Advertisement

Automatic Optimal Design of Fuzzy Systems Based on Universal Approximation and Evolutionary Programming

  • Mattias Nyberg
  • Yoh-Han Pao
Part of the International Series in Intelligent Technologies book series (ISIT, volume 3)

Abstract

The theory of fuzzy sets was initiated in 1965 by Zadeh [1]. Since then, it has been expanded and has found its way into a large number of applicationa, for exmaple in the areas of experts systems and control (Mamdani 1975 was the pioneer in control [2]). For several applications areas, there are many examples of solutions based on fuzzy sets that outperform traditional solutions, exmplaes in control are for control of cemnet kiln [3], car parking [4] and automatic train operation [5]. The reason fof this is its unique properties of handling nonlinearity as well as uncertainty. An advantage of fuzzy systems is that they are based on linguistic rules, and therefore it is often easy to understand the underlying fucntionality of the systems. This is of great help when these systems are designed, because expert knowledge and common sense can often contributre in a catural way. However, sometimes, sufficient knowledge is not available, which makes the design phase difficult. Also the process of designing fuzzy systems is usually heuristic, and systematic, approaches that lead to optimal systems do not exist. This chapter describes progress towards an universal systematic design strateggy for automatically producing optimal fuzzy systems. In this strategy, the fuzzy system is viewed as an universal approximator [10] and optimized by using Guided Evolutionary Simulated Annealing (GESA) [23]. This design strategy is tested on two applications: general function approximation and control.

Keywords

Membership Function Fuzzy System Fuzzy Logic Controller Inverted Pendulum Fuzzy Partition 
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,” Information and Control, vol. 8, pp. 338–352, 1965.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    E. H. Mamdani and Assilian S. “An Experiment with Linguistic Synthesis with a Fuzzy Logic Controller,” Int. Journal Man-Machine Studies, vol. 7, pp. 1–13, 1975.MATHCrossRefGoogle Scholar
  3. [3]
    L.P. Holmblad and J. J. Ostergaard, “Control of a Cement Kiln by Fuzzy Logic,” in Fuzzy Information and Decision Processes, Ed. M. M. Gupta and E. Sanchez, Amsterdam: North Holland 1982, pp. 389–399.Google Scholar
  4. [4]
    M. Sugeno and K. Murakami, “An experimental study on fuzzy parking control using a model car,” in Industrial Applications of Fuzzy Control, M. Sugeno, Ed. Amsterdam: North-Holland, 1985, pp. 125–138.Google Scholar
  5. [5]
    S. Yasunobu, S. Miyamoto, “Automatic train operation by predictive fuzzy control,” in Industrial Applications of Fuzzy Control, M. Sugeno, Ed. Amsterdam: North-Holland, 1985, pp. 1–18.Google Scholar
  6. [6]
    C. C. Lee, “Fuzzy Logic in Control Systems: Fuzzy Logic Controller-Part I,” IEEE Trans. Syst. Man Cybern., vol. SMC-20, no.2, pp. 404–418, 1990.CrossRefGoogle Scholar
  7. [7]
    C. C. Lee, “Fuzzy Logic in Control Systems: Fuzzy Logic Controller-Part II,” IEEE Trans. Syst. Man Cybern., vol. SMC-20, no.2, pp. 419–435, 1990.CrossRefGoogle Scholar
  8. [8]
    M. Braae and D. Rutherford, “Fuzzy relations in control setting,” Kybernetics, vol. 7, no.3, pp. 185–188, 1978.MATHGoogle Scholar
  9. [9]
    M. S. Stachowicz and M. E. Kochanska, “Fuzzy modeling of the process,” in Proc. 2nd IFSA Congress, Tokyo, Japan, July 1987, pp. 86–89.Google Scholar
  10. [10]
    L. X. Wang, “Fuzzy Systems are Universal Approximators,” Proc. IEEE Int. Conf. on Fuzzy Systems, San Diego, CA, 1992, pp. 1163–1169.Google Scholar
  11. [11]
    J. Lee and S. Chae, “Completeness of Fuzzy Controller Carrying a Mapping f: R1 → R1,” 1993 IEEE Int. Conf. on Fuzzy Systems, San Fransisco, CA, March 1993, pp 231–235.Google Scholar
  12. [12]
    B. Kosko, “Fuzzy Systems as Universal Approximators,” Proc. IEEE Int. Conf. on Fuzzy Systems, San Diego, CA, 1992, pp. 1153–1162.Google Scholar
  13. [13]
    H. Hellendoorn, “Design and Development of Fuzzy Systems at Siemens R&D,” 1993 IEEE Int. Conf. on Fuzzy Systems, San Fransisco, CA, March 1993, pp. 1365–1370.Google Scholar
  14. [14]
    D. Driankov, H. Hellendoorn and M. Reinfrank, An Introduction to Fuzzy Control, Berlin, Heidelberg: Springer-Verlag, 1993.MATHGoogle Scholar
  15. [15]
    T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Trans. Syst. Man Cybern., vol. SMC-15, no1, pp. 116–132, 1985.Google Scholar
  16. [16]
    J. Efstathiou, “Rule-based process control using fuzzy logic,” in Approximate Reasoning in intelligent systems, decision and control, E. Sanchez and L. A. Zadeh, Ed. Oxford: Pergamon Press, 1987, pp. 145–158.Google Scholar
  17. [17]
    Y. H. Pao, Adaptive Pattern Recognition and Neural Networks, Reading, MA: Addison-Wesley, 1989.MATHGoogle Scholar
  18. [18]
    D. Goldberg, Genetic algorithms in search, optimization, and machine learning, Addison-Wesley, Reading, MA: Addison-Wesley, 1989.MATHGoogle Scholar
  19. [19]
    L. J. Fogel, A. J. Owens and M. J. Walsh, Artificial intelligences through simulated evolution, New York: Wiley, 1966.Google Scholar
  20. [20]
    N. Metropolis et al, “Equation of state calculations by fast computing machines,” Journal of Chemical Physics, vol. 21, no. 6, pp. 1087–1092, 1953.CrossRefGoogle Scholar
  21. [21]
    S. Kirkpatrick, C. D. Gelatt Jr and M. P. Vecchi, “Optimization by simulated annealing,” Science, vol. 220, pp. 671–680, 1983.CrossRefMathSciNetGoogle Scholar
  22. [22]
    Y. Takefuji, Neural network parallel computing, Boston: Kluwer Academic Publishers, 1992.MATHGoogle Scholar
  23. [23]
    P. P. C. Yip and Y. H. Pao, “A fast universal training algorithm for neural networks,” Proc. World Congress on Neural Networks WCNN’93, Protland, Oregon, July 1993, pp. 614–621.Google Scholar
  24. [24]
    P. P. C. Yip and Y. H. Pao, “Combinatorial optimization with use of guided evolutionary simulated annealing,” IEEE Trans. Neural Network, accepted for publication, 1994.Google Scholar
  25. [25]
    P. P. C. Yip and Y. H. Pao, “A guided evolutionary technique as function optimizer,” Proc. the First IEEE Conf. on Evolutionary Computation, Orlando, Florida, June 1994, pp. 628–633.Google Scholar
  26. [26]
    E. Aarts, Simulated annealing and Boltzmann machines: a stochastic approach to combinatorial optimization and neural computing, New York: Wiley, 1989.MATHGoogle Scholar
  27. [27]
    Feller, An Introduction to Probability Theory and its Applications, New York: Wiley, 1950.MATHGoogle Scholar
  28. [28]
    T. J. Procyk and E. H. Mamdani, “A linguistic self-organising process controller,” Automatica, vol. 15, pp. 15–30, 1979.MATHCrossRefGoogle Scholar
  29. [29]
    B. Kosko, Neural networks and fuzzy systems: a dynamical systems approach to machine intelligence, Englewood Cliffs, NJ: Prentice-Hall, 1991.Google Scholar
  30. [30]
    D. Dubois and H. Prade, Fuzzy Sets and Systems: Theory and Applications, New York: Academic Press, 1980.MATHGoogle Scholar
  31. [31]
    A. Kandel, Fuzzy Mathematical Techniques with Applications, Reading, MA: Addison-Wesley, 1986.MATHGoogle Scholar
  32. [32]
    R. Jang, “Self-Learning Fuzzy Controllers Based on Temporal Back Propagation,” IEEE Trans. Neural Networks, vol. 3, no.5, 1992, pp. 714–723.CrossRefGoogle Scholar
  33. [33]
    M. Tsutomu et al, “Operator Tuning in Fuzzy Production Rules,” 1993 IEEE Int. Conf. on Fuzzy Systems, San Fransisco, CA, March 1993, pp. 641–646.Google Scholar
  34. [34]
    E. Khan and P. Venkatapuram, “Neufuz: Neural Network Based Fuzzy Logic Design Algorithms,” 1993 IEEE Int. Conf. on Fuzzy Systems, San Fransisco, CA, March 1993, pp. 647–654.Google Scholar
  35. [35]
    A. E. Bryson and D. G. Leuenberger, “The Synthesis of Regulator Logic Using State-Variable Concepts,” Proceedings of the IEEE, vol. 58, no.11, pp 1803–1811, 1970.Google Scholar
  36. [36]
    B. Widrow, “The Original Adaptive Net Broom-Balancer,” IEEE Int. Symposium on Circuits and Systems, May 1987, pp. 351–357.Google Scholar
  37. [37]
    V. Williams and K. Matsuoka, “Learning to Balance the Inverted Pendulum using Neural Networks,” 91 IEEE Int. Joint Conf. on Neural Networks (IJCNN’91), Singapore, Singapore, November 1991, pp 214–219.Google Scholar
  38. [38]
    M. A. Lee and H. Takagi, “Integrating Design Stages of Fuzzy Systems using Genetic Algorithms,” 1993 IEEE Int. Conf. on Fuzzy Systems, San Fransisco, CA, March 1993, pp 612–617.Google Scholar
  39. [39]
    M. Jamshidi et al, “A comparison of an Expert and an Adaptive Fuzzy Control Approach,” Proc. IEEE Conf. on Decision and Control, Brighton, England, December 1991, pp 1907–1908.Google Scholar
  40. [40]
    A. G. Barto, R.S. Sutton, and C. W. Anderson, “Neuronlike Adaptive Elements that can solve Difficult Learning Control Problems,” IEEE Trans. on Syst. Man Cybern., vol. SMC-13, no.5, pp. 834–846, 1983.Google Scholar
  41. [41]
    L. Råde and B. Westergren, BETA Mathematics Handbook, Lund, Sweden: Studentlitteratur, 1990.MATHGoogle Scholar
  42. [42]
    C. Karr and E. J. Gentry, “Fuzzy Control of pH using Genetic Algorithms,” IEEE Trans. on Fuzzy Systems, vol. 1, no.1, pp. 46–53, 1993.CrossRefGoogle Scholar
  43. [43]
    H. Ishibuchi, K. Nozaki and N. Yamamoto, “Selecting Fuzzy Rules by Genetic Algorithm for classification problems,” 1993 IEEE Int. Conf. on Fuzzy Systems, San Fransisco, CA, March 1993, pp 1119–1124.Google Scholar
  44. [44]
    P. Thrift, “Fuzzy Logic Synthesis with Genetic Algorithms,” Proceedings of the Fourth Int. Conf. on Genetic Algorithms, San Mateo, CA, 1991, pp 502–513.Google Scholar
  45. [45]
    A. M. Homaifar and E. McCormick, “Full Design of Fuzzy Controllers using Genetic Algorithms,” Proceedings of SPIE,vol. 1766, San Diego, CA, July 1992, pp 393–404.Google Scholar
  46. [46]
    B. Hu, “Cell State Algorithm and Neural Network Based Fuzzy Logic Controller Design,” 1993 IEEE Int. Conf. on Fuzzy Systems, San Fransisco, CA, March 1993, pp 247–250.Google Scholar
  47. [47]
    T. Whalen and B. Schott, “Lexicographic Tuning of a Fuzzy Controller using Box’s’ Complex’ Algorithm,” 1993 IEEE Int. Conf. on Fuzzy Systems, San Fransisco, CA, March 1993, pp 285–290.Google Scholar

Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Mattias Nyberg
    • 1
  • Yoh-Han Pao
    • 1
  1. 1.Case Western Reserve University ClevelandDepartment of Electrical Engineering and Applied PhysicsOHUSA

Personalised recommendations