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Event-based singularity-free fixed-time fuzzy control for active suspension systems with displacement constraint

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Abstract

This paper investigates the event-based adaptive fixed-time (FT) control problem for active suspension systems (ASSs) with actuator faults. The fuzzy approximator is utilized to estimate the continuous function with the unknown car body mass parameters. The FT controller with continuous piecewise function is presented to avoid the singularity problem caused by the derivation of the virtual controller in the backstepping method and to compensate the actuator faults. A switching threshold event-triggered mechanism is evolved for ASSs, which has the advantages of fixed threshold strategy and relative threshold strategy to reduce the communication burden more reasonably. The suspension vertical displacement is restricted by constructing a time-varying barrier Lyapunov function. It is proved that the signals in the closed-loop systems are bounded by Lyapunov stability criterion. Finally, simulation results show that the controller is effective in suppressing the vertical vibration of ASSs.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Kumar V, Rana KPS, Kumar J, Mishra P (2018) Self-tuned robust fractional order fuzzy PD controller for uncertain and nonlinear active suspension system. Neural Comput Appl 30(6):1827–1843

    Google Scholar 

  2. Sun Y, Xu J, Lin G, Sun N (2020) Adaptive neural network control for maglev vehicle systems with time-varying mass and external disturbance. Neural Comput Appl. https://doi.org/10.1007/s00521-021-05874-2

    Article  Google Scholar 

  3. Zhao J, Dong J, Wong PK, Ma X, Wang Y, Lv C (2022) Interval fuzzy robust non-fragile finite frequency control for active suspension of in-wheel motor driven electric vehicles with time delay. J Franklin Inst 359(12):5960–5990

    MathSciNet  MATH  Google Scholar 

  4. Zhao J, Wong PK, Li W, Ghadikolaeia MA, Xie Z (2022) Reliable fuzzy sampled-data control for nonlinear suspension systems against actuator faults. IEEE/ASME Trans Mechatron 27(6):5518–5528

    Google Scholar 

  5. Liu Y-J, Zeng Q, Tong S, Chen CLP, Liu L (2019) Actuator failure compensation-based adaptive control of active suspension systems with prescribed performance. IEEE Trans Industr Electron 67(8):7044–7053

    Google Scholar 

  6. Zeng Q, Liu Y-J, Liu L (2021) Adaptive vehicle stability control of half-car active suspension systems with partial performance constraints. IEEE Trans Syst Man Cybern Syst 51(3):1704–1714

    Google Scholar 

  7. Ren H, Cheng Z, Qin J, Lu R (2023) Deception attacks on event-triggered distributed consensus estimation for nonlinear systems. Automatica 154:111100

    MathSciNet  MATH  Google Scholar 

  8. Yao D, Li H, Shi Y (2012) Adaptive event-triggered sliding mode control for consensus tracking of nonlinear multi-agent systems with unknown perturbations. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2022.3172127

    Article  Google Scholar 

  9. Pan Y, Wu Y, Lam H-K (2022) Security-based fuzzy control for nonlinear networked control systems with dos attacks via a resilient event-triggered scheme. IEEE Trans Fuzzy Syst 30(10):4359–4368

    Google Scholar 

  10. Ma H, Ren H, Zhou Q, Li H, Wang Z (2010) Observer-based neural control of N-link flexible-joint robots. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2022.3203074

    Article  Google Scholar 

  11. Yao D, Li H, Lu R, Shi Y (2022) Event-triggered guaranteed cost leader-following consensus control of second-order nonlinear multiagent systems. IEEE Trans Syst Man Cybern Syst 52(4):2615–2624

    Google Scholar 

  12. Cao L, Pan Y, Liang H, Huang T (2010) Observer-based dynamic event-triggered control for multiagent systems with time-varying delay. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2022.3226873

    Article  Google Scholar 

  13. Cao L, Cheng Z, Liu Y, Li H (2020) Event-based adaptive NN fixed-time cooperative formation for multiagent systems. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2022.3210269

    Article  Google Scholar 

  14. Wang Y, Sun H, Hou L (2022) Dynamic event-triggered antidisturbance control for flexible spacecraft systems. IEEE Trans Aerosp Electron Syst 58(6):5766–5783

    Google Scholar 

  15. Zhou W, Fu J, Yan H, Du X, Wang Y, Zhou H (2023) Event-triggered approximate optimal path-following control for unmanned surface vehicles with state constraints. IEEE Trans Neural Netw Learn Syst 34(1):104–118

    MathSciNet  Google Scholar 

  16. Cao L, Li H, Wang N, Zhou Q (2019) Observer-based event-triggered adaptive decentralized fuzzy control for nonlinear large-scale systems. IEEE Trans Fuzzy Syst 27(6):1201–1214

    Google Scholar 

  17. Xing L, Wen C (2019) Liu: event-triggered output feedback control for a class of uncertain nonlinear systems. IEEE Trans Autom Control 64(1):290–297

    MATH  Google Scholar 

  18. Chen G, Yao D, Zhou Q, Li H, Lu R (2022) Distributed event-triggered formation control of USVs with prescribed performance. J Syst Sci Complex 35(3):820–838

    MathSciNet  MATH  Google Scholar 

  19. Li H, Wu Y, Chen M, Lu R (2023) Adaptive multigradient recursive reinforcement learning event-triggered tracking control for multiagent systems. IEEE Trans Neural Netw Learn Syst 34(1):144–156

    MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  21. Fu J, Ma R, Chai T (2015) Global finite-time stabilization of a class of switched nonlinear systems with the powers of positive odd rational numbers. Automatica 54(4):360–373

    MathSciNet  MATH  Google Scholar 

  22. Pan H, Sun W (2019) Nonlinear output feedback finite-time control for vehicle active suspension systems. IEEE Trans Industr Inf 15(4):2073–2082

    Google Scholar 

  23. Lin G, Li H, Ahn CK, Yao D (2009) Event-based finite-time neural control for human-in-the-loop UAV attitude systems. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2022.3166531

    Article  Google Scholar 

  24. Jin X, Zhao Z, Wu X, Chi J, Deng C (2022) Adaptive NN-based finite-time trajectory tracking control of wheeled robotic systems. Neural Comput Appl 34(7):5119–5133

    Google Scholar 

  25. Na J, Huang Y, Wu X, Su S-F, Li G (2020) Adaptive finite-time fuzzy control of nonlinear active suspension systems with input delay. IEEE Trans Cybern 50(6):2639–2650

    Google Scholar 

  26. Liu Y-J, Zhang Y-Q, Liu L, Tong S, Chen CLP (2020) Adaptive finite-time control for half-vehicle active suspension systems with uncertain dynamics. IEEE/ASME Trans Mechatron 26(1):168–178

    Google Scholar 

  27. Zuo Z, Han Q-L, Ning B, Ge X, Zhang X-M (2018) An overview of recent advances in fixed-time cooperative control of multiagent systems. IEEE Trans Industr Inf 14(6):2322–2334

    Google Scholar 

  28. Liu Y, Li H, Lu R, Zuo Z, Li X (2022) An overview of finite/fixed-time control and its application in engineering systems. IEEE/CAA J Automatica Sinica 9(12):2106–2120

    Google Scholar 

  29. Lu Q, Han Q-L, Peng D, Choi Y (2022) Decision and event-based fixed-time consensus control for electromagnetic source localization. IEEE Trans Cybern 52(4):2186–2199

    Google Scholar 

  30. Jia T, Pan Y, Liang H, Lam H-K (2022) Event-based adaptive fixed-time fuzzy control for active vehicle suspension systems with time-varying displacement constraint. IEEE Trans Fuzzy Syst 30(8):2813–2821

    Google Scholar 

  31. Pan Y, Du P, Xue H, Lam H-K (2021) Singularity-free fixed-time fuzzy control for robotic systems with user-defined performance. IEEE Trans Fuzzy Syst 29(8):2388–2398

    Google Scholar 

  32. Li H, Jing X, Karimi HR (2014) Output-feedback-based \(H_{\infty }\) control for vehicle suspension systems with control delay. IEEE Trans Industr Electron 61(8):436–446

    Google Scholar 

  33. Xia Y, Fu M, Li C, Pu F, Xu Y (2018) Active disturbance rejection control for active suspension system of tracked vehicles with gun. IEEE Trans Industr Electron 65(5):4051–4060

    Google Scholar 

  34. Zheng X, Zhang H, Yan H, Yang F, Wang Z, Vlacic L (2019) Active full-vehicle suspension control via cloud-aided adaptive backstepping approach. IEEE Trans Cybern 50(7):3113–3124

    Google Scholar 

  35. Sui S, Tong S, Chen CLP (2018) Finite-time filter decentralized control for nonstrict-feedback nonlinear large-scale systems. IEEE Trans Fuzzy Syst 26(6):3289–3300

    Google Scholar 

  36. Wang F, Chen B, Sun Y, Lin C (2019) Finite time control of switched stochastic nonlinear systems. Fuzzy Sets Syst 365(15):140–152

    MathSciNet  MATH  Google Scholar 

  37. Jin X (2019) Adaptive fixed-time control for MIMO nonlinear systems with asymmetric output constraints using universal barrier functions. IEEE Trans Autom Control 64(7):3046–3053

    MathSciNet  MATH  Google Scholar 

  38. Liu L, Li X (2020) Event-triggered tracking control for active seat suspension systems with time-varying full-state constraints. IEEE Trans Syst Man Cybern Syst 52(1):582–590

    Google Scholar 

  39. Pan H, Zhang D, Sun W, Yu X (2022) Event-triggered adaptive asymptotic tracking control of uncertain MIMO nonlinear systems with actuator faults. IEEE Trans Cybern 64(7):8655–8667

    Google Scholar 

  40. Zheng X, Li H, Ahn CK, Yao D (2009) NN-based fixed-time attitude tracking control for multiple unmanned aerial vehicles with nonlinear faults. IEEE Trans Aerosp Electron Syst. https://doi.org/10.1109/TAES.2022.3205566

    Article  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  42. Sun H, Hou L, Zong G, Yu X (2019) Fixed-time attitude tracking control for spacecraft with input quantization. IEEE Trans Aerosp Electron Syst 55(1):124–134

    Google Scholar 

  43. Liang H, Chen L, Pan Y, Lam H-K (2010) Fuzzy-based robust precision consensus tracking for uncertain networked systems with cooperative-antagonistic interactions. IEEE Trans Fuzzy Syst. https://doi.org/10.1109/TFUZZ.2022.3200730

    Article  Google Scholar 

  44. Liang H, Du Z, Huang T, Pan Y (2022) Neuroadaptive performance guaranteed control for multiagent systems with power integrators and unknown measurement sensitivity. IEEE Trans Neural Netw Learn Syst. https://doi.org/10.1109/TNNLS.2022.3160532

    Article  Google Scholar 

  45. Ma H, Zhou Q, Li H, Lu R (2022) Adaptive prescribed performance control of a flexible-joint robotic manipulator with dynamic uncertainties. IEEE Trans Cybern 52(12):12905–12915

    Google Scholar 

  46. Du P, Liang H, Zhao S, Ahn CK (2021) Neural-based decentralized adaptive finite-time control for nonlinear large-scale systems with time-varying output constraints. IEEE Trans Syst Man Cybern Syst 51(5):3136–3147

    Google Scholar 

  47. He Y, Zhang C, Zeng H, Wu M (2023) Additional functions of variable-augmented-based free-weighting matrices and application to systems with time-varying delay. Int J Syst Sci 54(5):991–1003

    MathSciNet  MATH  Google Scholar 

  48. Qian W, Xing W, Fei S (2021) \({H}_{\infty }\) state estimation for neural networks with general activation function and mixed time-varying delays. IEEE Trans Neural Netw Learn Syst 32(9):3909–3918

    MathSciNet  Google Scholar 

  49. Shangguan X, He Y, Zhang C, Yao W, Zhao Y, Jiang L, Wu M (2023) Resilient load frequency control of power systems to compensate random time delays and time-delay attacks. IEEE Trans Industr Electron 70(5):5115–5128

    Google Scholar 

  50. Sun J, Zhang H, Wang Y, Sun S (2022) Fault-tolerant control for stochastic switched IT2 fuzzy uncertain time-delayed nonlinear systems. IEEE Trans Cybern 52(2):1335–1346

    Google Scholar 

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Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (62103108) and the Basic Scientific Research Project of the Education Department of Liaoning Provincial (LJKQZ20222437).

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Authors and Affiliations

  1. College of Mathematical Sciences, Bohai University, Jinzhou, 121013, Liaoning, China

    Tinghan Jia & Liang Cao

  2. College of Control Science and Engineering, Bohai University, Jinzhou, 121013, Liaoning, China

    Pengchao Zhang & Yingnan Pan

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  1. Tinghan Jia
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  2. Liang Cao
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Correspondence to Liang Cao.

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Jia, T., Cao, L., Zhang, P. et al. Event-based singularity-free fixed-time fuzzy control for active suspension systems with displacement constraint. Neural Comput & Applic 35, 19751–19763 (2023). https://doi.org/10.1007/s00521-023-08780-x

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