SpringerLink
Log in

Global fixed-time event-triggered control for stochastic nonlinear systems with full state constraints

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

Abstract

This paper is devoted to solving the global fixed-time event-triggered stabilization problem for a class of nonstrict-feedback stochastic systems with full state constraints. Firstly, the nonlinear state constrained system is converted into a novel constrained free system with the help of nonlinear map**s, which eliminates the feasibility conditions of virtual control signals while satisfying the state constraints. Secondly, a lemma about the variable separation technique is put forward to deal with unknown nonlinear terms in stochastic systems, which avoids the restrictive growth assumption that unknown functions need to be satisfied. Then, a fixed-time event-triggered control strategy based on the symbol function technique is designed by combining the backstep** method with the fixed-time stability theory of stochastic systems. It is proved that all closed-loop signals are globally fixed-time stable in probability. Finally, a numerical example and a single-link robot system are simulated to verify the availability and feasibility of the developed approach.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Similar content being viewed by others

Data availability

All date generated or analyzed during this study are included in this published article.

References

  1. Chen, C., Gui, W., Guan, Z., Wang, R., Zhou, S.: Adaptive neural control for a class of stochastic nonlinear systems with unknown parameters, unknown nonlinear functions and stochastic disturbances. Neurocomputing 226, 101–108 (2017)

    Article  Google Scholar 

  2. Su, H., Zhang, W.: Adaptive fuzzy tracking control for a class of nonstrict-feedback stochastic nonlinear systems with actuator faults. IEEE Trans. Syst. Man Cybern. Syst. 50(9), 3456–3469 (2020)

    Article  Google Scholar 

  3. Wang, X., **a, J., Sun, W., Shen, H., Wei, W.: Adaptive fuzzy tracking control for nonstrict-feedback switched stochastic nonlinear systems with nonsymmetric dead-zone input: a mdadt switching approach. Nonlinear Dyn. 106(4), 3401–3413 (2021)

    Article  Google Scholar 

  4. Zhou, Q., Li, H., Wang, L., Lu, R.: Prescribed performance observer-based adaptive fuzzy control for nonstrict-feedback stochastic nonlinear systems. IEEE Trans. Syst. Man Cybern. Syst. 48(10), 1747–1758 (2018)

    Article  Google Scholar 

  5. Wang, H., Liu, P.X., Bao, J., **e, X., Li, S.: Adaptive neural output-feedback decentralized control for large-scale nonlinear systems with stochastic disturbances. IEEE Trans. Neural Netw. Learn. Syst. 31(3), 972–983 (2020)

    Article  MathSciNet  Google Scholar 

  6. Niu, B., Liu, J., Duan, P., Li, J., Yang, D.: Reduced-order observer-based adaptive fuzzy tracking control scheme of stochastic switched nonlinear systems. IEEE Trans. Syst. Man Cybern. Syst. 51(7), 4566–4578 (2021)

    Article  Google Scholar 

  7. Niu, B., Duan, P., Li, J., Li, X.: Adaptive neural tracking control scheme of switched stochastic nonlinear pure-feedback nonlower triangular systems. IEEE Trans. Syst. Man Cybern. Syst. 51(2), 975–986 (2021)

    Article  Google Scholar 

  8. Li, Z., Li, T., Feng, G., Zhao, R., Shan, Q.: Neural network-based adaptive control for pure-feedback stochastic nonlinear systems with time-varying delays and dead-zone input. IEEE Trans. Syst. Man Cybern. Syst. 50(12), 5317–5329 (2020)

    Article  Google Scholar 

  9. Guo, X., Liang, H., Pan, Y.: Observer-based adaptive fuzzy tracking control for stochastic nonlinear multi-agent systems with dead-zone input. Appl. Math. Comput. 379, 125269 (2020)

    MathSciNet  MATH  Google Scholar 

  10. Sun, Z., Shao, Y., Chen, C., Meng, Q.: Global output-feedback stabilization for stochastic nonlinear systems: a double-domination approach. Int. J. Robust Nonlinear Control 28(15), 4635–4646 (2018)

    MathSciNet  MATH  Google Scholar 

  11. Min, H., Xu, S., Zhang, B., Ma, Q.: Globally adaptive control for stochastic nonlinear time-delay systems with perturbations and its application. Automatica 102, 105–110 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  12. Wang, H., Zhu, Q.: Global stabilization of a class of stochastic nonlinear time-delay systems with siss inverse dynamics. IEEE Trans. Autom. Control 65(10), 4448–4455 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  13. Sun, W., Wang, L., Wu, Y.: Adaptive dynamic surface fuzzy control for state constrained time-delay nonlinear nonstrict feedback systems with unknown control directions. IEEE Trans. Syst. Man Cybern. Syst. 51(12), 7423–7434 (2021)

    Article  Google Scholar 

  14. Zhao, W., Liu, Y., Liu, L.: Observer-based adaptive fuzzy tracking control using integral barrier Lyapunov functionals for a nonlinear system with full state constraints. IEEE/CAA J. Autom. Sin. 8(3), 617–627 (2021)

    Article  MathSciNet  Google Scholar 

  15. Zhang, Q., Dong, J.: Disturbance-observer-based adaptive fuzzy control for nonlinear state constrained systems with input saturation and input delay. Fuzzy Sets Syst. 392, 77–92 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  16. **, X., Li, Y.: Adaptive fuzzy control of uncertain stochastic nonlinear systems with full state constraints. Inf. Sci. 574, 625–639 (2021)

    Article  MathSciNet  Google Scholar 

  17. Sun, W., Su, S., Wu, Y., **a, J.: Novel adaptive fuzzy control for output constrained stochastic nonstrict feedback nonlinear systems. IEEE Trans. Fuzzy Syst. 29(5), 1188–1197 (2021)

    Article  Google Scholar 

  18. Zhang, T., **a, M., Yi, Y.: Adaptive neural dynamic surface control of strict-feedback nonlinear systems with full state constraints and unmodeled dynamics. Automatica 81, 232–239 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  19. Zhao, K., Song, Y.: Removing the feasibility conditions imposed on tracking control designs for state-constrained strict-feedback systems. IEEE Trans. Autom. Control 64(3), 1265–1272 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  20. Zhao, K., Song, Y., Chen, C.P., Chen, L.: Control of nonlinear systems under dynamic constraints: a unified barrier function-based approach. Automatica 119, 109102 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  21. Postoyan, R., Tabuada, P., Nešić, D., Anta, A.: A framework for the event-triggered stabilization of nonlinear systems. IEEE Trans. Autom. Control 60(4), 982–996 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  22. Liu, T., Jiang, Z.: A small-gain approach to robust event-triggered control of nonlinear systems. IEEE Trans. Autom. Control 60(8), 2072–2085 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  23. **ng, L., Wen, C., Liu, Z., Su, H., Cai, J.: Event-triggered adaptive control for a class of uncertain nonlinear systems. IEEE Trans. Autom. Control 62(4), 2071–2076 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  24. Ma, H., Li, H., Liang, H., Dong, G.: Adaptive fuzzy event-triggered control for stochastic nonlinear systems with full state constraints and actuator faults. IEEE Trans. Fuzzy Syst. 27(11), 2242–2254 (2019)

    Article  Google Scholar 

  25. **a, J., Lian, Y., Su, S., Shen, H., Chen, G.: Observer-based event-triggered adaptive fuzzy control for unmeasured stochastic nonlinear systems with unknown control directions. IEEE Trans. Cybern. (2021). https://doi.org/10.1109/TCYB.2021.3069853

    Article  Google Scholar 

  26. Liu, Y., Zhu, Q.: Event-triggered adaptive neural network control for stochastic nonlinear systems with state constraints and time-varying delays. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2021.3105681

    Article  Google Scholar 

  27. Huang, Y., Liu, Y.: Practical tracking via adaptive event-triggered feedback for uncertain nonlinear systems. IEEE Trans. Autom. Control 64(9), 3920–3927 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  28. Zhang, C., Yang, G.: Event-triggered global finite-time control for a class of uncertain nonlinear systems. IEEE Trans. Autom. Control 65(3), 1340–1347 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  29. 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)

    Article  MathSciNet  MATH  Google Scholar 

  30. Sun, Z., Shao, Y., Chen, C.: Fast finite-time stability and its application in adaptive control of high-order nonlinear system. Automatica 106, 339–348 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  31. Jiang, M., **e, X., Zhang, K.: Finite-time stabilization of stochastic high-order nonlinear systems with ft-siss inverse dynamics. IEEE Trans. Autom. Control 64(1), 313–320 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  32. Li, S., Ahn, C.K., **ang, Z.: Command-filter-based adaptive fuzzy finite-time control for switched nonlinear systems using state-dependent switching method. IEEE Trans. Fuzzy Syst. 29(4), 833–845 (2021)

    Article  Google Scholar 

  33. Liu, W., Qi, X., Lu, J., Jia, X., Li, P.: Finite-time fault-tolerant control for nonlinear systems with input quantization and its application. IEEE Trans. Circuits Syst. II Express Briefs 67(7), 1249–1253 (2020)

    Google Scholar 

  34. Min, H., Xu, S., Zhang, Z.: Adaptive finite-time stabilization of stochastic nonlinear systems subject to full-state constraints and input saturation. IEEE Trans. Autom. Control 66(3), 1306–1313 (2021)

  35. Yu, J., Yu, S., Li, J., Yan, Y.: Fixed-time stability theorem of stochastic nonlinear systems. Int. J. Control 92(9), 2194–2200 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  36. Sun, Y., Wang, F., Liu, Z., Zhang, Y., Chen, C.P.: Fixed-time fuzzy control for a class of nonlinear systems. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.3018695

    Article  Google Scholar 

  37. Zhang, Y., Wang, F.: Observer-based fixed-time neural control for a class of nonlinear systems. IEEE Trans. Neural Netw. Learn. Syst. (2021). https://doi.org/10.1109/TNNLS.2020.3046865

    Article  Google Scholar 

  38. Yao, Y., Tan, J., Wu, J., Zhang, X.: Event-triggered fixed-time adaptive fuzzy control for state-constrained stochastic nonlinear systems without feasibility conditions. Nonlinear Dyn. 105(1), 403–416 (2021)

    Article  Google Scholar 

  39. Jia, F., Lu, J., Li, Y., Li, F.: Global state feedback stabilization of nonlinear systems with unknown functions. Nonlinear Dyn. 104(4), 3633–3641 (2021)

    Article  Google Scholar 

  40. Mao, X.: Stochastic Differential Equations and Applications. Horwood, Chichester (2007)

    MATH  Google Scholar 

  41. Li, K., Li, Y., Zong, G.: Adaptive fuzzy fixed-time decentralized control for stochastic nonlinear systems. IEEE Trans. Fuzzy Syst. 29(11), 3428–3440 (2021)

    Article  Google Scholar 

  42. Zhou, Q., Wang, L., Wu, C., Li, H., Du, H.: 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 

  43. **a, J., Li, B., Su, S., Sun, W., Shen, H.: Finite-time command filtered event-triggered adaptive fuzzy tracking control for stochastic nonlinear systems. IEEE Trans. Fuzzy Syst. 29(7), 1815–1825 (2021)

    Article  Google Scholar 

  44. Yang, B., Lin, W.: Robust output feedback stabilization of uncertain nonlinear systems with uncontrollable and unobservable linearization. IEEE Trans. Autom. Control 50(5), 619–630 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  45. Liu, Y., Tong, S.: Barrier Lyapunov functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints. Automatica 64, 70–75 (2016)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Funding

This work was supported in part by the NSFC under Grants 62221004, 62073166; the Postgraduate Research & Practice Innovation Program of Jiangsu Province under Grant KYCX22_0444; the Key Laboratory of Jiangsu Province; the Shandong Provincial Natural Science Foundation under Grant ZR2021ZD13; and the Project on the Technological Leading Talent Teams Led by Frontiers Science Center for Complex Equipment System Dynamics (FSCCESD220401).

Author information

Authors and Affiliations

  1. School of Automation, Nan**g University of Science and Technology, Nan**g, 210094, Jiangsu, China

    **ao**g Qi & Shengyuan Xu

  2. School of Science, Huzhou University, Huzhou, 313000, Zhejiang, China

    Yongmin Li & Yuming Chu

Authors
  1. **ao**g Qi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shengyuan Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yongmin Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yuming Chu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shengyuan Xu.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qi, X., Xu, S., Li, Y. et al. Global fixed-time event-triggered control for stochastic nonlinear systems with full state constraints. Nonlinear Dyn 111, 7403–7415 (2023). https://doi.org/10.1007/s11071-023-08263-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-08263-7

Keywords

Search

Navigation