System identification of Wiener systems with B-spline functions using De Boor recursion

References

• Bai , EW . 1998 . An Optimal Two-stage Identification Algorithm for Hammerstein–Wiener Nonlinear Systems . Automatica , 34 : 333 – 338 .
   Web of Science ®Google Scholar
• Bai , EW and Fu , MY . 2002 . A Blind Approach to Hammerstein Model Identification . IEEE Transactions on Signal Processing , 50 : 1610 – 1619 .
   Web of Science ®Google Scholar
• Bai , EW and Li , K . 2010 . Convergence of the Iterative Algorithm for a General Hammerstein System Identification . Automatica , 46 : 1891 – 1896 .
   Web of Science ®Google Scholar
• Bai , EW and Reyland , J . 2008 . Toward Identification of Wiener Systems with the Least Amount of a Prior Information on the Nonlinearity . Automatica , 44 : 910 – 919 .
   Web of Science ®Google Scholar
• Bai , EW and Reyland , J . 2009 . Toward Identification of Wiener Systems with the Least Amount of a Prior Information: IIR Cases . Automatica , 45 : 956 – 964 .
   PubMed Web of Science ®Google Scholar
• Balestrino , A , Landi , A , Ould-Zmirli , M and Sani , L . 2001 . Automatic Nonlinear Autotuning Method for Hammerstein Modelling of Electrical Drives . IEEE Transactions on Industrial Electronics , 48 : 645 – 655 .
   Web of Science ®Google Scholar
• Billings , SA and Fakhouri , SY . 1979 . Nonlinear System Identification using the Hammerstein Model . International Journal of Systems Science , 10 : 567 – 578 .
   Web of Science ®Google Scholar
• Bloemen , HHJ , Van Den Boom , TJ and Verbruggen , HB . 2001 . Model-based Predictive Control for Hammerstein–Wiener Systems . International Journal of Control , 74 : 482 – 295 .
   Web of Science ®Google Scholar
• Brown , M and Harris , CJ . 1994 . Neurofuzzy Adaptive Modelling and Control , Hemel Hempstead : Prentice Hall .
   Google Scholar
• Chaoui , FZ , Giri , F , Rochdi , Y , Haloua , M and Naitali , A . 2005 . System Identification Based Hammerstein Model . International Journal of Control , 78 : 430 – 442 .
   Web of Science ®Google Scholar
• Chen , HF . 2004 . Pathwise Convergence of Recursive Identification Algorithms for Hammerstein Systems . IEEE Transactions on Automatic Control , 49 : 1873 – 1896 .
   Web of Science ®Google Scholar
• De Boor , C . 1978 . A Practical Guide to Splines , New York : Spring Verlag .
   Google Scholar
• Farin , G . 1994 . Curves and Surfaces for Computer-aided Geometric Design: A Practical Guide , Boston : Academic Press .
   Google Scholar
• Farouki , RT and Goodman , TNT . 1996 . On the Optimal Stability of the Bernstein Basis . Mathematics of Computation , 65 : 1553 – 1566 .
   Web of Science ®Google Scholar
• Gomez , JC , Jutan , A and Baeyens , E . 2004 . Wiener Model Identification and Predictive Control of a pH Neutralisation Process . IEE Proceedings – Control Theory and Applications , 151 : 329 – 338 .
   Google Scholar
• Greblicki , W . 1989 . Nonparametric Orthogonal Series Identification of Hammerstein Systems . International Journal of Systems Science , 20 : 2355 – 2367 .
   Web of Science ®Google Scholar
• Greblicki , W . 1992 . Nonparametric Identification of Wiener Systems . IEEE Transactions on Information Theory , 38 : 1487 – 1493 .
   Web of Science ®Google Scholar
• Greblicki , W . 2002 . Stochastic Approximation in Nonparametric Identification of Hammerstein Systems . IEEE Transactions on Automatic Control , 47 : 1800 – 1810 .
   Web of Science ®Google Scholar
• Greblicki , W and Pawlak , M . 1986 . Identification of Discrete Hammerstein Systems using Kernel Regression Estimate . IEEE Transactions on Automatic Control , AC-31 : 74 – 77 .
   Web of Science ®Google Scholar
• Hagenblad , A , Ljung , L and Wills , A . 2008 . Maximum Likelihood Identification of Wiener Models . Automatica , 44 : 2697 – 2705 .
   Web of Science ®Google Scholar
• Harris , CJ , Hong , X and Gan , Q . 2002 . Adaptive Modelling, Estimation and Fusion from Data: A Neurofuzzy Approach , Berlin : Springer-Verlag .
   Google Scholar
• Hong , X and Mitchell , RJ . 2007 . A Hammerstein Model Identification Algorithm using Bezier–Bernstein Approximation . IEE Proceedings: Control Theory and Applications , 1 : 1149 – 1159 .
   Google Scholar
• Hsu , K , Vincent , T and Poolla , K . 2006 . “ A Kernel-Based Approach to Structured Nonlienar System Identification Part I: Algorithms, Part II: Convergence and Consistency ” . In in Proceedings of 14th IFAC Symposium on System Identification Australia
   Google Scholar
• Hughes , MC and Westwick , DT . 2005 . Identification of IIR Wiener System with Spline Nonliearitis that have Variable Knots . IEEE Transactions on Automatic Control , 50 : 1617 – 1622 .
   Web of Science ®Google Scholar
• Hunter , IW and Korenberg , MJ . 1986 . The Identification of Nonlinear Biological Systems: Wiener and Hammerstein Cascade Models . Biological Cybernetics , 55 : 135 – 144 .
   PubMed Web of Science ®Google Scholar
• Kalafatis , AD , Arifinand , N , Wang , L and Cluett , WR . 1995 . A New Approach to the Identification of pH Processes on the Wiener Model . Chemical Engineering Science , 50 : 3693 – 3701 .
   Web of Science ®Google Scholar
• Kalafatis , AD , Wang , L and Cluett , WR . 1997 . Identification of Wiener-type Nonlinear Systems in a Noisy Environment . International Journal of Control , 66 : 923 – 941 .
   Web of Science ®Google Scholar
• Kavli , T . 1993 . ASMOD – an Algorithm for Adaptive Spline Modelling of Observation Data . International Journal of Control , 58 : 947 – 967 .
   Web of Science ®Google Scholar
• Lang , ZQ . 1997 . A Nonparametric Polynomial Identification Algorithm for the Hammerstein System . IEEE Transactions on Automatic Control , 42 : 1435 – 1441 .
   Web of Science ®Google Scholar
• Schoukens , J , Nemeth , JG , Crama , P , Rolain , Y and Pintelon , R . 2003 . Fast Approximate Identification of Nonliear Systems . Automatica , 39 : 1267 – 1274 .
   Web of Science ®Google Scholar
• Skrjanc , I , Blazic , S and Agamennoni , OE . 2005 . Interval Fuzzy Modelling Applied to Wiener Models with Uncertainties . IEEE Transactions on Systems, Man and Cybernetics – Part B: Cybernetics , 35 : 1092 – 1095 .
   PubMed Web of Science ®Google Scholar
• Soderström , T and Stoica , P . 1989 . System Identification , Upper Saddle River, NJ : Prentice Hall .
   Google Scholar
• Stoica , P and Söderström , T . 1982 . Instrumental Variable Methods for Identification of Hammerstein Systems . International Journal of Control , 35 : 459 – 476 .
   Web of Science ®Google Scholar
• Turunen , J , Tanttu , JT and Loula , P . 2003 . Hammerstein Model for Speech Coding . EURASIP Journal of Applied Signal Processing , 12 : 1238 – 1249 .
   Google Scholar
• Verhaegen , M and Westwick , D . 1996 . Identifying MIMO Hammerstein Systems in the Context of Subspace Model Identification . International Journal of Control , 63 : 331 – 349 .
   Web of Science ®Google Scholar
• Westwick , D . 1996 . Identifying MIMO Wiener Systems using Subspace Model Identification Model Identification Methods . Signal Processing , 52 : 235 – 258 .
   Web of Science ®Google Scholar
• Wigren , T . 1993 . Recursive Prediction Error Identification using the Nonlinear Wiener Model . Automatica , 29 : 1011 – 1025 .
   Web of Science ®Google Scholar
• Wigren , T . 1994 . Convergence Analysis of Recursive Identification Algorithms Based on the Nonlinear Wiener Model . IEEE Transactions on Automatic Control , 39 : 2191 – 2206 .
   Web of Science ®Google Scholar
• Zhang , Q , Iouditski , A and Ljung , L . 1996 . “ Identification of Wiener System with Monotonous Nonliearity ” . In in IFAC Symposium on System Identification 166 – 171 . Newcastle, Australia
   Google Scholar
• Zhu , Y . 1999 . Distillution Column Identification for Control using Wiener Model . Proceedings of the American Control Conference . 1999 . pp. 3462 – 3466 . San Diego, CA , , USA
   Google Scholar
• Zhu , Y . 2002 . Estimation of an N–L–N Hammerstein–Wiener Model . Automatica , 38 : 1607 – 1614 .
   Web of Science ®Google Scholar