Abstract
Identification of systems that can be written as interconnected linear time-invariant (LTI) dynamical subsystems and static nonlinearities has been an active research area for several decades. These systems are often referred to as block-oriented systems since their structures can be characterised using linear dynamical and static nonlinear blocks. In particular, block-oriented systems where the blocks are connected in series have received special attention. For example, Wiener and Hammerstein systems are common examples of series connected block-oriented systems.
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References
Atalik, T.S., Utku, S.: Stochastic linearization of multi-degree-of-freedom non-linear systems. Earthquake Engineering and Structural Dynamics 4, 411–420 (1976)
Atherton, D.P.: Nonlinear Control Engineering, student edn. Van Nostrand Reinhold, New York (1982)
Barrett, J.F., Lampard, D.G.: An expansion for some second-order probability distributions and its application to noise problems. IRE Transactions on Information Theory 1(1), 10–15 (1955)
Billings, S.A., Fakhouri, S.Y.: Theory of separable processes with applications to the identification of nonlinear systems. Proceedings of the IEE 125(9), 1051–1058 (1978)
Billings, S.A., Fakhouri, S.Y.: Identification of systems containing linear dynamic and static nonlinear elements. Automatica 18(1), 15–26 (1982)
Booton Jr., R.C.: Nonlinear control systems with random inputs. IRE Transactions on Circuit Theory 1(1), 9–18 (1954)
Brillinger, D.R.: The identification of a particular nonlinear time series system. Biometrika 64(3), 509–515 (1977)
Brown Jr., J.L.: On a cross-correlation property for stationary random processes. IRE Transactions on Information Theory 3(1), 28–31 (1957)
Bussgang, J.J.: Crosscorrelation functions of amplitude-distorted Gaussian signals. Technical Report 216, MIT Research Laboratory of Electronics, Cambridge, Massachusetts (1952)
Crama, P., Schoukens, J.: Initial estimates of Wiener and Hammerstein systems using multisine excitation. IEEE Transactions on Instrumentation and Measurement 50(6), 1791–1795 (2001)
Crama, P., Schoukens, J.: Hammerstein-Wiener system estimator initialization. Automatica 40(9), 1543–1550 (2004)
Crama, P., Schoukens, J.: Computing an initial estimate of a Wiener-Hammerstein system with a random phase multisine excitation. IEEE Transactions on Instrumentation and Measurement 54(1), 117–122 (2005)
Enqvist, M.: Linear Models of Nonlinear Systems. PhD thesis, Linköping University, Linköping, Sweden (2005)
Enqvist, M.: Identification of Hammerstein systems using separable random multisines. In: Proceedings of the 14th IFAC Symposium on System Identification, Newcastle, Australia, pp. 768–773 (2006)
Enqvist, M., Ljung, L.: Linear approximations of nonlinear FIR systems for separable input processes. Automatica 41(3), 459–473 (2005)
Gardner, W.A.: Introduction to Random Processes. Macmillan Publishing Company, New York (1986)
Gut, A.: An Intermediate Course in Probability. Springer, New York (1995)
Hunter, I.W., Korenberg, M.J.: The identification of nonlinear biological systems: Wiener and Hammerstein cascade models. Biological Cybernetics 55, 135–144 (1986)
Kailath, T., Sayed, A.H., Hassibi, B.: Linear Estimation. Prentice Hall, Upper Saddle River (2000)
Khalil, H.K.: Nonlinear Systems, 3rd edn. Prentice Hall, Upper Saddle River (2002)
Korenberg, M.J.: Identifying noisy cascades of linear and static nonlinear systems. In: Proceedings of the 7th IFAC Symposium on Identification and System Parameter Estimation, York, UK, pp. 421–426 (1985)
Li, K.-C.: Sliced inverse regression for dimension reduction. Journal of the American Statistical Association 86(414), 316–327 (1991)
Li, K.-C.: On principal Hessian directions for data visualization and dimension reduction: Another application of Stein’s lemma. Journal of the American Statistical Association 87(420), 1025–1039 (1992)
Ljung, L.: Convergence analysis of parametric identification methods. IEEE Transactions on Automatic Control 23(5), 770–783 (1978)
Ljung, L.: System Identification: Theory for the User, 2nd edn. Prentice Hall, Upper Saddle River (1999)
Ljung, L.: Estimating linear time-invariant models of nonlinear time-varying systems. European Journal of Control 7(2-3), 203–219 (2001)
Lutes, L.D., Sarkani, S.: Stochastic Analysis of Structural and Mechanical Vibrations. Prentice Hall, Upper Saddle River (1997)
McGraw, D.K., Wagner, J.F.: Elliptically symmetric distributions. IEEE Transactions on Information Theory 14(1), 110–120 (1968)
Nuttall, A.H.: Theory and application of the separable class of random processes. Technical Report 343, MIT Research Laboratory of Electronics, Cambridge, Massachusetts (1958)
Nuttall, A.H.: Theory and Application of the Separable Class of Random Processes. PhD thesis, MIT, Cambridge, Massachusetts (1958)
Scarano, G., Caggiati, D., Jacovitti, G.: Cumulant series expansion of hybrid nonlinear moments of n variates. IEEE Transactions on Signal Processing 41(1), 486–489 (1993)
Schetzen, M.: The Volterra & Wiener Theories of Nonlinear Systems. John Wiley & Sons, Chichester (1980)
Wiener, N.: Extrapolation, Interpolation and Smoothing of Stationary Time Series. Technology Press & Wiley, New York (1949)
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Enqvist, M. (2010). Identification of Block-oriented Systems Using the Invariance Property. 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_10
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DOI: https://doi.org/10.1007/978-1-84996-513-2_10
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