Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
권호 표지
DOI QR코드

DOI QR Code

A Relaxed Stabilization Condition for Discrete T-S Fuzzy Model under Imperfect Premise Matching

불완전한 전반부 정합 하에서의 이산 T-S 퍼지 모델에 대한 완화된 안정화 조건

  • Lim, Hyeon Jun (School of Electrical and Electronics Engineering, Yonsei University) ;
  • Joo, Young Hoon (Department of Control and Robotics Engineering, Kunsan National University) ;
  • Park, Jin Bae (School of Electrical and Electronics Engineering, Yonsei University)
  • 임현준 (연세대학교 전기전자공학과) ;
  • 주영훈 (국립 군산대학교 제어로봇공학과) ;
  • 박진배 (연세대학교 전기전자공학과)
  • Received : 2016.11.25
  • Accepted : 2017.01.16
  • Published : 2017.02.25
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, a controller for discrete Takagi-Sugeno(T-S) fuzzy model under imperfect premise matching is proposed. Most of previous papers have obtained the stabilization condition using common quadratic Lyapunov function. However, the stabilization condition may be conservative due to the typical disadvantage of the common quadratic Lyapunov function. Hence, in order to solve this problem, we propose the stabilization condition of discrete T-S fuzzy model using fuzzy Lyapunov function. Finally, the proposed approach is verified by the simulation experiments.

본 논문은 이산 Takagi-Sugeno (T-S) 퍼지 모델의 제어기 설계 시 시스템과 제어기가 상이한 소속 함수를 가지는 불완전한 전반부 정합 하에서의 제어기 설계에 대해 다룬다. 이산 T-S 퍼지 모델의 안정화 조건을 구할 때, 단일 Lyapunov 함수를 이용하여 구한 기존의 보수적인 안정화 조건보다 완화된 안정화 조건을 구하기 위해 퍼지 Lyapunov 함수를 고려한다. 퍼지 Lyapunov 함수를 이용하여 선형 행렬 부등식 기반의 완화된 안정화 조건을 구하고 시뮬레이션을 통해 제안한 방법의 타당성을 검증한다.

Keywords

References

  1. K. Tanaka and H. O. Wang, "Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach," New York: Wiley, 2001.
  2. H. K. Khalil, "Nonlinear Systems," third ed., Prentice-Hall, Upper Saddle River, NJ, 2002.
  3. S. Boyd, L.E. Ghaoui, E. Feron, V. Blalkrishnan "Linear Matrix Inequalities in System and Control Theory," SIAM, Philadelphia, PA, 1994.
  4. H. K. Lam, "Stability Analysis and Performance Design for Fuzzy-model-based Control System under Imperfect Premise Matching," IEEE Trans, Fuzzy Syst., vol. 17, no. 4, pp. 949-961, Aug. 2009. https://doi.org/10.1109/TFUZZ.2008.928600
  5. H. J. Kim, J. B. Park and Y. H. Joo, "Stabilization Conditions of Takagi-Sugeno Fuzzy Systems based on the Fuzzy Lyapunov Functions under the Imperfect Premise Matching," American Control Conference, Washington, DC, USA, June 17-19, 2013.
  6. H. K. Lam, "Design of Stable Fuzzy Controller for Nonlinear Systems Subject to Imperfect premise Matching based on Grid-point Approach," Control Theory & Application, IET, vol. 4, no. 12. pp. 2770-2780, 2010. https://doi.org/10.1049/iet-cta.2009.0307
  7. K. Tanaka, T. Hori and H. O. Wang, "A Multiple Lyapunov Function Approach to Stabilization of Fuzzy Control Systems," IEEE Trans, Fuzzy Syst., vol. 11, no. 4, 2003.
  8. B-J. Rhee and S. Won "A New Fuzzy Lyapunov Function Approach For a Takagi-Sugeno Fuzzy Control System Design," Fuzzy Sets and Systems, vol. 9, pp. 1211-1228, 2006.
  9. K. Tanaka, T. Hori and H. O. Wang, "A Fuzzy Lyapunov Approach to Fuzzy Control System Design," American Control Conference, Arlington, VA, 2001, 00. 4790-4795.
  10. K. Tanaka, T. Hori and H. O. Wang "New Parallel Distributed Compensation using Time Derivative of Membership Functions: A Fuzzy Lyapunov Approach," IEEE Conf. on Decision Control, Orland, FL, 2001, pp. 3942-3947.
  11. T. Takagi and M. Sugeno, "Fuzzy Identification of Systems and Its Applications to Modeling and Control," IEEE Trans., Sys., Man., Cybern., vol. SMC-15, no. 1, pp. 116-132, Jan, 1985. https://doi.org/10.1109/TSMC.1985.6313399
  12. H. O. Wang, K. Tanaka, and M. F. Griffin "An Approach to Fuzzy Control of Nonlinear Systems: Stability and the Design Issues," IEEE Trans. Fuzzy Syst., vol. 6, no. 2, pp. 250-265, May 1998. https://doi.org/10.1109/91.669023
  13. K. Tanaka, T. Ikeda and H. O. Wang, "Fuzzy Regulators and Fuzzy Observers: Relaxed Stability Conditions and LMI-based Designs," IEEE Trans. Fuzzy Syst., vol. 6, no. 2, pp. 250-265, May 1998. https://doi.org/10.1109/91.669023
  14. H. K. Lam and L. D. Seneviratne, "Stability analysis of polynomial fuzzy-model-based control systems under perfect/imperfect premise matching," IET Control Theory Appl., vol. 5, no. 15, pp. 1689-1697, 2011. https://doi.org/10.1049/iet-cta.2010.0619
  15. G. B. Koo, Y. H. Joo and Jin Bae Park, "Design of an Observer-based Decentralized Fuzzy Controller for Discrete-time Interconnected Fuzzy Systems," JKIIS, vol. 25, no. 5, PP. 451-456, Oct 2015 https://doi.org/10.5391/JKIIS.2015.25.5.451
  16. T.M Guerra and L. Vermeiren, "LMI-based Relaxed Nonquadratic Stabilization Conditions for Nonlinear Systems in the Takagi-Sugeno's Form," Automatica, vol. 40, pp. 823-829, 2004 https://doi.org/10.1016/j.automatica.2003.12.014
  17. G. B. Koo, J. B. Park, Y. H. Joo, "Decentralized Fuzzy Observer-based Output-feedback Control for Nonlinear Large-scale Systems: an LMI Approach," IEEE Trans., Fuzzy Syst., vol. 22, 406-419, 2014 https://doi.org/10.1109/TFUZZ.2013.2259497
  18. H. J. Lee, J. B. Park and Y. H. Joo, "Further Refinement on LMI-based Digital Redesign: Delta-operator Approach," IEEE Trans. on Circuits and Systems II: Express Briefs 53 (6), 473-477, 2006. https://doi.org/10.1109/TCSII.2006.870550
  19. D. H. Lee, J. B. Park, Y. H. Joo, K. C. Lin and C. H. Ham, "Robust $H_{\infty}$ Control for Uncertain Nonlinear Active Magnetic Bearing Systems via Takagi-Sugeno Fuzzy Models," International Journal of Control, Automation and Systems 8 (3), 636-646, 2010 https://doi.org/10.1007/s12555-010-0317-2
  20. D. W. Kim, J. B. Park and Y. H. Joo, "Theoretical Justification of Approximate Norm Minimization Method for Intelligent Digital Redesign," Automatica 44 (3), 851-856, 2008 https://doi.org/10.1016/j.automatica.2007.07.003
  21. M. K. Song, J. B. Park, J. K. Kim and Y. H. Joo. "Delay-range-dependent Stability Analysis and Stabilization for Nonlinear Systems : T-S Fuzzy Model Approach," JKIIS, 19.3 (2009.6): 337-342. https://doi.org/10.5391/JKIIS.2009.19.3.337
  22. M. H. Kim, Y. H. Joo and J. B. Park "TS Fuzzy Classifier using a Linear Matrix Inequality," JKIIS, vol. 14, no. 1, pp. 46-51, 2004 https://doi.org/10.5391/JKIIS.2004.14.1.046
  23. H. J. Lee, Y. H. Joo, S. Y. Lee, J. B. Park, "Stochastic Stabilization of TS Fuzzy System with Markovian Input Delay," JKIIS, 11.6 (2001.12): 459-464.
  24. Y. H. Joo, H. J. Lee and J. B. Park, "Design of Fuzzy Controller for Input-delayed TS Fuzzy Systems." JKIIS, 11.3 (2001.6): 208-214.
  25. H. J. Lee, Y. H. Joo and J. B. Park "Output Tracking Controller Design of Discrete-Time TS Fuzzy Systems," JKIIS, 11.1 (2001.2): 45-51.