Advertisement

Fuzzy Dynamic Systems: Analysis, Control and Identification

  • A. N. Venetsanopoulos
  • S. G. Tzafestas
  • S. Terzakis
Part of the International Series on Microprocessor-Based and Intelligent Systems Engineering book series (ISCA, volume 11)

Abstract

This chapter dels with fuzzy dynamic systems paying attention to three important issues, namely analysis, control and identification. Analysis is concernced with the study of input- output descriptions which are based on fuzzy relational equations. One of the models that played a central role in the analysis of classical (crisp) dynamic systems is the state-space model. This model can be extended to cover the case of fuzzy dynamic systems, and is studied in the present chapter. Control is concerned with the problem of determining a control sequence which brings the system state, in one or more time steps, from the present fuzzy value Xk to a desired final fuzzy value Xf. This problem is equivalent ot solving the relevant equation Xf=UkoXkoR with respect to Uk. The fuzzy system identification problem solved here consists in estimating the system fuzzy relational matrix R from a given set of fuzzy input-outpu pairs (Xi, Yi), i=1,2...,N. The non-noise case is considered, since the case where noise is present is still a challenging open problem. An algorithm is provided for determining good upper and lower bounds that confince R. Also, the state prediction problem of fuzzy state space models is considered. The chapter closes with a review of three practical fuzzy controllers which have been applied with success to several industrial systems. These controllers are: (i) the fuzzy self-organized controller (SOC), the fuzzy PID supervisor, and the fuzzy PID incremental controller.

Keywords

Relational Equation Fuzzy System Fuzzy Controller Fuzzy Subset Fuzzy Relation 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L.A. Zadeh: Fuzzy Sets, Inform, and Control, Vol. 8, pp. 338–353, 1965.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    L.A. Zadeh: Outline of a New Approach to the Analysis of Complex Systems and Decision Processes, IEEE Trans. Syst. Man, Cybern., Vol. SMC-3, pp. 28–44, 1973.MathSciNetGoogle Scholar
  3. 3.
    W. Pedrycz: An Approach to the Analysis of Fuzzy Sytems, Int. J. Control, Vol. 34, No.3, pp. 403–421, 1981.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    E. Sanchez: Eigenfuzzy Sets and Fuzzy Relations, J. Math. Anal. Appl., Vol. 81, pp. 399–421, 1981.MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    E.H. Mamdani, and T. J. Procyk: A linguistic self-organizing process controller, Automatica, Vol.15, pp. 15–30, 1979.CrossRefGoogle Scholar
  6. 6.
    H.R. Van Nauta Lemke, and W. De-Zhao: Fuzzy PID supervisor, 24th IEEE CDC. Paper WP9-5:15, pp. 602–608. Ft. Lauderdale, FL. 1985.Google Scholar
  7. 7.
    S.G. Tzafestas, and N. Papanikolopoulos: Intelligent PID control based on fuzzy logic, Proc. IFAC Symp. on Distributed Intelligence Systems Methods and Applications (DIS’ 88), Varna — Bulgaria, June 1988.Google Scholar
  8. 8.
    P.J. MacVicar-Whelan: Fuzzy sets for man-machine interaction, Intl. J. Man-Machine Studies, Vol. 8, 687–697, 1976.MATHCrossRefGoogle Scholar
  9. 9.
    P.J. King and E.H. Mamdani: The application of fuzzy control systems to industrial processes, Proc 6th IFAC World Congress, Boston 1975, Automatica, Vol 13, pp. 235–242, 1977.CrossRefGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • A. N. Venetsanopoulos
    • 1
  • S. G. Tzafestas
    • 2
  • S. Terzakis
    • 2
  1. 1.Department of Electrical EngineeringUniversity of TorontoTorontoCanada
  2. 2.Intelligent Robotics and Control UnitNational Technical University of Athens Zografou CampusAthensGreece

Personalised recommendations