퍼지 제어 시스템의 완화된 안정조건에 관한 연구

A Study on the Relaxed Stability of Fuzzy Control Systems

  • 김은태 (국립 한경대학교 제어계측공학과) ;
  • 이창훈 (연세대학교 전기컴퓨터공학과) ;
  • 박민용 (연세대학교 전기컴퓨터공학과)
  • 발행 : 2000.09.01

초록

본 논문에서는 퍼지 제어 시스템의 2차 안정도를 판정하는 새로운 방법을 제안한다. 퍼지 부 시스템간의 상호 작용을 선형행렬부등식을 이용하여 수치적으로 다룸으로서 제안한 방법은 안정도가 보장되는 퍼지 시스템의 영역을 넓히는 결과를 갖는다. 기존의 방식과 비교하여 제안된 안정조건은 기존의 안정조건을 완화한 것으로 엄밀한 방식으로 제안된 방식이 기존의 방식을 포함한 완화된 조건임을 보인다.

In this paper, we propose a new condition to test the quadratic stability of fuzzy control systems. The Proposed one enlarges the class of fuzzy control systems whose stability is ensured by representing the interactions among the fuzzy subsystems in a single power matrix and solving it by LMI (linear matrix inequality). Compared with the previous methods, the proposed one relaxes the stability condition to release the conservatism. Finally, the relationship between the suggested condition and the conventional well-known stability conditions reported in the previous literatures is discussed and it is shown in a rigorous manner that the proposed one includes the conventional conditions.

키워드

참고문헌

  1. Zadeh, L. A., 'Fuzzy Sets,' Information and Control 8, pp.338-353, 1965 https://doi.org/10.1016/S0019-9958(65)90241-X
  2. E. H. Mamdani, 'Applications of fuzzy algorithms for control of simple dynanmic plant,' Proc. IEE, vol.121, No.2, pp 1585-1588, 1974
  3. R. Palm, D. Driankov and H. Hellendoom, Model Based Fuzzy Control, Springer-Verlag:Berlin, 1996
  4. T. Takagi and M. Sugeno, 'Fuzzy identification of systems and its applications to modeling and control,' IEEE Trans. Systems Man Cybemet, vol. 15, No.1, pp116-132, 1985
  5. K. Tanaka and M. Sugeno, 'Stability analysis and design of fuzzy control systems,' Fuzzy Sets and Systems, vol. 45, 136-156, 1992 https://doi.org/10.1016/0165-0114(92)90113-I
  6. K. Tanaka, A Theory of Advanced Fuzzy Control, Japan:Kyuoritsu Pub, 1994. (In Japanese)
  7. K. Tanaka and M. Sano, 'A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck,trailer,' IEEE Trans. Fuzzy Systems, vol. 2, No.2, pp 119- 134, May 1994 https://doi.org/10.1109/91.277961
  8. H. O. Wang, K. Tanaka M. F. Griffin, 'An approach to fuzzy control of nonlinear systems: stability and design issues,' IEEE Trans. Fuzzy Systems, vol. 4, No. 1, pp 14-23, Feb 1996 https://doi.org/10.1109/91.481841
  9. K. Tanaka, T. Ikeda and H. O. Wang, 'A unified approach to controlling chaos via LMI-based fuzzy control system design,' IEEE Trans. Circuits and Syst. -Part 1: Fundamental Theory and Appl., vol. 45. no. 10, pp. 1021-1040. Oct. 1998 https://doi.org/10.1109/81.728857
  10. M.A.L. Thathachar and P. Viswanath, 'On the stability of fuzzy Systems,' IEEE Trans. FuzzY Systems, vol. 5, No.1, pp 145-151, Feb 1997 https://doi.org/10.1109/91.554461
  11. S. H. Zak, 'Stabilizing fuzzy system models using linear controllers,' IEEE Trans. Fuzzy Systems, vol. 7, No.2, pp 236-240, Apr., 1999 https://doi.org/10.1109/91.755404
  12. X. Ma, Z. Sun, and Y. He, 'Analysis and design of fuzzy controller and fuzzy observer,' IEEE Trans. Fuzzy Systems, vol. 6, No.1, pp 41-51, Feb., 1998
  13. S. Cao, N. W. Rees and G. Feng, 'Analysis and design of fuzzy control systems using dynamic fuzzy-state space models,' IEEE Trans. Fuzzy Systems, vol. 7, No.2, pp 192-200, Apr., 1999 https://doi.org/10.1109/91.755400
  14. K. Tanaka T. Ikeda and H. O. Wang, 'Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs,' IEEE Trans. Fuzzy Systems, vol. 6, No.2, pp 250-265, May, 1998 https://doi.org/10.1109/91.669023
  15. K. Tanaka. T. Ikeda and H. O. Wang, 'An LMI approach to fuzzy controller designs based on the relaxed stability conditions,' in Proc. of IEEE Int. Conf. Fuzzy Systems (FUZZ/IEEE), pp.l71-176, 1997 https://doi.org/10.1109/FUZZY.1997.616364
  16. S. Boyd, L. Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM:Philadelphia, 1994