0042-xSearch in Google Scholar

Sansone, G. (1959). Orthogonal Functions, Interscience, New York, NY.Search in Google Scholar

Serfling, R.J. (1980). Approximation Theorems of MathematicalStatistics, Wiley, New York, NY.10.1002/9780470316481Search in Google Scholar

Skubalska-Rafajłowicz, E. (2001). Pattern recognition algorithms based on space-filling curves and orthogonal expansions, IEEE Transactions on Information Theory47(5): 1915-1927. 10.1109/18.930927Search in Google Scholar

Śliwiński, P. (2010). On-line wavelet estimation of Hammerstein system nonlinearity, International Journal of AppliedMathematics and Computer Science 20(3): 513-523, DOI: 10.2478/v10006-010-0038-y. 10.2478/v10006-010-0038-ySearch in Google Scholar

Śliwiński, P. (2013). Nonlinear System Identification byHaar Wavelets, Lecture Notes in Statistics, Vol. 210, Springer-Verlag, Heidelberg.Search in Google Scholar

Stone, C.J. (1980). Optimal rates of convergence for nonparametric regression, Annals of Statistics8(6): 1348-1360.10.1214/aos/1176345206Search in Google Scholar

Szego, G. (1974). Orthogonal Polynomials, 3rd Edn., American Mathematical Society, Providence, RI.Search in Google Scholar

Van der Vaart, A. (2000). Asymptotic Statistics, Cambridge University Press, Cambridge.Search in Google Scholar

Vörös, J. (2003). Recursive identification of Hammerstein systems with discontinuous nonlinearities containing dead-zones, IEEE Transactions on Automatic Control48(12): 2203-2206.10.1109/TAC.2003.820146Search in Google Scholar

Walter, G.G. and Shen, X. (2001). Wavelets and Other OrthogonalSystems With Applications, 2nd Edn., Chapman & Hall, Boca Raton, FL.Search in Google Scholar

Westwick, D.T. and Kearney, R.E. (2003). Identification ofNonlinear Physiological Systems, IEEE Press Series on Biomedical Engineering, Wiley-IEEE Press, Piscataway, NJ.Search in Google Scholar

Wheeden, R. L. and Zygmund, A. (1977). Measure and Integral:An Introduction to Real Analysis, Pure and Applied Mathematics, Marcel Dekker Inc., New York, NY.Search in Google Scholar

Zhou, D. and DeBrunner, V.E. (2007). Novel adaptive nonlinear predistorters based on the direct learning algorithm, IEEETransactions on Signal Processing 55(1): 120-133. 10.1109/TSP.2006.882058Search in Google Scholar