Skip to main content
Log in

Observer-Based Adaptive Fuzzy Control of Nonlinear Non-strict Feedback System with Input Delay

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

This paper investigates the adaptive fuzzy output feedback control problem for nonlinear non-strict feedback system with input delay. In the control design, the Pade approximation method and fuzzy logic system are used to handle the input delay and unknown functions, and a state observer is designed to approximate the unmeasured states of the system. By backstepping technique, an observer-based adaptive fuzzy control design method is given. The stability of the controlled system and the tracking performance of the system are demonstrated by utilizing the Lyapunov function theory. Finally, a simulation example of electromechanical system is provided to confirm the effectiveness of the proposed control method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Li, Z.J., Xiao, S.T., Ge, S.S., Su, H.: Constrained multi-legged robot system modeling and fuzzy control with uncertain kinematics and dynamics incorporating foot force optimization. IEEE Trans. Syst. Man Cybern. Syst. 46(1), 1–15 (2016)

    Article  Google Scholar 

  2. Fan, Y.Q., Wang, Y.H., Wang, W.Q.: Adaptive fuzzy tracking control with compressor and limiters for uncertain nonlinear systems. Int. J. Fuzzy Syst. 16(1), 31–38 (2014)

    Google Scholar 

  3. Wang, C.H., Wang, J.H., Chen, C.Y.: Analysis and design of indirect adaptive fuzzy controller for nonlinear hysteretic systems. Int. J. Fuzzy Syst. 17(1), 84–93 (2015)

    Article  MathSciNet  Google Scholar 

  4. Li, Z.J., Deng, J., Lu, R.Q., Xu, Y., Bai, J.J., Su, C.Y.: Trajectory tracking control of mobile robot systems incorporating neural-dynamic optimized model predictive approach. IEEE Trans. Syst. Man Cybern. Syst. 46(6), 740–749 (2016)

    Article  Google Scholar 

  5. Pan, Y.P., Yu, H.Y.: Biomimetic hybrid feedback feedforward neural-network learning control. IEEE Trans. Neural Netw. Learn. Syst. 28(6), 1481–1487 (2017)

    Article  Google Scholar 

  6. Tong, S.C., Li, C.Y., Li, Y.M.: Fuzzy adaptive observer backstepping control for MIMO nonlinear systems. Fuzzy Sets Syst. 160(19), 2755–2775 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhou, Q., Shi, P., Lu, J., Xu, S.Y.: Adaptive output-feedback fuzzy tracking control for a class of nonlinear systems. IEEE Trans. Fuzzy Syst. 19(5), 972–982 (2011)

    Article  Google Scholar 

  8. Pan, Y.P., Er, M.J., Liu, Y.Q., Pan, L., Yu, H.Y.: Composite learning fuzzy control of uncertain nonlinear systems. Int. J. Fuzzy Syst. 18(6), 990–998 (2016)

    Article  MathSciNet  Google Scholar 

  9. Zhang, D., Shi, P., Wang, Q.G., Li, Y.: Analysis and synthesis of networked control systems: a survey of recent advances and challenges. ISA Trans. 66, 376–392 (2017)

    Article  Google Scholar 

  10. Liu, Z., Wang, F., Zhang, Y., Chen, X., Chen, C.L.P.: Adaptive fuzzy output-feedback controller design for nonlinear systems via backstepping and small-gain approach. IEEE Trans. Cybern. 44(10), 1714–1725 (2014)

    Article  Google Scholar 

  11. Pan, Y.P., Yu, H.Y.: Composite learning from adaptive dynamic surface control. IEEE Trans. Autom. Control 61(9), 2603–2609 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zhang, D., Nguang, S.K., Srinivasan, D., Li, Y.: Distributed filtering for discrete-time T-S fuzzy systems with incomplete measurements. IEEE Trans. Fuzzy Syst. (2017). doi:10.1109/TFUZZ.2017.2725228

    Google Scholar 

  13. Chen, B., Liu, X.P., Ge, S.S., Lin, C.: Adaptive fuzzy control of a class of nonlinear systems by fuzzy approximation approach. IEEE Trans. Fuzzy Syst. 20(6), 1012–1021 (2012)

    Article  Google Scholar 

  14. Wang, H.Q., Chen, B., Liu, K., Liu, X., Lin, C.: Adaptive neural tracking control for a class of nonstrict-feedback stochastic nonlinear systems with unknown backlash-like hysteresis. IEEE Trans. Neural Netw. Learn. Syst. 21(5), 947–958 (2014)

    Article  Google Scholar 

  15. Zhou, Q., Wang, L.J., Wu, C.W., Li, H.Y., Du, H.P.: Adaptive fuzzy control for nonstrict-feedback systems with input saturation and output constraint. IEEE Trans. Syst. Man Cybern. Syst. 47(1), 1–12 (2017)

    Article  Google Scholar 

  16. 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)

    Article  MathSciNet  Google Scholar 

  17. Tong, S.C., Li, Y.M., Sui, S.: Adaptive fuzzy tracking control design for uncertain non-strict feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 24, 1441–1454 (2016)

    Article  Google Scholar 

  18. Wang, H.Q., Liu, X.P., Liu, K.F., Karimi, H.R.: Approximation-based adaptive fuzzy tracking control for a class of nonstrict-feedback stochastic nonlinear time-delay systems. IEEE Trans. Fuzzy Syst. 23(5), 1746–1760 (2015)

    Article  Google Scholar 

  19. Liu, Z., Lai, G., Zhang, Y., Chen, X., Chen, C.L.P.: Adaptive neural control for a class of nonlinear time-varying delay systems with unknown hysteresis. IEEE Trans. Neural Netw. Learn. Syst. 25(12), 2129–2140 (2014)

    Article  Google Scholar 

  20. Hamdy, M., Ramadan, A.: Design of smith predictor and fuzzy decoupling for MIMO chemical processes with time delays. Asian J. Control 19(2), 1–10 (2017)

    MathSciNet  MATH  Google Scholar 

  21. Zhou, J., Wang, W., Wen, C.Y.: Adaptive backstepping control of uncertain systems with unknown input time-delay. Automatica 45(6), 1415–1422 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  22. Lee, C H., Cheng, H.T.: Identification and fuzzy controller design for nonlinear uncertain systems with input time-delay. Int. J. Fuzzy Syst. 11(2), 73–85 (2009)

    MathSciNet  Google Scholar 

  23. Zhu, Q., Fei, S., Zhang, T., Zhang, K., Li, T.: Adaptive RBF neural-networks control for a class of time-delay nonlinear systems. Neurocomputing 71(16), 3617–3624 (2008)

    Article  Google Scholar 

  24. Khanesar, M.A., Kaynak, O., Yin, S., Gao, H.: Adaptive indirect fuzzy sliding mode controller for networked control systems subject to time-varying network-induced time delay. IEEE Trans. Fuzzy Syst. 23(1), 205–214 (2015)

    Article  Google Scholar 

  25. Dawson, D.M., Carroll, J.J., Schneider, M.: Integrator backstepping control of a brush DC motor turning a robotic load. IEEE Trans. Control Syst. Technol. 2(3), 233–244 (1994)

    Article  Google Scholar 

  26. Wang, L.X.: Stable adaptive fuzzy control of nonlinear systems. IEEE Trans. Fuzzy Syst. 1(2), 146–155 (1993)

    Article  Google Scholar 

  27. Hamdy, M.: State observer based dynamic fuzzy logic system control for a class of SISO nonlinear systems. Int. J. Autom. Comput. 10(2), 118–124 (2013)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 61773188, 61573175).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shaocheng Tong.

Ethics declarations

Conflict of interest

The author declares that there is no conflict of interests regarding the publication of this paper.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, N., Tong, S. & Li, Y. Observer-Based Adaptive Fuzzy Control of Nonlinear Non-strict Feedback System with Input Delay. Int. J. Fuzzy Syst. 20, 236–245 (2018). https://doi.org/10.1007/s40815-017-0388-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-017-0388-9

Keywords

Navigation