A Study on On-line modeling of Fuzzy System via Extended Kalman Filter

확장 칼만필터를 이용한 온라인 퍼지 모델링 알고리즘에 대한 연구

  • 김은태 (연세대학교 전기전자공학부)
  • Published : 2003.09.01

Abstract

In this paper, an explanation regarding on-line identification of a fuzzy system is presented. The fuzzy system to be identified is assumed to be in the type of singleton consequent parts and be represented by a linear combination of fuzzy basis functions. For on-line identification, squared-cosine membership function is introduced to reduce the number of parameters to be identified and make the system consistent and differentiable. Then the parameters of the fuzzy system are identified on-line by the gradient search method and Extended Kalman Filter. Finally, a computer simulation is peformed to illustrate the validity of the suggested algorithms.

본 논문에서는 퍼지 모델의 온라인 동정 알고리즘을 제안한다. 본 논문에서 고려하는 퍼지 모델은 후건부가 싱글톤인 퍼지 시스템으로 퍼지 기저함수의 선형 합으로 표현된다. 온라인 동정을 위해서 제곱 코사인 소속함수를 제안한다. 제곱 코사인 함수는 다른 소속함수에 비해 적은 파라미터를 갖으며 전 구간에서 미분 가능한 특징을 갖는다. 퍼지 모델의 파라미터는 그레디언트 하강법과 확장칼만필터를 이용하여 온라인으로 결정한다. 끝으로 컴퓨터 모의 실험을 통하여 제안한 방법의 타당성을 확인한다.

Keywords

References

  1. J. C. Bezdek, 'Editorial: Fuzzy Models - What Are They, and Why ?,' IEEE Trans. Fuzzy Systems, vol. 1, No. 1, pp. 1-6, Feb. 1993 https://doi.org/10.1109/TFUZZ.1993.6027269
  2. W. Pedrycz, 'An identification algorithm in fuzzy relational systems,' Fuzzy Sets and Systems, vol. 13, pp. 153-167, 1984 https://doi.org/10.1016/0165-0114(84)90015-0
  3. W. Pedrycz, Fuzzy Control and Fuzzy Systems, John Willey and Sons, New York, 1993
  4. T. Takagi and M. Sugeno, 'Fuzzy identification of systems and its applications of modeling and control,' IEEE Trans. Systems Man Cybernet, vol. 15, No. 1, pp. 116-132, 1985 https://doi.org/10.1109/TSMC.1985.6313399
  5. M. Sugeno and G. T. Kang, 'Structure identification of fuzzy model,' Fuzzy Sets and Systems, vol. 28, pp. 15-33, 1988 https://doi.org/10.1016/0165-0114(88)90113-3
  6. M. Sugeno and T. Yasukawa, 'A fuzzy-logic-based approach to qualitative modeling,' IEEE Trans. Fuzzy Systems, Vol. 1, No. 1, pp. 7-31, Feb. 1993 https://doi.org/10.1109/TFUZZ.1993.390281
  7. E. Kim, M. Park, S. Ji and M. Park, 'A new approach to fuzzy modeling,' IEEE Trans. Fuzzy Systems, vol. 5, No. 3, pp. 328-337, Aug, 1997 https://doi.org/10.1109/91.618271
  8. E. Kim, M. Park, S. Kim and M. Park, 'A transformed input-domain approach to fuzzy modeling,' IEEE Trans. Fuzzy Systems, vol. 6, no. 4, pp. 596-604, 1998 https://doi.org/10.1109/91.728458
  9. W. A. Farag, V. H. Quintana and G. Lambert-Torres, 'A genetic-based neuro-fuzzy approach for modeling and control of dynamical systems,' IEEE Trans. Neural Networks, vol. 9, no. 5, pp. 756-765, 1998 https://doi.org/10.1109/72.712150
  10. Y. Lin and G. A. Cunningham III, 'A new approach to fuzzy-neural modeling,' IEEE Trans. Fuzzy Systems, Vol. 3, No. 2, pp. 190-197, May, 1995 https://doi.org/10.1109/91.388173
  11. M. Sugeno and K. Tanaka, 'Successive identification of a fuzzy model and its applications to prediction of a complex system,' Fuzzy Sets and Systems, vol. 42, pp. 315-334, 1991 https://doi.org/10.1016/0165-0114(91)90110-C
  12. G. Chen, Approximate Kalman Filtering, World Scientific Publishing Co., 1993
  13. B. D. O. Anderson and J. B. Moore, Optimal Filtering, Englewood Cliffs, NJ: Prentice-Hall, 1979