Prediction Using Relational Models

  • José Valente de Oliveira
Part of the International Series in Intelligent Technologies book series (ISIT, volume 7)

Abstract

Prediction is the problem of extrapolating a given signal sequence (or time series) into the future. The many theoretical assumptions required for the formulation of well-posed problems using relational models are stated. Specific issues of the identification and modelling of dynamic systems are studied. These include model feedback topologies, and the concerns with the maintenance of the set-theoretical (or logical) nature of fuzzy models during parameter estimation. Examples are included. A typical prediction application crystalized in the form of a predictive control algorithm is presented and applied to the control of a physical system.

Keywords

Lution Reso Estima Claris 

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References

  1. 1.
    Billings, S. A. (1980) “Identification of nonlinear systems — a survey”, IEE Proc, 127, 272.MathSciNetGoogle Scholar
  2. 2.
    Box, G.E.P, Jenkins, G.M. Time Series Analysis, Forecasting and Control, Holden Day, San Francisco.Google Scholar
  3. 3.
    Castro, J.L. “Fuzzy logic controllers are universal approximators”, IEEE Trans. on Systems, Man, and Cybernetics, Vol 25, No 4, 1995, pp. 629–635.CrossRefGoogle Scholar
  4. 4.
    Klir, G.F., and Folger, T.A., Fuzzy Sets, Uncertainty, and Information, (Engle-wood Cliffs, N.J., Prentice-Hall).Google Scholar
  5. 5.
    Kosko, B., (1992) Neural Networks and Fuzzy Systems (Englewood Cliffs, NJ: Prentice Hall).MATHGoogle Scholar
  6. 6.
    Lee, O.C. (1990), “Fuzzy logic in control systems: fuzzy logic controller — part I and II”, IEEE Trans, on Systems, Man, and Cybernetics, 20, pp. 404–418, 419–435.MATHCrossRefGoogle Scholar
  7. 7.
    Ljung, L. (1987) System Identification: Theory for the user, Prentice-Hall, Englewood Cliffs, NJ.MATHGoogle Scholar
  8. 8.
    Mosca, E., Zappa, C, and Lemos, J.M., “Robustness of multipredictor adaptive regulators: MUSMAR”, (1989), Automatica 25 521–529.MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Narendra, k.S., Annaswamy, A. M. (1989) Stable Adaptive Systems, (Englewood Cliffs, N.J, Prentice-Hall).MATHGoogle Scholar
  10. 10.
    Narendra, K. S., Parthasarathy, K. (1990), “Identification and control of dynamic systems using neural networks”, IEEE Trans, on Neural Networks, vol. 1, no. 1, pp. 4–26.CrossRefGoogle Scholar
  11. 11.
    Nijmeijer, H. and Van der Schaft, A.J., (1990) Non-linear Dynamical Control of Systems, New York: Springer-Verlag.Google Scholar
  12. 12.
    Pedrycz, W. (1984) “An identification algorithm in fuzzy relational systems”, Fuzzy Sets and Systems, vo. 13, pp.153–167.MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Pedrycz, W. (1993) Fuzzy Control and Fuzzy Systems (Research Studies Press/J. Wiley & Sons, Chichester).MATHGoogle Scholar
  14. 14.
    Pedrycz, W. and Valente de Oliveira, J. (1993), “Optimization of fuzzy relational models”, Proc. 5th IFSA World Congress, Seoul, pp. 1187–1190.Google Scholar
  15. 15.
    Pedrycz, W., and Valente de Oliveira, J., (1994), “Fuzzy relational modelling of dynamic systems with regenerative I/O interfaces”, Proc. IEEE Conf. on Fuzzy Sys., Orlando, FL, 372–377.Google Scholar
  16. 16.
    Rao S.S., (1978), Optimization: Theory and Applications (Bombay: Wiley Eastern Limited)Google Scholar
  17. 17.
    Valente de Oliveira, J., (1993), “Neuron inspired learning rules for fuzzy relational structures”, Fuzzy Sets and Systems 57 41–53.MathSciNetCrossRefGoogle Scholar
  18. 18.
    Valente de Oliveira, J., (1993), “On optimal fuzzy systems I/O interfaces”, (1993) Proc. of the Second IEEE Int. Conf. on Fuzzy Systems, San Francisco, CA, pp. 851–856.Google Scholar
  19. 19.
    Valente de Oliveira, J., (1993), “A design methodology for fuzzy systems interfaces” IEEE Trans, on Fuzzy Systems, accepted for publication.Google Scholar
  20. 20.
    Valente de Oliveira, J. and Lemos, J.M. (1995), “Long-range predictive adaptive fuzzy relational control”, Fuzzy Sets and Systems, 70 337–357.MathSciNetCrossRefGoogle Scholar
  21. 21.
    Valente de Oliveira, J. (1995), “Sampling, fuzzy discretization, and signal reconstruction”, Fuzzy Sets and Systems, in press.Google Scholar
  22. 22.
    Van der Rhee, F. (1988), “Fuzzy modelling and control based on cell structures”, PhD dissertation, Delft University of Technology.Google Scholar
  23. 23.
    Willaeys, D. and Malvache, N., (1981) “The use of fuzzy sets for the treatment of fuzzy information by computer”, Fuzzy Sets and Systems 5 323–327.MATHCrossRefGoogle Scholar
  24. 24.
    Zadeh, L. A., (1971) “Toward a theory of fuzzy systems”, Aspects on Networks and Systems Theory, Kaiman, R. E., De Claris, N. (Edts). Holt, Rinehart, Winston, New York, pp. 209–245.Google Scholar
  25. 25.
    Zeng, X.-J., Singh, M. G. (1994) “Approximation theory of fuzzy systems — SISO Case”, IEEE Trans, on Fuzzy Systems, vol. 2, no. 2, pp. 162–176.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • José Valente de Oliveira
    • 1
  1. 1.Research Group on Control of Dynamic SystemsINESCLisboaPortugal

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