Nonlinear System Identification with Neurofuzzy Methods

  • Oliver Nelles


This chapter discusses nonlinear system identification with neurofuzzy methods. In a general part, summary and overview of the most important types of fuzzy models are given. Their properties, advantages, and drawbacks are illustrated. In a more specific part a new algorithm for the construction of Takagi-Sugeno fuzzy systems is presented in detail. It is successfully applied to the identification of two nonlinear dynamic real-world processes.


Membership Function Fuzzy System Fuzzy Model Validity Function Gaussian Membership Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [Babuška and Verbruggen, 1996]
    Babuška, R. and Verbruggen, H. (1996), “An overview of fuzzy modeling for control,” Control Engineering Practice 4:11.Google Scholar
  2. [Bellman, 1961]
    Bellman, R. (1961), Adaptive Control Processes, Princeton University Press, NJ.zbMATHGoogle Scholar
  3. [Boy, 1980]
    Boy, P. (1980), Beitrag zur Berechnung des instationären Betriebsverhaltens von mittelschnelllaufenden chiffsdieselmotoren, Dissertationen TU Hannover, Hannover.Google Scholar
  4. [Brown and Harris, 1994]
    Brown, M. and Harris, C. (1994), Neurofuzzy Adaptive Modelling and Control, Prentice Hall, New York.Google Scholar
  5. [Chen et al., 1991]
    Chen, S., Cowan, C., and Grant, P. (1991), “Orthogonal least-squares learning algorithm for radial basis function networks,” IEEE Transactions on Neural Networks 2:2.CrossRefGoogle Scholar
  6. [Friedman, 1991]
    Friedman, J. (1991), “Multivariate adaptive regression splines (with discussion),” Annals of Statistics. Google Scholar
  7. [Geman et al., 1992]
    Geman, S., Bienenstock, E., and Doursat, R. (1992), “Neural networks and the bias/variance dilemma,” Neural Computation 4.Google Scholar
  8. [Golub and Loan, 1987]
    Golub, G. and Loan, C. V. (1987), Matrix Computations, Mathematical Sciences. The Johns Hopkins University Press.Google Scholar
  9. [Hecker et al., 1997]
    Hecker, O., Nelles, O., and Moseler, O. (1997), “Nonlinear system identification and predictive control of a heat exchanger based on local linear model trees,” American Control Conference (ACC), Albuquerque.Google Scholar
  10. [Hunt et al., 1996]
    Hunt, K., Haas, R., and Murray-Smith, R. (1996), “Extending the functional equivalence of radial basis functions networks and fuzzy inference systems,” IEEE Transactions on Neural Networks 7:3.CrossRefGoogle Scholar
  11. [Isermann, 1992]
    Isermann, R. (1992), Identifikation dynamischer Systeme—Band 1, Springer, Berlin.Google Scholar
  12. [Isermann et al., 1997]
    Isermann, R., Ernst, S., and Nelles, O. (1997), “Identification with dynamic neural networks—architectures, comparisons, applications (plenary),” IFAC Symposium on System Identification (SYSID), Fukuoka.Google Scholar
  13. [Johansen and Foss, 1993]
    Johansen, T. and Foss, B. (1993), “Constructing narmax models using armax models,” International Journal of Control, 58:5.MathSciNetCrossRefGoogle Scholar
  14. [Kim and Mendel, 1995]
    Kim, H and Mendel, J. (1995), “Fuzzy basis functions: comparisons with other basis functions,” IEEE Transactions on Fuzzy Systems 3:2.Google Scholar
  15. [Kortmann, 1989]
    Kortmann, M. (1989), Die Identifikation nichtlinearer Ein-und Mehrgr ensysteme auf der Basis nichtlinearer Modellans tze,Number 177. VDI Verlag, Reihe 8: Me -, Steuerungs-und Regelungstechnik, Düsseldorf.Google Scholar
  16. [Kroll, 1996]
    Kroll, A. (1996), “Identification of functional fuzzy models using multidimensional reference fuzzy sets,” Fuzzy Sets and Systems 80.Google Scholar
  17. [Leontaritis and Billings, 1985]
    Leontaritis, I. and Billings, S. (1985), “Input-output parametric models for nonlinear systems, part 1: Deterministic nonlinear systems,” International Journal of Control 41.Google Scholar
  18. [Lindskog, 1996]
    Lindskog, P. (1996), Methods, Algorithms and Tools for System Identification Based on Prior Knowledge, Number 436 Link ping Studies in Science and Technology. Dissertations, Linköping.Google Scholar
  19. [Ljung, 1987]
    Ljung, L. (1987), System Identification—Theory for the User, Prentice-Hall, Englewood Cliffs, NJ.zbMATHGoogle Scholar
  20. [Mendel, 1995]
    Mendel, J. (1995), “Fuzzy logic systems for engineering: a tutorial,” Proceedings of the IEEE 83:3.CrossRefGoogle Scholar
  21. [Miller, 1990]
    Miller, A. (1990), Subset Selection in Regression, Statistics and Applied Probability, Chapman and Hall, London.Google Scholar
  22. [Murray-Smith, 1994]
    Murray-Smith, R. (1994), A Local Model Network Approach to Nonlinear Modeling, PhD thesis University of Strathclyde.Google Scholar
  23. [Nelles, 1997]
    Nelles, O. (1997),Orthonormal basis functions for nonlinear system identification with local linear model trees (lolimot)IFAC Symposium on System Identification (SYSID), Fukuoka.Google Scholar
  24. [Nelles and Fischer, 1996]
    Nelles, O. and Fischer, M. (1996), “Local linear model trees (lolimot) for nonlinear system identification of a cooling blast,” European Congress on Intelligent Techniques and Soft Computing (EUFIT), Aachen.Google Scholar
  25. Nelles, O., Hecker, O., and Isermann, R. (1997), “Automatic model selection in local linear model trees for nonlinear system identification of a transport delay process,” IFAC Symposium on System Identification (SYSID),Fukuoka.Google Scholar
  26. [Nelles and Isermann, 1996]
    Nelles, O. and Isermann, R. (1996), “Basis function networks for interpolation of local linear models,” IEEE Conference on Decision and Control (CDC), Kobe.Google Scholar
  27. [Nelles et al., 1996]
    Nelles, O., Sinsel, S., and Isermann, R. (1996), “Local basis function networks for identification of a turbocharger,” IEE UKACC International Conference on Control, Exeter.Google Scholar
  28. [Pucher, 1985]
    Pucher, H. (1985), Aufladung von Verbrennungsmotoren, Expert-Verlag, Sindelfingen.Google Scholar
  29. [Sjöberg, 1995]
    Sjöberg, J. (1995), Nonlinear System Identification with Neural Networks, Number 381. Link ping Studies in Science and Technology. Dissertations, Linköping.Google Scholar
  30. [Sugeno and Kang, 1988]
    Sugeno, M. and Kang, G. (1988), “Structure identification of fuzzy model,” Fuzzy Sets and Systems 28:1.MathSciNetCrossRefGoogle Scholar
  31. [Wang and Mendel, 1992]
    Wang, L.-X. and Mendel, J. (1992), “Fuzzy basis function, universal approximation and orthogonal least-squares learning,” IEEE Transactions on Neural Networks 3:5.CrossRefGoogle Scholar
  32. [Werntges, 1993]
    Werntges, H. (1993), “Partitions of unity improve neural function approximators,” IEEE International Conference on Neural Networks (ICNN), San Francisco.Google Scholar
  33. [Zinner, 1985]
    [Zinner, 1985] Zinner, K. (1985). Aufladung von Verbrennungsmotoren. Springer, Berlin.Google Scholar

Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Oliver Nelles
    • 1
  1. 1.Institut für RegelungstechnikTechnische Hochschule DarmstadtDarmstadtGermany

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