Encyclopedia of Systems and Control

2015 Edition
| Editors: John Baillieul, Tariq Samad

Nonlinear System Identification: An Overview of Common Approaches

  • Qinghua Zhang
Reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5058-9_104

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.

Keywords

Black-box models Block-oriented models Gray-box models Nonlinear system identification 
This is a preview of subscription content, log in to check access.

Bibliography

  1. Bai EW (1998) An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems. Automatica 34(3):333–338MathSciNetGoogle Scholar
  2. 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):910–919MathSciNetGoogle Scholar
  3. Bohlin T (2006) Practical grey-box process identification – theory and applications. Springer, LondonGoogle Scholar
  4. 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, OxfordGoogle Scholar
  5. Garnier H, Wang L (eds) (2008) Identification of continuous-time models from sampled data. Springer, LondonGoogle Scholar
  6. Gauthier J-P, Kupka I (2001) Deterministic observation theory and applications. Cambridge University Press, Cambridge/New YorkGoogle Scholar
  7. Gerdin M, Schön T, Glad T, Gustafsson F, Ljung L (2007) On parameter and state estimation for linear differential-algebraic equations. Automatica 43:416–425Google Scholar
  8. Giri F, Bai E-W (eds) (2010) Block-oriented nonlinear system identification Springer, Berlin/HeidelbergGoogle Scholar
  9. 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):767–775MathSciNetGoogle Scholar
  10. Greblicki W (1992) Nonparametric identification of Wiener systems. IEEE Trans Inf Theory 38(5):1487–1493Google Scholar
  11. Greblicki W, Pawlak M (1989) Nonparametric identification of Hammerstein systems. IEEE Trans Inf Theory 35(2):409–418MathSciNetGoogle Scholar
  12. 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):1725–1750Google Scholar
  13. Ljung L (1999) System identification – theory for the user, 2nd edn. Prentice-Hall, Upper Saddle RiverGoogle Scholar
  14. Ljung L, Glad T (1994) On global identifiability for arbitrary model parametrizations. Automatica 30(2):265–276MathSciNetGoogle Scholar
  15. Nadaraya EA (1964) On estimating regression. Theory Probab Appl 9:141–142Google Scholar
  16. Nelles O (2001) Nonlinear system identification. Springer, Berlin/New YorkGoogle Scholar
  17. 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):647–656MathSciNetGoogle Scholar
  18. Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. MIT, CambridgeGoogle Scholar
  19. 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):1691–1724Google Scholar
  20. Specht DF (1991) A general regression neural network. IEEE Trans Neural Netw 2(5):568–576Google Scholar
  21. Suykens JAK, Van Gestel T, De Brabanter J, De Moor B, Vandewalle J (2002) Least squares support vector machines. World Scientific, SingaporeGoogle Scholar
  22. Takagi T, Sugeno M (1985) Fuzzy identification of systems and its applications to modeling and control. IEEE Trans Syst Man Cybern 15(1):116–132Google Scholar
  23. Toth R (2010) Modeling and identification of linear parameter-varying Systems. Springer, BerlinGoogle Scholar
  24. Wills A, Schön T, Ljung L, Ninness B (2013) Identification of Hammerstein-Wiener models. Automatica 49(1):70–81MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London 2015

Authors and Affiliations

  • Qinghua Zhang
    • 1
  1. 1.InriaCampus de BeaulieuRennes CedexFrance