Fuzzy Logic pp 263-276 | Cite as

Indirect Adaptive Fuzzy Control of Nonlinear Systems with Terminal Sliding Modes

  • Shuanghe Yu
  • Xinghuo Yu
  • Man Zhihong
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 81)


A global fast terminal sliding mode controller with fast terminal adaptive fuzzy approximator is proposed for general single input single output nonlinear systems. The finite time convergence property of the fast terminal sliding mode is used in the design of the controller. It is applied not only in the reaching phase and the sliding phase of the sliding mode control system, but also in the adaptive fuzzy approximator for the unknown nonlinear system. Stability of the control system and convergence of the approximation are proved.


Fuzzy Logic System Adaptive Fuzzy Control Adaptive Fuzzy Controller Fuzzy Inference Engine Terminal Sliding Mode Control 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Lee, C. (1990) Fuzzy Logic in Control Systems: Fuzzy Logic Controller — Part I, II, IEEE Transactions on Systems, Man and Cybernetics, vol. 20, no. 2, pp. 404–418, pp. 419–435CrossRefGoogle Scholar
  2. 2.
    Zinober, A. (1993) Variable Structure and Lyapunov Control, London: Springer-VerlagGoogle Scholar
  3. 3.
    L. X. Wang, L. and Mendel, J. (1992) Fuzzy Basis Functiòns, Universal Approximation, and Orthogonal Least Squares Learning, IEEE Transaction on Neural Networks, vol. 3, pp. 807–814, Sept.CrossRefGoogle Scholar
  4. 4.
    Wang, L. (1993) Stable Adaptive Fuzzy Control of Nonlinear Systems, IEEE Transactions on Fuzzy Systems, vol. 1, no. 2, pp. 146 – 155, MayCrossRefGoogle Scholar
  5. 5.
    Wang, L. (1996) Stable Adaptive Fuzzy Controllers with Application to Inverted Pendulum Tracking, IEEE Transactions on Systems, Man and Cybernetics — Part B: Cybernetics, vol. 26, no. 5, pp. 677–691, OctoberCrossRefGoogle Scholar
  6. 6.
    Su, C., Stepanenko, Y. (1994) Adaptive Control of a Class of Nonlinear Systems with Fuzzy Logic, IEEE Transactions on Fuzzy Systems, vol. 2, no. 4, pp. 285–294, Nov.CrossRefGoogle Scholar
  7. 7.
    Tsay, D., Chung, H., Lee, C. (1999) The Adaptive Control of Nonlinear Systems Using the Sugeno-type of Fuzzy Logic, IEEE Transactions on Fuzzy Systems, vol. 7, no. 2, pp. 225–229, Apr.CrossRefGoogle Scholar
  8. 8.
    Utkin, V. (1992) Sliding Modes in Control Optimization. Berlin, Heidelberg: Springer-VerlagCrossRefGoogle Scholar
  9. 9.
    Slotine, J. and Li, W. (1991) Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, New JerseyGoogle Scholar
  10. 10.
    Yu, X. and Man, Z. (1996) Model Reference Adaptive Control Systems with Terminal Sliding Modes, International Journal of Control, vol. 64, no. 6, pp. 1165–1176MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Man, Z. and Yu, X. (1997) Terminal Sliding Mode Control of MIMO Systems, IEEE Transactions on Circuits and Systems — Part I, vol. 44, pp. 1065–1070MathSciNetGoogle Scholar
  12. 12.
    Yu, X., Wu, Y. and Man, Z. (1999) On Global Stabilisation of Nonlinear Dynamical Systems, In Variable Structure Systems, Sliding Mode and Nonlinear Control, Lecture Notes in Control and Information Science, D. Young and U. Ozguner (Eds), vol. 247, pp. 109–122, Springer-VerlagGoogle Scholar
  13. 13.
    Yu, X. and Man, Z. (2000) Fast Terminal Sliding Mode Control for Single Input Systems, accepted for presentation at 2000 Asian Control Conference, ShanghaiGoogle Scholar
  14. 14.
    Haimo, V. (1986) Finite Time Controller, SIAM Journal of Control and Optimization, vol. 24, no. 4, pp. 760–770, JulyMathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Bhat, S. and Bernstein, D. (1995) Lyapunov Analysis of Finite-time Differential Equations, Proceedings of the American Control Conference, Seattle, pp. 1831–1832Google Scholar
  16. 16.
    Bhat, S. and Bernstein, D. (2000) Finite-time Stability of Continuous Autonomous Systems, SIAM J. Control and Optimization, vol. 38, no. 3, pp. 751–766MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    F. Esfandlary, F. and Khalil, H. (1991) Stability Analysis of a Continuous Implementation of Variable Structure Control, IEEE Transactions on Automatic Control, vol. 36, no. 5, pp. 616–619CrossRefGoogle Scholar
  18. 18.
    Hung, J., Gao, W (1993) Variable Structure Control: A Survey, IEEE Transactions on Industrial Electronics, vol. 40, pp. 2–22CrossRefGoogle Scholar
  19. 19.
    Shtessel, Y. and Buffington, J. (1998) Continuous Sliding Mode Control, Proceedings of the American control Conference, Philadelphia, June 2426, pp. 562–563Google Scholar
  20. 20.
    Yoo, B. and Ham, W. (1998) Adaptive Fuzzy Sliding Mode Control of Nonlinear System, IEEE Transactions on Fuzzy Systems, vol. 6, no. 2, pp. 315–321, MayCrossRefGoogle Scholar
  21. 21.
    Sun, F., Sun, Z. and Feng, G. (1999) An Adaptive Fuzzy Controller Based on Sliding Mode for Robot Manipulators,“ IEEE Transactions on Systems, Man and Cybernetics — Part B: Cybernetics, vol. 29, no. 4, pp. 661 –667, AugustCrossRefGoogle Scholar
  22. 22.
    Lin, C. and Wang, S. (1999) Fuzzy system identification using an adaptive learning rule with terminal attractors, Fuzzy Sets and Systems, vol. 101, pp. 343–352MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Shuanghe Yu
    • 1
  • Xinghuo Yu
    • 1
  • Man Zhihong
    • 2
  1. 1.Faculty of Informatics and CommunicationCentral Queensland UniversityRockhamptonAustralia
  2. 2.Department of Computer Science and Electrical EngineeringUniversity of TasmaniaHobartAustralia

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