Design of the Optimal Controller for Takagi-Sugeno Fuzzy Systems and Its Application to Spacecraft control

Takagi-Sugeno 퍼지시스템에 대한 최적 제어기 설계 및 우주 비행체의 자세 제어 응용

  • Park, Yeon-Muk (Korea Advanced Institute of Science and Technology) ;
  • Tak, Min-Je (Korea Advanced Institute of Science and Technology)
  • 박연묵 (한국과학기술원 항공우주공학전공) ;
  • 탁민제 (한국과학기술원 항공우주공학전공)
  • Published : 2001.07.01

Abstract

In this paper, a new design methodology for the optimal control of nonlinear systems described by the TS(Takagi-Sugeno) fuzzy model is proposed. First, a new theorem concerning the optimal stabilizing control of a general nonlinear dynamic system is proposed. Next, based on the proposed theorem and the inverse optimal approach, an optimal controller synthesis procedure for a TS fuzzy system is given, Also, it is shown that the optimal controller can be found by solving a linear matrix inequality problem. Finally, the proposed method is applied to the attitude control of a rigid spacecraft to demonstrate its validity.

References

  1. T. Takagi and M. Sugeno, 'Fuzzy identification of systems and its applications to modeling and control,' IEEE Transactions on Systems, Man and Cybernetics, vol. 15, no. 1, pp. 116-132, 1985
  2. K. Tanaka and M. Sugeno, 'Stability analysis and design of fuzzy control system,' Fuzzy Sets and Systems, vol. 45, no. 2, pp. 135-156, 1992 https://doi.org/10.1016/0165-0114(92)90113-I
  3. H. Wang, K. Tanaka, and M. Griffin, 'An approach to fuzzy control of nonlinear systems: stability and design issues,' IEEE Transactions on Fuzzy Systems, vol. 4, no. 1, pp. 14-23, 1996 https://doi.org/10.1109/91.481841
  4. K. Tanaka, T. Ikeda, and H. Wang, 'Design of fuzzy control systems based on LMI stability conditions,' Proc. of the 35th Conf. Decision and Control, pp. 598-603, 1996 https://doi.org/10.1109/CDC.1996.574389
  5. M. Thathachar and P. Viswanath, 'On the stability of fuzzy systems,' IEEE Transactions on Fuzzy Systems, vol. 5, no. 1, pp. 145-151, 1997 https://doi.org/10.1109/91.554461
  6. K. Tanaka, T. Ikeda, and H. Wang, 'Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs,' IEEE Transactions on Fuzzy Systems, vol. 6, no. 2, pp. 250-265, 1998 https://doi.org/10.1109/91.669023
  7. S. J. Wu and C. T. Lin, 'Optimal fuzzy controller design: local concept approach,' IEEE Transactions on Fuzzy Systems, vol. 8, no. 2, pp. 171-185, 2000 https://doi.org/10.1109/91.842151
  8. Y. Park, M. J. Tahk, and J. Park, 'Optimal stabilization of Takagi-Sugeno fuzzy systems with application to spacecraft control,' to appear in Journal of Guidance, Control, and Dynamics, vol. 24, no. 4, July-Aug., 2001
  9. B. D. O. Anderson and J. B. Moore, Optimal Control: Linear Quadratic Methods, Prentice Hall, NJ, 1990
  10. R. Sepulchre, M. Jankovic, and P. V. Kokotovic, Constructive Nonlinear Control, Springer-Verlag, NY, 1997
  11. R. E. Kalman, 'When is a linear control system optimal ?,' Transactions of the ASME Series D: Journal of Basic Engineering, vol. 86, pp. 51-60, 1964
  12. R. A. Freeman and P. V. Kokotovic, 'Inverse optimality in robust stabilization,' SIAM Journal on Control and Optimization, vol. 34, no. 4, pp. 1365-1391, 1996 https://doi.org/10.1137/S0363012993258732
  13. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, Studies in Applied Mathematics Series, vol. 15, SIAM, Philadelphia, PA, 1994
  14. P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox, MathWorks, Inc., Natica, MA, 1995
  15. C. K. Carrington and J. L. Junkins, 'Optimal nonlinear feedback control for spacecraft attitude maneuvers,' Journal of Guidance, Control, and Dynamics, vol. 9, no. 1, pp. 99-107, 1986
  16. P. Tsiotras, 'Stabilization and optimality results for the attitude control problem,' Journal of Guidance, Control, and Dynamics, vol. 19, no. 4, pp. 772-779, 1996
  17. P. Tsiotras, 'Optimal regulation and passivity results for axisymmetric rigid bodies using two controls,' Journal of Guidance, Control, and Dynamics, vol. 20, no. 3, pp. 457-463, 1997
  18. M. Krstic and P. Tsiotras, 'Inverse optimal stabilization of a rigid spacecraft,' IEEE Transactions on Automatic Control, vol. 44, no. 5, pp. 1042-1049, 1999 https://doi.org/10.1109/9.763225
  19. M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, Nonlinear and Adaptive Control Design, Wiley, NY, 1995
  20. H. K. Khalil, Nonlinear Systems, 2nd ed., Prentice Hall, NJ, 1996