Skip to main content
SpringerLink
Log in

Event-triggered adaptive neural tracking control of nonstrict-feedback nonlinear systems with unknown measurement

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

This paper studies the event-triggered control (ETC) of the nonstrict-feedback nonlinear system with unknown measurement and unknown model dynamics, where the output function \(y=h(x_1)\) is uncertain and nonlinear. The radial basis function neural networks (RBF NNs) are utilized to compensate for the packaged uncertainties including \(x_1-h(x_1)\). An event-triggered state observer is established to achieve the output-feedback control. The observer-based control design is thereby carried out following from the backstepping method. With two levels approximating structures, the problem of “algebraic loop” is overcome by using the property of the basis function. It should be noted that the ETC works in the sensor-to-controller (SC) channel. While it is combined with backstepping, the consequent problem called “jumps of virtual control laws (JVCL)” [1] is solved by introducing the average dwell time (ADT) technique. A composite triggering condition with the dead zone is constructed to guarantee the semi-globally uniformly ultimate boundedness (SGUUB) of all the errors, as well as to avoid the “Zeno” behavior. Three numerical examples verify the effectiveness of the proposed scheme.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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
Fig. 14
Fig. 15

Similar content being viewed by others

Data availability

The data for supporting the findings will be made available upon the reasonable request for academic use by contacting the corresponding author.

References

  1. Deng, Y., Zhang, X., Zhang, G., Han, X.: Adaptive neural tracking control of strict-feedback nonlinear systems with event-triggered state measurement. ISA Trans. 117, 28–39 (2021)

    Article  Google Scholar 

  2. Liu, Z., Shi, P., Chen, B., Lin, C.: Control design for uncertain switched nonlinear systems: adaptive neural approach. IEEE Trans. Syst. Man Cybern. Syst. 51(4), 2322–2331 (2021)

    Article  Google Scholar 

  3. Chen, B., Zhang, H., 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 

  4. Zhang, L., Chen, B., Lin, C., Shang, Y.: Fuzzy adaptive fixed-time consensus tracking control of high-order multi-agent systems. IEEE Trans. Fuzzy Syst. (2021). https://doi.org/10.1109/TFUZZ.2020.3042239

    Article  Google Scholar 

  5. Zhang, J., Xiang, Z.: Event-triggered adaptive neural network sensor failure compensation for switched interconnected nonlinear systems with unknown control coefficients. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3069817

    Article  Google Scholar 

  6. Deng, Y., Liu, T., Zhao, D.: Event-triggered output-feedback adaptive tracking control of autonomous underwater vehicles using reinforcement learning. Appl. Ocean Res. 113, 102676 (2021)

    Article  Google Scholar 

  7. Deng, Y., Zhang, X., Zhao, B., Zhao, H.: Event-triggered compound learning tracking control of autonomous surface vessels in the measurement network. Ocean Eng. 228, 108817 (2021)

    Article  Google Scholar 

  8. Li, Y., Wang, T., Liu, W., Tong, S.: Neural network adaptive output-feedback optimal control for active suspension systems. IEEE Trans. Syst. Man Cybern. Syst. (2021). https://doi.org/10.1109/TSMC.2021.3089768

    Article  Google Scholar 

  9. Jia, T., Pan, Y., Liang, H., Lam, H.K.: Event-based adaptive fixed-time fuzzy control for active vehicle suspension systems with time-varying displacement constraint. IEEE Trans. Fuzzy Syst. (2021). https://doi.org/10.1109/TFUZZ.2021.3075490

    Article  Google Scholar 

  10. Tong, S., Li, Y., Sui, S.: Adaptive fuzzy tracking control design for SISO uncertain nonstrict feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 24(6), 1441–1454 (2016)

    Article  Google Scholar 

  11. Chen, B., Liu, K., Liu, X., Shi, P., Lin, C., Zhang, H.: Approximation-based adaptive neural control design for a class of nonlinear systems. IEEE Trans. Cybern. 44(5), 610–619 (2014)

    Article  Google Scholar 

  12. Tong, S., Li, Y., Sui, S.: Adaptive fuzzy output feedback control for switched nonstrict-feedback nonlinear systems with input nonlinearities. IEEE Trans. Fuzzy Syst. 24(6), 1426–1440 (2016)

    Article  Google Scholar 

  13. Liu, Y., Zhu, Q.: Adaptive fuzzy finite-time control for nonstrict-feedback nonlinear systems. IEEE Trans. Cybern. (2021). https://doi.org/10.1109/TCYB.2021.3063139

    Article  MATH  Google Scholar 

  14. Chen, B., Zhang, H., Liu, X., Lin, C.: Neural observer and adaptive neural control design for a class of nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst. 29(9), 4261–4271 (2018)

    Article  Google Scholar 

  15. Zhai, J., Qian, C.: Global control of nonlinear systems with uncertain output function using homogeneous domination approach. Int. J. Robust Nonlinear Control 22(14), 1543–1561 (2012)

    Article  MathSciNet  Google Scholar 

  16. Chen, C., Qian, C., Sun, Z.: Global output feedback stabilization of a class of nonlinear systems with unknown measurement sensitivity. IEEE Trans. Autom. Control 63(7), 2212–2217 (2018)

    Article  MathSciNet  Google Scholar 

  17. Hua, C., Ning, P., Li, K., Guan, X.: Fixed-time prescribed tracking control for stochastic nonlinear systems with unknown measurement sensitivity. IEEE Trans. Cybern. (2021). https://doi.org/10.1109/TCYB.2020.3012560

    Article  Google Scholar 

  18. Zhang, X., Lin, W.: Robust output feedback control of polynomial growth nonlinear systems with measurement uncertainty. Int. J. Robust Nonlinear Control 29(13), 4562–4576 (2019)

    Article  MathSciNet  Google Scholar 

  19. Zha, W., Qian, C., Zhai, J., Fei, S.: Robust control for a class of nonlinear systems with unknown measurement drifts. Automatica 71, 33–37 (2016)

    Article  MathSciNet  Google Scholar 

  20. Qian, C., He, S., Zou, Y.: Compensator-based output feedback stabilizers for a class of planar systems with unknown structures and measurements. IEEE Trans. Autom. Control (2021). https://doi.org/10.1109/TAC.2021.3079360

    Article  Google Scholar 

  21. Li, Y., Yang, G.: Event-triggered adaptive backstepping control for parametric strict-feedback nonlinear systems. Int. J. Robust Nonlinear Control 28(3), 976–1000 (2018)

    Article  MathSciNet  Google Scholar 

  22. Cao, L., Zhou, Q., Dong, G., Li, H.: Observer-based adaptive event-triggered control for nonstrict-feedback nonlinear systems with output constraint and actuator failures. IEEE Trans. Syst. Man Cybern. Syst. 51(3), 1380–1391 (2021)

    Article  Google Scholar 

  23. Ma, J., Xu, S., Ma, Q., Zhang, Z.: Event-triggered adaptive neural network control for nonstrict-feedback nonlinear time-delay systems with unknown control directions. IEEE Trans. Neural Netw. Learn. Syst. 31(10), 4196–4205 (2020)

    Article  MathSciNet  Google Scholar 

  24. Xu, Y., Zhou, Q., Li, T., Liang, H.: Event-triggered neural control for non-strict-feedback systems with actuator failures. IET Control Theory Appl. 13(2), 171–182 (2019)

    Article  MathSciNet  Google Scholar 

  25. Wang, A., Liu, L., Qiu, J., Feng, G.: Event-triggered adaptive fuzzy output-feedback control for nonstrict-feedback nonlinear systems with asymmetric output constraint. IEEE Trans. Cybern. 52(1), 712–722 (2022)

    Article  Google Scholar 

  26. Wang, H., Xu, K., Qiu, J.: Event-triggered adaptive fuzzy fixed-time tracking control for a class of nonstrict-feedback nonlinear systems. IEEE Trans. Circuits Syst. I Regular Papers 68(7), 3058–3068 (2021)

    Article  Google Scholar 

  27. Wang, L., Chen, C.L.P.: Reduced-order observer-based dynamic event-triggered adaptive NN control for stochastic nonlinear systems subject to unknown input saturation. IEEE Trans. Neural Netw. Learn. Syst. 32(4), 1678–1690 (2021)

    Article  MathSciNet  Google Scholar 

  28. Deng, Y., Zhang, X., Zhang, G., Huang, C.: Parallel guidance and event-triggered robust fuzzy control for path following of autonomous wing-sailed catamaran. Ocean Eng. 190, 106442 (2019)

    Article  Google Scholar 

  29. Deng, Y., Zhang, X., Zhang, Q., Hu, Y.: Event-triggered composite adaptive fuzzy control of sailboat with heeling constraint. Ocean Eng. 211, 107627 (2020)

    Article  Google Scholar 

  30. Yan, S., Nguang, S.K., Gu, Z.: \({\rm H}_\infty \) weighted integral event-triggered synchronization of neural networks with mixed delays. IEEE Trans. Ind. Inf. 17(4), 2365–2375 (2021)

    Article  Google Scholar 

  31. Yan, S., Gu, Z., Nguang, S.K.: Memory-event-triggered \({\rm H}_\infty \) output control of neural networks with mixed delays. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/tnnls.2021.3083898

    Article  Google Scholar 

  32. Yan, S., Gu, Z., Park, J.H., Xie, X.: Adaptive memory-event-triggered static output control of t-s fuzzy wind turbine systems. IEEE Trans. Fuzzy Syst. (2021). https://doi.org/10.1109/tfuzz.2021.3133892

    Article  Google Scholar 

  33. Wang, W., Li, Y., Tong, S.: Neural-network-based adaptive event-triggered consensus control of nonstrict-feedback nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst. 32(4), 1750–1764 (2021)

    Article  MathSciNet  Google Scholar 

  34. Li, Y., Yang, G.: Model-based adaptive event-triggered control of strict-feedback nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst. 29(4), 1033–1045 (2018)

    Article  MathSciNet  Google Scholar 

  35. Szanto, N., Narayanan, V., Jagannathan, S.: Event-sampled direct adaptive NN output-and state-feedback control of uncertain strict-feedback system. IEEE Trans. Neural Netw. Learn. Syst. 29(5), 1850–1863 (2018)

    Article  MathSciNet  Google Scholar 

  36. Deng, Y., Zhang, X., Im, N., Zhang, G., Zhang, Q.: Model-based event-triggered tracking control of underactuated surface vessels with minimum learning parameters. IEEE Trans. Neural Netw. Learn. Syst. 31(10), 4001–4014 (2020)

    Article  MathSciNet  Google Scholar 

  37. Deng, Y., Zhang, X.: Event-triggered composite adaptive fuzzy output feedback control for path following of autonomous surface vessels. IEEE Trans. Fuzzy Syst. 29(9), 2701–2713 (2021)

    Article  Google Scholar 

  38. Wang, M., Wang, Z., Chen, Y., Sheng, W.: Adaptive neural event-triggered control for discrete-time strict-feedback nonlinear systems. IEEE Trans. Cybern. 50(7), 2946–2958 (2020)

    Article  Google Scholar 

  39. Fossen, T.I.: Handbook of Marine Craft Hydrodynamics and Motion Control. Wiley, New York (2011)

    Book  Google Scholar 

  40. Yan, J., Guo, Z., Yang, X., Luo, X., Guan, X.: Finite-time tracking control of autonomous underwater vehicle without velocity measurements. IEEE Trans. Syst. Man Cybern. Syst. (2021). https://doi.org/10.1109/tsmc.2021.3095975

    Article  Google Scholar 

Download references

Funding

This work is supported by the Natural Science Foundation of China (No.52101375), and the Hebei Province Natural Science Fund (No.E2021203142).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Hebei Provincial Key Laboratory of Heavy Machinery Fluid Power Transmission and Control, Yanshan University, Qinhuangdao, 066044, China

    Yingjie Deng

  2. Institute of Complexity Science, Qingdao University, Qingdao, 266071, China

    Zhiliang Liu & Bing Chen

Authors
  1. Yingjie Deng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhiliang Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bing Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yingjie Deng.

Ethics declarations

Conflict of interest

There is no potential conflict of interest in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deng, Y., Liu, Z. & Chen, B. Event-triggered adaptive neural tracking control of nonstrict-feedback nonlinear systems with unknown measurement. Nonlinear Dyn 109, 863–875 (2022). https://doi.org/10.1007/s11071-022-07454-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-022-07454-y

Keywords

Search

Navigation