Abstract
A great deal of interest has recently been paid to Wiener system identification Figure 12.1. However, most proposed solutions have been developed in the case of parametric systems, see e.g.[13, 14, 15, 17, 19]. As the internal signal x(t) is not accessible for measurement, and may even be of no physical meaning, the system output then turns out to be a bilinear (but fully known) function of the unknown parameters (those of the nonlinearity, on one hand, and those of the linear subsystem, on the other hand). Such bilinearity feature has been carried out following different approaches.
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References
Bai, E.W.: Frequency domain identification of Wiener models. Automatica 39, 1521–1530 (2003)
Bruls, J., Chou, C.T., Heverkamp, B.R.J., Verhaegen, M.: Linear and nonlinear system identification using separable least squares. European Journal of Control 5, 116–128 (1999)
Carbon, M., Ghorbanzadeh, D.: Mathematical Elements for Signals. Dunod, Paris (1997) ISBN: 210 0034642
Chen, H.F.: Recursive identification for Wiener model with discontinuous piece-wise linear function. IEEE Transactions on Automatic Control 51, 390–400 (2006)
Gardiner, A.: Frequency domain identification of nonlinear systems. In: IFAC Symposium of System Identification and Estimation, Rotterdam, The Netherlands, pp. 831–834 (1993)
Giri, F., Rochdi, Y., Chaoui, F.Z.: An Analytic Geometry Approach to Wiener System Frequency Identification. IEEE Transactions on Automatic Control 54(4), 683–696 (2009)
Greblicki, W.: Nonparametric identification of Wiener systems. IEEE Transactions on Automatic Control 51, 390–400 (1992)
Greblicki, W.: Nonparametric approach to Wiener system identification. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 44, 538–545 (1997)
Greblicki, W.: Recursive identification of Wiener system. Applied Mathematics and Computer Science 11, 977–991 (2001)
Greblicki, W.: Nonlinearity recovering in Wiener system driven with correlated signal. IEEE Transactions on Automatic Control 49, 1805–1810 (2004)
Hagenblad, A., Ljung, L., Wills, A.: Maximum likelihood identification of Wiener models. Automatica 44, 2697–2705 (2008)
Hu, X.L., Chen, H.F.: Strong consistence of recursive identification for Wiener systems. Automatica 41, 1905–1916 (2005)
Hunter, I.W., Korenberg, M.J.: The identification of nonlinear biological systems: Wiener and Hammerstein cascade models. Biological Cybernetics 55, 135–144 (1986)
Nordsjö, A.E., Zetterberg, L.H.: Identification of certain time-varying nonlinear Wiener and Hammerstein systems. IEEE Transaction on Signal Processing 49, 577–592 (2001)
Pajunen, G.A.: Adaptive control of Wiener type nonlinear systems. Automatica 28, 781–785 (1992)
Pawlak, M., Hasiewicz, Z., Wachel, P.: On Nonparametric identification of Wiener systems. Transactions on Signal Processing 55(2), 482–492 (2007)
Vörös, J.: Parameter identification of Wiener systems with discontinuous nonlinearities. Systems and Control Letters 44, 363–372 (2001)
Weisstein, E.W.: Lissajous Curve. In: MathWorld (2006), a Wolfram Web Resource, http://mathworld.wolfram.com/LissajousCurve.html
Westwick, D.T., Kearney, R.E.: A new algorithm for the identification of multiple-input Wiener systems. Biological Cybernetics 68, 75–85 (1992)
Wigren, T.: Recursive prediction error identification using the nonlinear Wiener model. Automatica 29, 1011–1025 (1993)
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Giri, F., Rochdi, Y., Gning, JB., Chaoui, FZ. (2010). Frequency Identification of Nonparametric Wiener Systems. In: Giri, F., Bai, EW. (eds) Block-oriented Nonlinear System Identification. Lecture Notes in Control and Information Sciences, vol 404. Springer, London. https://doi.org/10.1007/978-1-84996-513-2_12
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