Skip to main content
Log in

Event-Triggered Adaptive Fuzzy Finite Time Control of Fractional-Order Non-Strict Feedback Nonlinear Systems

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

In this article, the problem of event-triggered adaptive fuzzy finite time control of non-strict feedback fractional order nonlinear systems is investigated. By using the property of fuzzy basis function, the obstacle caused by algebraic loop problems is successfully circumvented. Moreover, a new adaptive event-triggered scheme is designed under the unified framework of backstepping control method, which can largely reduce the amount of communications. The stability of the closed-loop system is ensured through fractional Lyapunov stability analysis. Finally, the effectiveness of the proposed scheme is verified by simulation examples.

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.

Similar content being viewed by others

References

  1. Monje C A, Chen Y Q, Vinagre B M, et al., Fractional-Order Systems and Controls: Fundamentals and Applications, Springer, London, 2010.

    Book  MATH  Google Scholar 

  2. Wang L X, Stable adaptive fuzzy control of nonlinear systems, IEEE Transactions on Fuzzy Systems, 1993, 12: 46–155.

    Google Scholar 

  3. He W, Chen Y, and Yin Z, Adaptive neural network control of an uncertain robot with full-state constraints, IEEE Transactions on Cybernetics, 2015, 46(3): 620–629.

    Article  Google Scholar 

  4. Wang F, Liu Z, and Lai G, Fuzzy adaptive control of nonlinear uncertain plants with unknown dead zone output, Fuzzy Sets and Systems, 2015, 263: 27–48.

    Article  MathSciNet  MATH  Google Scholar 

  5. Wang M, Chen B, Liu X, et al., Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems, Fuzzy Sets and Systems, 2008, 159(8): 949–967.

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen M, Ge S S, and Ren B, Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints, Automatica, 2011, 47(3): 452–465.

    Article  MathSciNet  MATH  Google Scholar 

  7. Muhammadhaji A and Teng Z, General decay synchronization for recurrent neural networks with mixed time delays, Journal of Systems Science and Complexity, 2020, 33(3): 672–684.

    Article  MathSciNet  MATH  Google Scholar 

  8. Chaouki A, and El Abed A, Finite-time and fixed-time synchronization of inertial neural networks with mixed delays, Journal of Systems Science and Complexity, 2021, 34(1): 206–235.

    Article  MathSciNet  MATH  Google Scholar 

  9. Wei Y, Chen Y, Liang S, et al., A novel algorithm on adaptive backstepping control of fractional order systems, Neurocomputing, 2015, 165: 395–402.

    Article  Google Scholar 

  10. Wei Y, Peter W T, Yao Z, et al., Adaptive backstepping output feedback control for a class of nonlinear fractional order systems, Nonlinear Dynamics, 2016, 86(2): 1047–1056.

    Article  MathSciNet  MATH  Google Scholar 

  11. Liu H, Li S, Cao J, et al., Adaptive fuzzy prescribed performance controller design for a class of uncertain fractional-order nonlinear systems with external disturbances, Neurocomputing, 2017, 219: 422–430.

    Article  Google Scholar 

  12. Liu H, Li S, Wang H, et al., Adaptive fuzzy control for a class of unknown fractional-order neural networks subject to input nonlinearities and dead-zones, Information Sciences, 2018, 454: 30–45.

    Article  MathSciNet  MATH  Google Scholar 

  13. Song S, Park J H, Zhang B, et al., Observer-based adaptive hybrid fuzzy resilient control for fractional-order nonlinear systems with time-varying delays and actuator failures, IEEE Transactions on Fuzzy Systems, 2021, 29(3): 471–485.

    Article  Google Scholar 

  14. Song S, Zhang B, Song X, et al., Neuro-fuzzy-based adaptive dynamic surface control for fractional-order nonlinear strict-feedback systems with input constraint, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 51(6): 3575–3586.

    Article  Google Scholar 

  15. Liu H, Pan Y, and Cao J, Composite learning adaptive dynamic surface control of fractional-order nonlinear systems, IEEE Transactions on Cybernetics, 2019, 50(6): 2557–2567.

    Article  Google Scholar 

  16. Song S, Park J H, Zhang B, et al., Adaptive command filtered neuro-fuzzy control design for fractional-order nonlinear systems with unknown control directions and input quantization, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(11): 7238–7249.

    Article  Google Scholar 

  17. Ma Z and Ma H, Adaptive fuzzy backstepping dynamic surface control of strict-feedback fractional-order uncertain nonlinear systems, IEEE Transactions on Fuzzy Systems, 2019, 28(1): 122–133.

    Article  Google Scholar 

  18. Li Y X, Wang Q Y, and Tong S, Fuzzy adaptive fault-tolerant control of fractional-order nonlinear systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(3): 1372–1379.

    Google Scholar 

  19. Liu H, Pan Y, Cao J, et al. Adaptive neural network backstepping control of fractional-order nonlinear systems with actuator faults, IEEE Transactions on Neural Networks and Learning Systems, 2020, 31(12): 5166–5177.

    Article  MathSciNet  Google Scholar 

  20. Ma Z and Ma H, Reduced-order observer-based adaptive backstepping control for fractional-order uncertain nonlinear systems, IEEE Transactions on Fuzzy Systems, 2019, 28(12): 3287–3301.

    Article  Google Scholar 

  21. Chen B, Liu X P, Ge S S, et al., Adaptive fuzzy control of a class of nonlinear systems by fuzzy approximation approach, IEEE Transactions on Fuzzy Systems, 2012, 20(6): 1012–1021.

    Article  Google Scholar 

  22. Wang H, Liu X, Liu K, et al., Approximation-based adaptive fuzzy tracking control for a class of nonstrict-feedback stochastic nonlinear time-delay systems, IEEE Transactions on Fuzzy systems, 2014, 23(5): 1746–1760.

    Article  Google Scholar 

  23. Li Y, Liu L, and Feng G, Robust adaptive output feedback control to a class of non-triangular stochastic nonlinear systems, Automatica, 2018, 89: 325–332.

    Article  MathSciNet  MATH  Google Scholar 

  24. Chen B, Zhang H, and Lin C, Observer-based adaptive neural network control for nonlinear systems in nonstrict-feedback form, IEEE Transactions on Neural Networks and Learning Systems, 2015, 27(1): 89–98.

    Article  MathSciNet  Google Scholar 

  25. Mu X and Liu H, Stabilization for a class of large-scale stochastic nonlinear systems with decentralized controller design, Journal of Systems Science and Complexity, 2007, 20(1): 127–134.

    Article  MathSciNet  MATH  Google Scholar 

  26. Tong S, Min X, and Li Y, Observer-based adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown control gain functions, IEEE Transactions on Cybernetics, 2020, 50(9): 3903–3913.

    Article  Google Scholar 

  27. Tabuada P, Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control, 2007, 52(9): 1680–1685.

    Article  MathSciNet  MATH  Google Scholar 

  28. Liu T and Jiang Z P, Event-based control of nonlinear systems with partial state and output feedback, Automatica, 2015, 53: 10–22.

    Article  MathSciNet  MATH  Google Scholar 

  29. Heemels W P M H, Donkers M C F, and Teel A R, Periodic event-triggered control for linear systems, IEEE Transactions on Automatic Control, 2012, 58(4): 847–861.

    Article  MathSciNet  MATH  Google Scholar 

  30. Postoyan R, Tabuada P, Nesic D, et al., A framework for the event-triggered stabilization of nonlinear systems, IEEE Transactions on Automatic Control, 2014, 60(4): 982–996.

    Article  MathSciNet  MATH  Google Scholar 

  31. Zhang J, Liu L, Li S, et al., Event-triggered L1-gain control of nonlinear positive switched systems, Journal of Systems Science and Complexity, 2021, 34(3): 873–898.

    Article  MathSciNet  MATH  Google Scholar 

  32. Sun Y, Hu J, and Liu J, Periodic event-triggered control of flywheel energy storage matrix systems for wind farms, IET Control Theory & Applications, 2020, 14(11): 1467–1477.

    Article  MathSciNet  Google Scholar 

  33. Hu J, Geng J, and Zhu H, An observer-based consensus tracking control and application to event-triggered tracking, Communications in Nonlinear Science and Numerical Simulation, 2015, 20(2): 559–570.

    Article  MathSciNet  MATH  Google Scholar 

  34. Xing L, Wen C, Liu Z, et al., Event-triggered adaptive control for a class of uncertain nonlinear systems, IEEE Transactions on Automatic Control, 2016, 62(4): 2071–2076.

    Article  MathSciNet  MATH  Google Scholar 

  35. Xing L, Wen C, Liu Z, et al., Event-triggered output feedback control for a class of uncertain nonlinear systems, IEEE Transactions on Automatic Control, 2018, 64(1): 290–297.

    Article  MathSciNet  MATH  Google Scholar 

  36. Li Y X and Yang G H, Model-based adaptive event-triggered control of strict-feedback nonlinear systems, IEEE Transactions on Neural Networks and Learning Systems, 2017, 29(4): 1033–1045.

    Article  MathSciNet  Google Scholar 

  37. Li Y X and Yang G H, Event-triggered adaptive backstepping control for parametric strict-feedback nonlinear systems, International Journal of Robust and Nonlinear Control, 2018, 28(3): 976–1000.

    Article  MathSciNet  MATH  Google Scholar 

  38. Qiu J, Sun K, Wang T, et al., Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance, IEEE Transactions on Fuzzy Systems, 2019, 27(11): 2152–2162.

    Article  Google Scholar 

  39. Li H, Zhang Z, Yan H, et al., Adaptive event-triggered fuzzy control for uncertain active suspension systems, IEEE Transactions on Cybernetics, 2018, 49(12): 4388–4397.

    Article  Google Scholar 

  40. Wang J, Liu Z, Zhang Y, et al., Neural adaptive event-triggered control for nonlinear uncertain stochastic systems with unknown hysteresis, IEEE Transactions on Neural Networks and Learning Systems, 2019, 30(11): 3300–3312.

    Article  MathSciNet  Google Scholar 

  41. Jia T, Pan Y, Liang H, et al., Event-based adaptive fixed-time fuzzy control for active vehicle suspension systems with time-varying displacement constraint, IEEE Transactions on Fuzzy Systems, 2021, DOI: https://doi.org/10.1109/TFUZZ.2021.3075490.

  42. Hong Y and Jiang Z P, Finite-time stabilization of nonlinear systems with parametric and dynamic uncertainties, IEEE Transactions on Automatic Control, 2006, 51(12): 1950–1956.

    Article  MathSciNet  MATH  Google Scholar 

  43. Huang X, Lin W, and Yang B, Global finite-time stabilization of a class of uncertain nonlinear systems, Automatica, 2005, 41(5): 881–888.

    Article  MathSciNet  MATH  Google Scholar 

  44. Wu Y, Hu J, Xiang L, et al., Finite-time output regulation of linear heterogeneous multi-agent systems, IEEE Transactions on Circuits and Systems II: Express Briefs, 2021, DOI: https://doi.org/10.1109/TC-SII.2021.3098095.

  45. Li Y X, Finite time command filtered adaptive fault tolerant control for a class of uncertain nonlinear systems, Automatica, 2019, 106: 117–123.

    Article  MathSciNet  MATH  Google Scholar 

  46. Gong P, Lan W, and Han Q L, Robust adaptive fault-tolerant consensus control for uncertain nonlinear fractional-order multi-agent systems with directed topologies, Automatica, 2020, 117: 109011.

    Article  MathSciNet  MATH  Google Scholar 

  47. Podlubny I, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Elsevier, Amsterdam, Holland, 1998.

    MATH  Google Scholar 

  48. Zhang Z, Park J H, Shao H, et al., Exact tracking control of uncertain non-linear systems with additive disturbance, IET Control Theory & Applications, 2015, 9(5): 736–744.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yuanxin Li.

Additional information

This work was supported in part by the Funds of National Science of China under Grant Nos. 61973146 and 61773188, and in part by the Distinguished Young Scientific Research Talents Plan in Liaoning Province under Grant Nos. XLYC1907077 and JQL201915402.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xin, C., Li, Y. & Niu, B. Event-Triggered Adaptive Fuzzy Finite Time Control of Fractional-Order Non-Strict Feedback Nonlinear Systems. J Syst Sci Complex 35, 2166–2180 (2022). https://doi.org/10.1007/s11424-022-1244-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-022-1244-z

Keywords

Navigation