Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Design of the Robust Fuzzy Controller based on Fuzzy Lyapunov Functions

퍼지 리아푸노프 함수 기반 강인한 퍼지 제어기 설계

  • 김호준 (연세대학교 전기전자공학과) ;
  • 박진배 (연세대학교 전기전자공학과) ;
  • 주영훈 (군산대학교 제어로봇공학과)
  • Received : 2011.07.25
  • Accepted : 2011.10.15
  • Published : 2011.10.25
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Abstract

This paper is concerned with the stability analysis and stabilization for the Takagi-Sugeno(T-S) fuzzy systems with parametric uncertainties. To reduce conservativeness in stability analysis for T-S fuzzy systems, fuzzy Lyapunov functions are used. Stability analysis is performed and robust fuzzy controller is designed for stabilization of the system with parametric uncertainties. The stability and stabilization conditions are formulated in terms of linear matrix inequalities (LMIs). Finally, simulation example is presented to show the effectiveness of the proposed approach.

본 논문은 매개변수 불확실성을 가지는 Takagi-Sugeno(T-S) 퍼지 시스템의 안정도 해석과 안정화 조건을 고려한다. T-S 퍼지 시스템의 안정도 해석 시 conservativeness를 줄이기 위해 퍼지 리아푸노프 함수를 이용한다. 매개변수 불확실성을 가지고 있는 시스템의 안정도를 해석하고 시스템을 안정화 시키는 퍼지 강인 제어기 설계 기법을 제시한다. 안정도조건과 안정화조건은 선형행렬부등식의 형태로 표현된다. 모의실험을 통해 제안된 접근 방법의 효용성을 보인다.

Keywords

References

  1. Lee, H. J., J. B. Park and G. Chen, "Robust fuzzy control of nonlinear systems with parametric uncertainties," IEEE. Trans, Vol. 9 , No. 2 , pp. 369-379, 2001
  2. Mozelli, L. A, R. M. Palhares and G. S. C. Avellar, "A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems," Information Sciences, Vol. 179, No. 8 pp. 1149-1162, 2009. https://doi.org/10.1016/j.ins.2008.12.002
  3. H.K.Lam and M. Narimani, "Stability Analysis and Performance Design for Fuzzy-Model-Based Control System Under Imperfect Premise Matching, " IEEE Trans. Fuzzy Systems, Vol. 17, No. 4, pp. 949-961, 2009. https://doi.org/10.1109/TFUZZ.2008.928600
  4. Feng, G., "Stability analysis of discrete-time fuzzy dynamic systems based on piecewise Lyapunov functions", IEEE. Trans. Fuzzy Systems, Vol. 12 No. 1, pp. 22-28, 2004. https://doi.org/10.1109/TFUZZ.2003.819833
  5. K. Tanaka, T. Hori, and H. O. Wang, "A multiple Lyapunov function approach to stabilization of fuzzy control systems", IEEE Trans. Fuzzy Systems, Vol. 11, No. 4, pp. 582-589, 2003. https://doi.org/10.1109/TFUZZ.2003.814861
  6. Sala, A., "On the conservativeness of fuzzy and fuzzy- polynomial control of nonlinear system", Annual Reviews in Control, Vol. 33, No. 1, pp. 48-58, 2009. https://doi.org/10.1016/j.arcontrol.2009.02.001
  7. K.Tanaka and M.Segeno, "Stability analysis and design of fuzzy control of nonlinear systems: Stability and the design issues", Fuzzy Sets Syst., Vol. 45, No.2, pp. 1697-1700, 1992.
  8. M. Bernal, T. M. Guerra, A. Kruszewski, "A membership- function-dependent approach for stability analysis and controller synthesis of Takagi-Sugeno models." Fuzzy Sets and Systems. Vol. 160, no. 19, pp. 2776-2795, 2009. https://doi.org/10.1016/j.fss.2009.02.005
  9. Chang, W., et al., "Design of robust fuzzy-model- based controller with sliding mode control for SISO nonlinear systems", Fuzzy Sets and Systems. Vol. 125, No. 1, pp. 1-22, 2002. https://doi.org/10.1016/S0165-0114(01)00038-0
  10. L. Xie, "Output feedback $H_{{\infty}}$ control of systems with parameter uncertainties", Int. J. Contr., Vol. 63, No. 4, pp. 741-750, 1996. https://doi.org/10.1080/00207179608921866