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Nonlinear System Identification: An Overview of Common Approaches

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Encyclopedia of Systems and Control
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Abstract

Nonlinear mathematical models are essential tools in various engineering and scientific domains, where more and more data are recorded by electronic devices. How to build nonlinear mathematical models essentially based on experimental data is the topic of this entry. Due to the large extent of the topic, this entry provides only a rough overview of some well-known results, from gray-box to black-box system identification.

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Bibliography

  • Bai EW (1998) An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems. Automatica 34(3):333–338

    MathSciNet  Google Scholar 

  • Bai E-W, Reyland Jr J (2008) Towards identification of Wiener systems with the least amount of a priori information on the nonlinearity. Automatica 44(4):910–919

    MathSciNet  Google Scholar 

  • Bohlin T (2006) Practical grey-box process identification – theory and applications. Springer, London

    Google Scholar 

  • Doucet A, Johansen AM (2011) A tutorial on particle filtering and smoothing: fifteen years later. In: Crisan D, Rozovsky B (eds) Nonlinear filtering handbook. Oxford University Press, Oxford

    Google Scholar 

  • Garnier H, Wang L (eds) (2008) Identification of continuous-time models from sampled data. Springer, London

    Google Scholar 

  • Gauthier J-P, Kupka I (2001) Deterministic observation theory and applications. Cambridge University Press, Cambridge/New York

    Google Scholar 

  • Gerdin M, Schön T, Glad T, Gustafsson F, Ljung L (2007) On parameter and state estimation for linear differential-algebraic equations. Automatica 43:416–425

    Google Scholar 

  • Giri F, Bai E-W (eds) (2010) Block-oriented nonlinear system identification Springer, Berlin/Heidelberg

    Google Scholar 

  • Giri F, Rochdi Y, Chaoui FZ, Brouri A (2008) Identification of Hammerstein systems in presence of hysteresis-backlash and hysteresis-relay nonlinearities. Automatica 44(3):767–775

    MathSciNet  Google Scholar 

  • Greblicki W (1992) Nonparametric identification of Wiener systems. IEEE Trans Inf Theory 38(5):1487–1493

    Google Scholar 

  • Greblicki W, Pawlak M (1989) Nonparametric identification of Hammerstein systems. IEEE Trans Inf Theory 35(2):409–418

    MathSciNet  Google Scholar 

  • Juditsky A, Hjalmarsson H, Benveniste A, Delyon B, Ljung L, Sjöberg J, Zhang Q (1995) Nonlinear black-box models in system identification: mathematical foundations. Automatica 31(11):1725–1750

    Google Scholar 

  • Ljung L (1999) System identification – theory for the user, 2nd edn. Prentice-Hall, Upper Saddle River

    Google Scholar 

  • Ljung L, Glad T (1994) On global identifiability for arbitrary model parametrizations. Automatica 30(2):265–276

    MathSciNet  Google Scholar 

  • Nadaraya EA (1964) On estimating regression. Theory Probab Appl 9:141–142

    Google Scholar 

  • Nelles O (2001) Nonlinear system identification. Springer, Berlin/New York

    Google Scholar 

  • Paduart J, Lauwers L, Swevers J, Smolders K, Schoukens J, Pintelon R (2010) Identification of nonlinear systems using polynomial nonlinear state space models. Automatica 46(4):647–656

    MathSciNet  Google Scholar 

  • Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. MIT, Cambridge

    Google Scholar 

  • Sjöberg J, Zhang Q, Ljung L, Benveniste A, Delyon B, Glorennec P-Y, Hjalmarsson H, Juditsky A (1995) Non-linear black-box modeling in system identifications unified overview. Automatica 31(11):1691–1724

    Google Scholar 

  • Specht DF (1991) A general regression neural network. IEEE Trans Neural Netw 2(5):568–576

    Google Scholar 

  • Suykens JAK, Van Gestel T, De Brabanter J, De Moor B, Vandewalle J (2002) Least squares support vector machines. World Scientific, Singapore

    Google Scholar 

  • Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 15(1):116–132

    Google Scholar 

  • Toth R (2010) Modeling and identification of linear parameter-varying Systems. Springer, Berlin

    Google Scholar 

  • Wills A, Schön T, Ljung L, Ninness B (2013) Identification of Hammerstein-Wiener models. Automatica 49(1):70–81

    MathSciNet  Google Scholar 

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Zhang, Q. (2015). Nonlinear System Identification: An Overview of Common Approaches. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5058-9_104

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