Nonlinear Dynamics

, Volume 79, Issue 1, pp 417–426 | Cite as

Design of adaptive fuzzy-based tracking control of input time delay nonlinear systems

Original Paper


This paper proposes an adaptive fuzzy logic tracking control for unknown nonlinear systems having input time delay. In the controller design, a filtered tracking error is introduced to facilitate handling of the time delay. Approximation capability of fuzzy logic systems are exploited to provide approximations of unknown nonlinear functions that appear in the tracking controller. Lyapunov stability analysis shows that the designed tracking control yields bounded signals of the closed-loop system. Simulation examples are provided to validate the effectiveness of the proposed controller in achieving desired tracking with bounded control signals.


Input delay Nonlinear system  Adaptive fuzzy control 


  1. 1.
    Richard, J.: Time-delay systems: an overview of som erecent advanes and open problems. Automatica 39, 1667–1694 (2003)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    Wu, M., He, Y., She, J., Liu, G.: Delay-dependent criteria for robuststability of time-varying delay systems. Automatica 40, 1435–1439 (2004)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Krastic, M.: Input delay compensation for forward complete and feed-forward nonlinear systems. IEEE Trans. Autom. Control 55(2), 287–303 (2010)CrossRefGoogle Scholar
  4. 4.
    Bekiaris-Liberis, N., Krastic, M.: Compensation of state-dependent input delay of nonlinear systems. IEEE Trans. Autom. Control 58(2), 275–289 (2013)CrossRefGoogle Scholar
  5. 5.
    Shin, H.-S., Choi, H.-L., Lim, J.-T.: Feedback linearization of uncertain nonlinera systems with time delay. IEEE Proc Control Theory Appl. 153(6):732–736 (2006)Google Scholar
  6. 6.
    Yue, D., Won, S., Kwon, O.: Notes on robust stabilization of uncertain input-delay systems by sliding mode control with delay compensation. Trans. Control Autom. Syst. Eng. 4(3), 195–198 (2002)Google Scholar
  7. 7.
    Marquez-Martines, L.A., Moog, C.H.: Input–output linearization of time-delay systems. IEEE Trans. Autom. Control. 40(5), 781–786 (2004)CrossRefGoogle Scholar
  8. 8.
    Marquez-Martines, L.A., Moog, C.H.: Trajectory tracking control for nonlinera time-delay systems. Kybernetica 57(4), 370–380 (2001)Google Scholar
  9. 9.
    Fischer, N., Dani, A., Sharma, N., Dixon, W.E.: Saturated control of uncertain nonlinera system with input delay. Automatica 49, 1741–1747 (2013)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Liu, Y.-J., Li, Y.-X.: Adaptive fuzzy output-feedback control of uncertain SISO nonlinear systems. Nonlinear Dyn. 61(4), 749–761 (2010)CrossRefMATHGoogle Scholar
  11. 11.
    Li, Y., Ren, C., Tong, S.: Adaptive fuzzy backstepping output feedback control of nonlinear uncertain time-delays systems based on high-gain filters. Nonlinear Dyn. 69(3), 781–792 (2012)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Zou, A.-M., Hou, Z.-G., Tan, M.: Adaptive control of a class of nonlinear pure-feedback systems using fuzzy backstepping approach. IEEE Trans. Fuzzy Syst. 16, 886–897 (2008)CrossRefGoogle Scholar
  13. 13.
    Li, Y., Tong, S., Liu, Y., Li, T.: Adaptive fuzzy robust output feedback control of nonlinear systems with unknown dead zones based on a small-gain approach. IEEE Trans. Fuzzy Syst. 22, 164–176 (2014)CrossRefGoogle Scholar
  14. 14.
    Liu, Y.-J., Wang, Z.-F.: Adaptive fuzzy controller design of nonlinear systems with unknown gain sign. Nonlinear Dyn. 58, 687–695 (2009)CrossRefMATHGoogle Scholar
  15. 15.
    Sun, G., Wang, D., Li, T., Peng, Z., Wang, H.: Single neural network approximation based adaptive control for a class of uncertain strict-feedback nonlinear systems. Nonlinear Dyn. 72, 175–184 (2013)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Wang, H., Chen, B., Lin, C.: Adaptive neural tracking control for a class of perturbed pure-feedback nonlinear systems. Nonlinear Dyn. 72, 207–220 (2013)CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Chen, B., Liu, X., Liu, K., Lin, C.: Fuzzy-approximation-based adaptive control of strict-feedback nonlinear systems with time delays. IEEE Trans. Fuzzy Syst. 18(5), 883–892 (2010)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Zhou, Q., Shi, P., Xu, S., Li, H.: Adaptive output feedback control for nonlinear time-delay systems by fuzzy approximation approach. IEEE Trans. Fuzzy Syst. 21(2), 301–313 (2013)CrossRefGoogle Scholar
  19. 19.
    Hua, C., Wang, Q.-G., Guan, X.: Robust adaptive controller design for nonlinear time-delay systems via T–S fuzzy approach. IEEE Trans. Fuzzy Syst. 17(4), 901–910 (2009)CrossRefGoogle Scholar
  20. 20.
    Chen, B., Liu, X., Liu, K., Shi, P., Lin, C.: Direct adaptive fuzzy control for nonlinear systems with time varying delays. Inf. Sci. 180(5), 776–792 (2010)CrossRefMATHMathSciNetGoogle Scholar
  21. 21.
    Chen, B., Liu, X., Liu, K., Lin, C.: Adaptive control for nonlinear MIMO time-delay systems based on fuzzy approximation. Inf. Sci. 222(10), 576–592 (2013)CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    Zhu, Q., Song, A.-G., Zhang, T.-P., Yang, Y.-Q.: Fuzzy adaptive control of delayed high order nonlinear systems. Int. J. Autom. Comput. 9(2), 191–199 (2012)CrossRefGoogle Scholar
  23. 23.
    Yousef, H.A., Hamdy, M., Shafiq, M.: Adaptive fuzzy-based tracking control for a class of strict feedback SISO nonlinear time-delay systems without backstepping. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 20(3), 339–353 (2012)CrossRefMATHMathSciNetGoogle Scholar
  24. 24.
    Yousef, H.A., Hamdy, M.: Observer-based adaptive fuzzy control for a class of nonlinear time-delay systems. Int. J. Autom. Comput. 10(4), 275–280 (2013)CrossRefGoogle Scholar
  25. 25.
    Wang, L.X.: Fuzzy System and Control: Design and Stability Analysis. Prentice-Hall, Englewood Cliffs, NJ (1994)Google Scholar
  26. 26.
    Khalil, H.: Nonlinear Systems. Prentice-Hall, Englewood Cliffs, NJ (2002)MATHGoogle Scholar
  27. 27.
    Wang, L.-X.: A Course in Fuzzy Systems and Control. Prentice-Hall, Englewood Cliffs, NJ (1997)MATHGoogle Scholar
  28. 28.
    Choi, H.-L., Lim, J.-T.: Asymptotic stabilization of an input-delayed chain of integrators. Syst. Control Lett. 59, 374–379 (2010)CrossRefMATHMathSciNetGoogle Scholar
  29. 29.
    Detcheva, V., Spassov, V.: A simple nonlinear oscillator: analytic and numerical solution. Phys. Educ. 28, 39–42 (1993)CrossRefGoogle Scholar
  30. 30.
    Machowski, J., Bialek, J.W., Bumby, J.: Power System Dynamics: Stability and Control, 2nd edn. Wiley, London (2008)Google Scholar
  31. 31.
    Kavasseri, R.G.: Delay induced oscillations in a fundamental power system model, arXiv:nlin/0604006, April 2006, pp. 1–8
  32. 32.
    Yousef, H.A., Hamdy, M., Shafiq, M.: Flatness-based adaptive fuzzy output tracking excitation control for power system generators. J. Frankl. Inst. 350, 2334–2353 (2013)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringSultan Qaboos UniversityMuscatSultanate of Oman

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