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.
Introduction
The wide success of linear system identification in various applications (Ljung 1999), “System Identification – An Overview” Lennart Ljung does not necessarily mean that the underlying dynamic systems are intrinsically linear. Quite often, linear system identification can be successfully applied to a nonlinear system if its working range is restricted to a neighborhood of some working point. Nevertheless, some advanced engineering systems may exhibit significant nonlinear behaviors under their normal working conditions, so do most biological or...
Bibliography
Bai EW (1998) An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems. Automatica 34(3):333–338
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
Bohlin T (2006) Practical grey-box process identification – theory and applications. Springer, London
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
Garnier H, Wang L (eds) (2008) Identification of continuous-time models from sampled data. Springer, London
Gauthier J-P, Kupka I (2001) Deterministic observation theory and applications. Cambridge University Press, Cambridge/New York
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
Giri F, Bai E-W (eds) (2010) Block-oriented nonlinear system identification Springer, Berlin/Heidelberg
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
Greblicki W (1992) Nonparametric identification of Wiener systems. IEEE Trans Inf Theory 38(5):1487–1493
Greblicki W, Pawlak M (1989) Nonparametric identification of Hammerstein systems. IEEE Trans Inf Theory 35(2):409–418
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
Ljung L (1999) System identification – theory for the user, 2nd edn. Prentice-Hall, Upper Saddle River
Ljung L, Glad T (1994) On global identifiability for arbitrary model parametrizations. Automatica 30(2):265–276
Nadaraya EA (1964) On estimating regression. Theory Probab Appl 9:141–142
Nelles O (2001) Nonlinear system identification. Springer, Berlin/New York
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
Rasmussen CE, Williams CKI (2006) Gaussian processes for machine learning. MIT, Cambridge
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
Specht DF (1991) A general regression neural network. IEEE Trans Neural Netw 2(5):568–576
Suykens JAK, Van Gestel T, De Brabanter J, De Moor B, Vandewalle J (2002) Least squares support vector machines. World Scientific, Singapore
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
Toth R (2010) Modeling and identification of linear parameter-varying Systems. Springer, Berlin
Wills A, Schön T, Ljung L, Ninness B (2013) Identification of Hammerstein-Wiener models. Automatica 49(1):70–81
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer-Verlag London
About this entry
Cite this entry
Zhang, Q. (2014). Nonlinear System Identification: An Overview of Common Approaches. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_104-1
Download citation
DOI: https://doi.org/10.1007/978-1-4471-5102-9_104-1
Received:
Accepted:
Published:
Publisher Name: Springer, London
Online ISBN: 978-1-4471-5102-9
eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering
Publish with us
Chapter history
-
Latest
Nonlinear System Identification: An Overview of Common Approaches- Published:
- 26 September 2019
DOI: https://doi.org/10.1007/978-1-4471-5102-9_104-2
-
Original
Nonlinear System Identification: An Overview of Common Approaches- Published:
- 29 March 2014
DOI: https://doi.org/10.1007/978-1-4471-5102-9_104-1