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Indirect Adaptive Fuzzy Control of Nonlinear Systems with Terminal Sliding Modes

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Book cover Fuzzy Logic

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 81))

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Abstract

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.

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References

  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. 419–435

    Article  Google Scholar 

  2. Zinober, A. (1993) Variable Structure and Lyapunov Control, London: Springer-Verlag

    Google Scholar 

  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.

    Article  Google Scholar 

  4. Wang, L. (1993) Stable Adaptive Fuzzy Control of Nonlinear Systems, IEEE Transactions on Fuzzy Systems, vol. 1, no. 2, pp. 146 – 155, May

    Article  Google Scholar 

  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, October

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  8. Utkin, V. (1992) Sliding Modes in Control Optimization. Berlin, Heidelberg: Springer-Verlag

    Book  Google Scholar 

  9. Slotine, J. and Li, W. (1991) Applied Nonlinear Control, Prentice Hall, Englewood Cliffs, New Jersey

    Google Scholar 

  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. 1165–1176

    Article  MathSciNet  MATH  Google Scholar 

  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. 1065–1070

    MathSciNet  Google Scholar 

  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-Verlag

    Google Scholar 

  13. Yu, X. and Man, Z. (2000) Fast Terminal Sliding Mode Control for Single Input Systems, accepted for presentation at 2000 Asian Control Conference, Shanghai

    Google Scholar 

  14. Haimo, V. (1986) Finite Time Controller, SIAM Journal of Control and Optimization, vol. 24, no. 4, pp. 760–770, July

    Article  MathSciNet  MATH  Google Scholar 

  15. Bhat, S. and Bernstein, D. (1995) Lyapunov Analysis of Finite-time Differential Equations, Proceedings of the American Control Conference, Seattle, pp. 1831–1832

    Google Scholar 

  16. Bhat, S. and Bernstein, D. (2000) Finite-time Stability of Continuous Autonomous Systems, SIAM J. Control and Optimization, vol. 38, no. 3, pp. 751–766

    Article  MathSciNet  MATH  Google Scholar 

  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. 616–619

    Article  Google Scholar 

  18. Hung, J., Gao, W (1993) Variable Structure Control: A Survey, IEEE Transactions on Industrial Electronics, vol. 40, pp. 2–22

    Article  Google Scholar 

  19. Shtessel, Y. and Buffington, J. (1998) Continuous Sliding Mode Control, Proceedings of the American control Conference, Philadelphia, June 2426, pp. 562–563

    Google Scholar 

  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, May

    Article  Google Scholar 

  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, August

    Article  Google Scholar 

  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. 343–352

    Article  MathSciNet  MATH  Google Scholar 

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© 2002 Springer-Verlag Berlin Heidelberg

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Yu, S., Yu, X., Zhihong, M. (2002). Indirect Adaptive Fuzzy Control of Nonlinear Systems with Terminal Sliding Modes. In: Dimitrov, V., Korotkich, V. (eds) Fuzzy Logic. Studies in Fuzziness and Soft Computing, vol 81. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1806-2_19

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  • DOI: https://doi.org/10.1007/978-3-7908-1806-2_19

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-2496-4

  • Online ISBN: 978-3-7908-1806-2

  • eBook Packages: Springer Book Archive

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