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Fuzzy Adaptive Practical Finite-Time Control for Time Delays Nonlinear Systems

  • Kewen Li
  • Shaocheng TongEmail author
Article
  • 35 Downloads

Abstract

This paper focuses on fuzzy adaptive practical finite-time output feedback control problem for a class of single-input and single-output nonlinear system with time-varying delays in nonstrict feedback form. Fuzzy logic systems are adopted to approximate the unknown nonlinear functions, and state observer is constructed to estimate the unmeasured states. By combining practical finite-time Lyapunov stability theory with the backstepping design, an observer-based fuzzy adaptive practical finite-time control strategy is proposed. Meanwhile, the stability of the closed-loop system is proved, which means that the output can follow the given reference signal in a finite time, and the closed-loop system is semi-global practical finite-time stability. Finally, two simulation examples are provided to elaborate the effectiveness of the presented control strategy.

Keywords

Practical finite-time stability Fuzzy adaptive control Nonstrict feedback system Backstepping design Time-varying delays 

Notes

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grants 61773188 and 61573175.

References

  1. 1.
    Hamdy, M., El Ghazaly, G.: Adaptive neural decentralized control for strict feedback nonlinear interconnected systems via backstepping. Neural Comput. Appl. 24(2), 259–269 (2014)CrossRefGoogle Scholar
  2. 2.
    Chen, W.S., Jiao, L.C., Li, J., Li, R.H.: Adaptive NN backstepping output-feedback control for stochastic nonlinearly strict-feedback systems with time-varying delays. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 40(3), 939–950 (2010)CrossRefGoogle Scholar
  3. 3.
    Yang, Y.S., Feng, G., Ren, J.S.: A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems. IEEE Trans. Syst. Man Cybern. Part A Syst. Hum. 34(3), 406–420 (2004)CrossRefGoogle Scholar
  4. 4.
    Wang, M., Liu, X.P., Shi, P.: Adaptive neural control of pure-feedback nonlinear time-delay systems via dynamic surface technique. IEEE Trans. Syst. Man Cybern. Part B (Cybern.) 41(6), 1681–1692 (2011)CrossRefGoogle Scholar
  5. 5.
    Zhou, Q., Wang, L.J., Wu, C.W., Li, H.Y.: Adaptive fuzzy tracking control for a class of pure-feedback nonlinear systems with time-varying delay and unknown dead zone. Fuzzy Sets Syst. 329, 36–60 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Li, H.Y., Wang, L.J., Du, H.P., Boulkroune, A.: Adaptive fuzzy backstepping tracking control for strict-feedback systems with input delay. IEEE Trans. Fuzzy Syst. 25(3), 642–652 (2017)CrossRefGoogle Scholar
  7. 7.
    Zhou, Q., Shi, P., Xu, S.Y., Li, H.Y.: Observer-based adaptive neural network control for nonlinear stochastic systems with time delay. IEEE Trans. Neural Netw. Learn. Syst. 24(1), 71–80 (2013)CrossRefGoogle Scholar
  8. 8.
    Chen, B., Liu, X.P., Liu, K.F., Lin, C.: Fuzzy-approximation-based adaptive control of strict-feedback nonlinear systems with time delays. IEEE Trans. Fuzzy Syst. 18(5), 883–892 (2010)CrossRefGoogle Scholar
  9. 9.
    Li, Y.M., Ren, C.E., Tong, S.C.: Adaptive fuzzy backstepping output feedback control for a class of MIMO time-delay nonlinear systems based on high-gain observer. Nonlinear Dyn. 67(2), 1175–1191 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Wang, H.Q., Liu, X.P., Liu, K.F., Karimi, H.R.: Approximation-based adaptive fuzzy control for a class of nonstrict-feedback stochastic nonlinear time-delay systems. IEEE Trans. Fuzzy Syst. 23(5), 1746–1760 (2015)CrossRefGoogle Scholar
  11. 11.
    Yoo, S.J.: Approximation-based adaptive tracking of a class of uncertain nonlinear time-delay systems in nonstrict-feedback form. Int. J. Syst. Sci. 48(7), 1347–1355 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Wang, H.Q., Liu, K.F., Liu, X.P., Chen, B., Lin, C.: Neural-based adaptive output-feedback control for a class of nonstrict-feedback stochastic nonlinear systems. IEEE Trans. Cybern. 45(9), 1977–1987 (2015)CrossRefGoogle Scholar
  13. 13.
    Chen, B., Lin, C., Liu, X.P., Liu, K.F.: Observer-based adaptive fuzzy control for a class of nonlinear delayed systems. IEEE Trans. Syst. Man Cybern. Syst. 46(1), 27–36 (2016)CrossRefGoogle Scholar
  14. 14.
    Tong, S.C., Li, Y.M., Sui, S.: Adaptive fuzzy tracking control design for SISO uncertain nonstrict feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 24(6), 1441–1454 (2016)CrossRefGoogle Scholar
  15. 15.
    Chen, B., Zhang, H.G., Lin, C.: Observer-based adaptive neural network control for nonlinear systems in nonstrict-feedback form. IEEE Trans. Neural Netw. Learn. Syst. 27(1), 89–98 (2016)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Bhat, S.P., Bernstein, D.S.: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Autom. Control 43(5), 678–682 (1998)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Bhat, S.P., Bernstein, D.S.: Finite-time stability of continuous autonomous systems. SIAM J. Control Optim. 38(3), 751–766 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Wang, F., Chen, B., Lin, C., Zhang, J., Meng, X.Z.: Adaptive neural network finite-time output feedback control of quantized nonlinear systems. IEEE Trans. Cybern. 48(6), 1839–1848 (2018)CrossRefGoogle Scholar
  19. 19.
    Chen, B., Wang, F., Liu, X.P., Lin, C.: Finite-time adaptive fuzzy tracking control design for nonlinear systems. IEEE Trans. Fuzzy Syst. 26(3), 1207–1216 (2018)CrossRefGoogle Scholar
  20. 20.
    Sun, Y.M., Chen, B., Lin, C., Wang, H.H.: Finite-time adaptive control for a class of nonlinear systems with nonstrict feedback structure. IEEE Trans. Cybern. 48(10), 2774–2782 (2018)CrossRefGoogle Scholar
  21. 21.
    Lv, W.S., Wang, F.: Finite-time adaptive fuzzy tracking control for a class of nonlinear systems with unknown hysteresis. Int. J. Fuzzy Syst. 20(3), 782–790 (2017)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Sui, S., Tong, S.C., Chen, C.L.P.: Finite-time filter decentralized control for nonstrict-feedback nonlinear large-scale systems. IEEE Trans. Fuzzy Syst. 26(7), 3289–3300 (2018)CrossRefGoogle Scholar
  23. 23.
    Huang, J.S., Wen, C.Y., Wang, W., Song, Y.D.: Design of adaptive finite-time controllers for nonlinear uncertain systems based on given transient specifications. Automatica 69, 395–404 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Yang, Y.N., Hua, C.C., Guan, X.P.: Adaptive fuzzy finite-time coordination control for networked nonlinear bilateral teleoperation system. IEEE Trans. Fuzzy Syst. 22(3), 631–641 (2014)CrossRefGoogle Scholar
  25. 25.
    Wu, J., Li, J., Zong, G.D., Chen, W.S.: Global finite-time adaptive stabilization of nonlinearly parametrized systems with multiple unknown control directions. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1405–1414 (2017)CrossRefGoogle Scholar
  26. 26.
    Khoo, S.Y., Yin, J.L., Man, Z.H., Yu, X.H.: Finite-time stabilization of stochastic nonlinear systems in strict-feedback form. Automatica 49(5), 1403–1410 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Cai, M.J., Xiang, Z.R.: Adaptive finite-time control of a class of non-triangular nonlinear systems with input saturation. Neural Comput. Appl. 29(7), 565–576 (2016)CrossRefGoogle Scholar
  28. 28.
    Cai, M.J., Xiang, Z.R.: Adaptive practical finite-time stabilization for uncertain nonstrict feedback nonlinear systems with input nonlinearity. IEEE Trans. Syst. Man Cybern. Syst. 47(7), 1668–1678 (2017)CrossRefGoogle Scholar

Copyright information

© Taiwan Fuzzy Systems Association 2019

Authors and Affiliations

  1. 1.Department of MathematicsLiaoning University of TechnologyJinzhouChina

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