International Journal of Control, Automation, and Systems

  • 제3권2호
  • /
  • Pages.225-235
  • /
  • 2005
  • /
  • 1598-6446(pISSN)
  • /
  • 2005-4092(eISSN)
제어로봇시스템학회 (Institute of Control, Robotics and Systems)
권호 표지

Robust Stabilization of Uncertain Nonlinear Systems via Fuzzy Modeling and Numerical Optimization Programming

  • Lee Jongbae (Korea Electronics Technology Institute) ;
  • Park Chang-Woo (Korea Electronics Technology Institute) ;
  • Sung Ha-Gyeong (Korea Electronics Technology Institute) ;
  • Lim Joonhong (School of Electrical Engineering and Computer Science, Hanyang University)
  • 발행 : 2005.06.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents the robust stability analysis and design methodology of the fuzzy feedback linearization control systems. Uncertainty and disturbances with known bounds are assumed to be included in the Takagi-Sugeno (TS) fuzzy models representing the nonlinear plants. $L_2$ robust stability of the closed system is analyzed by casting the systems into the diagonal norm bounded linear differential inclusions (DNLDI) formulation. Based on the linear matrix inequality (LMI) optimization programming, a numerical method for finding the maximum stable ranges of the fuzzy feedback linearization control gains is also proposed. To verify the effectiveness of the proposed scheme, the robust stability analysis and control design examples are given.

키워드

참고문헌

  1. T. Takagi and M. Sugeno, 'Fuzzy identification of systems and its applications to modeling and control,' IEEE Trans. on Systems, Man and Cybernetics, vol. 15, no. 1, pp. 116-132, 1985
  2. M. Sugeno, Fuzzy Control, Nikangoubyou- Shinnbun-sha, Tokyo, 1988
  3. Y. W. Cho, C. W. Park, J. H. Kim, and M. Park, 'Indirect model reference adaptive fuzzy control of dynamic fuzzy state space model,' IEE Proceedings-Control Theory and Applications, vol. 148, no. 4, pp. 273-282, July 2001
  4. K. Fischle and D. Schroder, 'An improved stable adaptive fuzzy control method,' IEEE Trans. on Fuzzy Systems, vol. 7, no. 1, pp. 27-40, 1999 https://doi.org/10.1109/91.746301
  5. D. L. Tsay, H. Y. Chung, and C. J. Lee, 'The adaptive control of nonlinear systems using the Sugeno-type of fuzzy logic,' IEEE Trans. on Fuzzy Systems, vol. 7, no. 2, pp. 225-229, 1999 https://doi.org/10.1109/91.755402
  6. C. C. Fuh and P. C. Tung, 'Robust stability analysis of fuzzy control systems,' Fuzzy Sets and Systems, vol. 88, no. 3, pp. 289-298, 1997 https://doi.org/10.1016/S0165-0114(96)00087-5
  7. H. J. Kang, C. Kwon, C. H. Lee, and M. Park, 'Robust stability analysis and design method for the fuzzy feedback linearization regulator,' IEEE Trans. on Fuzzy Systems, vol. 6, no. 4, pp. 464-472, 1998 https://doi.org/10.1109/91.728433
  8. C. W. Park, H. Y. Kang, Y. H. Yee, and M. Park, 'Numerical robust stability analysis of fuzzy feedback linearization regulator based on linear matrix ineuqality approach,' IEE Proceedings- Control Theory and Applications, vol. 149, no. 1, pp. 82-88, 2002
  9. S. Boyd, Linear Matrix Inequalities in Systems and Control Theory, SIAM, Philadelphia, 1994
  10. Y. Nesterov and A. Nemirovsky, Interior-Point Polynomial Methods in Convex Programming, SIAM, Philadelphia, 1994
  11. H. O. Wang, K. Tanaka, and F. G. Grifiin, 'An approach to fuzzy control of nonlinear system: stability and design issues,' IEEE Trans. on Fuzzy Systems, vol. 4, no. 1, pp. 14-23, 1996 https://doi.org/10.1109/91.481841
  12. K. Tanaka, T. Ikeda, and H. O. Wang, 'Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, control theory, and linear matrix inequalities,' IEEE Trans. on Fuzzy Systems, vol. 4, no. 1, pp. 1-13, 1996 https://doi.org/10.1109/91.481840
  13. E. Kim, H. J. Kang, and M. Park, 'Numerical stability analysis of fuzzy control systems via quadratic programming and linear matrix inequalities,' IEEE Trans. on Fuzzy Systems, vol. 29, no. 4, pp. 333-346, 1999
  14. E. Kim and D. Kim, 'Stability analysis and synthesis for an affine fuzzy system via LMI and ILMI: discrete case,' IEEE Trans. on Systems, Man and Cybernetics, vol. 31, no. 1 pp. 132-140, 2001
  15. P. Gahinet, A. Nemirovski, A. Laub, and M. Chilali, LMI Control Toolbox, The MathWorks, Inc., Natick, 1995
  16. M. Vidyasagar, Nonlinear System Analysis, Prentice-Hall, Englewood Cliffs, 1993
  17. A. Isidori, Nonlinear Control Systems II, Springer Verlag, London, 1999