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Event-based adaptive neural network asymptotic control design for nonstrict feedback nonlinear system with state constraints

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Abstract

This article presents an event-triggered adaptive neural network (ANN) asymptotic tracking control scheme for nonstrict feedback nonlinear systems with state constraints. The neural networks are explored to address the unknown dynamics and nonstrict feedback structure. With the help of barrier Lyapunov functions, the state constraints are properly addressed. By employing some well defined smooth functions and backstepping technique, the asymptotic tracking controller is recursively constructed. In addition, event-triggered mechanism is incorporated into the asymptotic tracking design framework to reduce the data transmission. Through Lyapunov stability analysis, the tracking errors can converge to zero asymptotically and the boundedness of the considered systems are guaranteed. Simulation results are given to elucidate the validity of the proposed ANN asymptotic controller.

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References

  1. Krstić M, Kanellakopoulos I, Kokotović PV (1995) Nonlinear and adaptive control design. Wiley, New York

    MATH  Google Scholar 

  2. Slotine JJ, Li WP (1991) Applied nonlinear control. Prentice-Hall, Englewood Cliffs

    MATH  Google Scholar 

  3. Chen M, Jiang B, Jiang CS, Wu QX (2010) Robust control for a class of time-delay uncertain nonlinear systems based on sliding mode observer. Neural Comput Appl 19(2):945–951

    Article  Google Scholar 

  4. Zong GD, Li YK, Bin S (2019) Composite anti-disturbance resilient control for Markovian jump nonlinear systems with general uncertain transition rate. Sci China Inf Sci 62:022205:1-022205:18

    Article  MathSciNet  Google Scholar 

  5. Gagliano S, Cairone F, Amenta A, Bucolo M (2019) A real time feed forward control of slug flow in microchannels. Energies 12(13):1–11

    Article  Google Scholar 

  6. Ma YS, Che WW, Deng C, Wu ZG (2021) Distributed model-free adaptive control for learning nonlinear MASs under DoS attacks. IEEE Trans Neural Netw Learn Syst

  7. Zhao N, Shi P, Xing W, Jonathon C (2021) Observer-based event-triggered approach for stochastic networked control systems under denial of service attacks. IEEE Trans Control Netw Syst 8(1):158–167

    Article  MathSciNet  Google Scholar 

  8. Wang QZ, He Y (2021) Time-triggered intermittent control of continuous systems. Int J Robust Nonlinear Control 31(14):6867–6879

    Article  MathSciNet  Google Scholar 

  9. Chen B, Liu XP, Liu KF, Lin C (2009) Direct adaptive fuzzy control of nonlinear strict-feedback systems. Automatica 45(6):1530–1535

    Article  MathSciNet  MATH  Google Scholar 

  10. Li DJ, Zhang J, Cui Y, Liu L (2013) Intelligent control of nonlinear systems with application to chemical reactor recycle. Neural Comput Appl 23(5):1495–1502

    Article  Google Scholar 

  11. Zong GD, Sun HB, Nguang SK (2021) Decentralized adaptive neuro-output feedback saturated control for INS and its application to AUV. IEEE Trans Neural Netw Learn Syst 32:5492–5501

    Article  MathSciNet  Google Scholar 

  12. Kumar A, Das S, Yadav VK (2021) Global quasi-synchronization of complex-valued recurrent neural networks with time-varying delay and interaction terms. Chaos Solitons Fractals 152:111323

    Article  MathSciNet  Google Scholar 

  13. Liu YC, Zhu QD (2021) Event-triggered adaptive neural network control for stochastic nonlinear systems with state constraints and time-varying delays. IEEE Trans Neural Netw Learn Syst

  14. Li YM, Tong SC, Li TS (2013) Direct adaptive fuzzy backstepping control of uncertain nonlinear systems in the presence of input saturation. Neural Comput Appl 23(5):1207–1216

    Article  Google Scholar 

  15. Zou AM, Hou ZG, Tan M (2008) Adaptive control of a class of nonlinear pure-feedback systems using fuzzy backstepping approach. IEEE Trans Fuzzy Syst 16(4):886–897

    Article  Google Scholar 

  16. Shen QK, Shi P, Zhang TP, Lim CC (2014) Novel neural control for a class of uncertain pure-feedback systems. IEEE Trans Neural Netw Learn Syst 25(4):718–727

    Article  Google Scholar 

  17. Kumar A, Das S, Yadav VK, Cao JD, Huang CX (2021) Synchronizations of fuzzy cellular neural networks with proportional time-delay. AIMS Math 6(10):10620–10641

    Article  MathSciNet  MATH  Google Scholar 

  18. Li YM, Tong SC (2014) Adaptive fuzzy output-feedback control of pure-feedback uncertain nonlinear systems with unknown dead zone. IEEE Trans Fuzzy Syst 22(5):1341–1347

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  21. Wang HQ, Chen B, Liu KF, Liu XP, Lin C (2014) Adaptive neural tracking control for a class of nonstrict-feedback stochastic nonlinear systems with unknown backlash-like hysteresis. IEEE Trans Neural Netw Learn Syst 25(5):947–958

    Article  Google Scholar 

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

    Article  Google Scholar 

  23. Wang HQ, Liu KF, Liu XP, Chen B, Lin C (2015) Neural-based adaptive output-feedback control for a class of nonstrict-feedback stochastic nonlinear systems. IEEE Trans Cybern 45(9):1977–1987

    Article  Google Scholar 

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

    Article  Google Scholar 

  25. Li YM, Shao XF, Tong SC (2020) Adaptive fuzzy prescribed performance control of non-triangular structure nonlinear systems. IEEE Trans Fuzzy Syst 28(10):2416–2426

    Article  Google Scholar 

  26. Liu ZL, Chen B, Lin C (2017) Adaptive neural backstepping for a class of switched nonlinear system without strict-feedback form. IEEE Trans Syst Man Cybern Syst 47(7):1315–1320

    Article  Google Scholar 

  27. Zhu GB, Ma Y, Li ZX, Malekian R, Sotelo M (2021) Adaptive neural output feedback control for MSVs with predefined performance. IEEE Trans Veh Technol 70(4):2994–3006

    Article  Google Scholar 

  28. Kumar U, Das S, Huang CX, Cao JD (2020) Fixed-time synchronization of quaternion-valued neural networks with time-varying delay. Proc R Soc A 476(2241):1–13

    Article  MathSciNet  MATH  Google Scholar 

  29. Liu L, Zhu CQ, Liu YJ, Wang R, Tong SC (2022) Performance improvement of active suspension constrained system via neural network identification. IEEE Trans Neural Netw Learn Syst

  30. Kumar R, Sarkar S, Das S, Cao JD (2019) Projective synchronization of delayed neural networks with mismatched parameters and impulsive effects. IEEE Trans Neural Netw Learn Syst 31(4):1211–1221

    Article  MathSciNet  Google Scholar 

  31. Zhu GB, Ma Y, Li ZX, Malekian R, Sotelo M (2021) Event-triggered adaptive neural fault-tolerant control of underactuated MSVs with input saturation. IEEE Trans Intell Transp Syst

  32. Zhou J, Wen CY, Zhang Y (2006) Adaptive output control of nonlinear systems with uncertain dead-zone nonlinearity. IEEE Trans Autom Control 51(3):504–511

    Article  MathSciNet  MATH  Google Scholar 

  33. Li YX, Yang GH (2016) Adaptive asymptotic tracking control of uncertain nonlinear systems with input quantization and actuator faults. Automatica 72:177–185

    Article  MathSciNet  MATH  Google Scholar 

  34. Liang YJ, Li YX, Che WW, Hou ZS (2021) Adaptive fuzzy asymptotic tracking for nonlinear systems with nonstrict-feedback structure. IEEE Trans Cybern 51(2):853–861

    Article  Google Scholar 

  35. Tee KP, Ge SS, Tay EH (2009) Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica 45:918–927

    Article  MathSciNet  MATH  Google Scholar 

  36. Liu YJ, Tong SC (2017) Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems. Automatica 76:143–152

    Article  MathSciNet  MATH  Google Scholar 

  37. Zhu QD, Liu YC, Wen GX (2020) Adaptive neural network output feedback control for stochastic nonlinear systems with full state constraints. ISA Trans 101:60–68

    Article  Google Scholar 

  38. Liu L, Gao TT, Liu YJ, Tong SC, Chen CLP, Ma L (2021) Time-varying IBLFs-based adaptive control of uncertain nonlinear systems with full state constraints. Automatica 129(109595):1–9

    MathSciNet  MATH  Google Scholar 

  39. Li YM, Liu YJ, Tong SC (2021) Observer-based neuro-adaptive optimized control of strict-feedback nonlinear systems with state constraints. IEEE Trans Neural Netw Learn Syst

  40. Liu L, Chen AQ, Liu YJ (2021) Adaptive fuzzy output-feedback control for switched uncertain nonlinear systems with full-state constraints. IEEE Trans Cybern

  41. Li YX (2020) Barrier Lyapunov function-based adaptive asymptotic tracking of nonlinear systems with unknown virtual control coefficients. Automatica 121:1–9

    Article  MathSciNet  Google Scholar 

  42. Tallapragada P, Chopra N (2013) On event triggered tracking for nonlinear systems. IEEE Trans Autom Control 58(9):2343–2348

    Article  MathSciNet  MATH  Google Scholar 

  43. Xing LT, Wen CY, Liu ZT, Su HY, Cai JP (2017) Event-triggered adaptive control for a class of uncertain nonlinear systems. IEEE Trans Autom Control 62(4):2071–2076

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  45. Cao L, Li HY, Zhou Q (2018) Adaptive intelligent control for nonlinear strict-feedback systems with virtual control coefficients and uncertain disturbances based on event-triggered mechanism. IEEE Trans Cybern 48(12):3390–3420

    Article  Google Scholar 

  46. Wang W, Tong SC (2019) Distributed adaptive fuzzy event-triggered containment control of nonlinear strict-feedback systems. IEEE Trans Cybern

  47. Cao L, Li HY, 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

    Article  Google Scholar 

  48. Liang HJ, Liu GL, Zhang HG, Huang TW (2020) Neural-network-based event-triggered adaptive control of nonaffine nonlinear multiagent systems with dynamic uncertainties. IEEE Trans Neural Netw Learn Syst

  49. Wang LJ, Chen CLP, Li HY (2020) Event-triggered adaptive control of saturated nonlinear systems with time-varying partial state constraints. IEEE Trans Cybern 50(4):1485–1497

    Article  Google Scholar 

  50. Liu L, Liu YJ, Tong SC, Gao ZW (2021) Relative threshold-based event-triggered control for nonlinear constrained systems with application to aircraft wing rock motion. IEEE Trans Ind Inf 18:911–921

    Article  Google Scholar 

  51. Wu LB, Park JH, Xie XP, Liu YJ (2020) Neural network adaptive tracking control of uncertain MIMO nonlinear systems with output constraints and event-triggered inputs. IEEE Trans Neural Netw Learn Syst 32:695–707

    Article  MathSciNet  Google Scholar 

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Funding

This work was supported in part by Green Intelligent Inland Ship Innovation Programme under Grant MC-202002-C01 and in part by the National Natural Science Foundation of China under Grant 52171299 (Grant No. 61803116).

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Correspondence to Qidan Zhu.

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Liu, Y., Zhu, Q. & Liu, Z. Event-based adaptive neural network asymptotic control design for nonstrict feedback nonlinear system with state constraints. Neural Comput & Applic 34, 14451–14462 (2022). https://doi.org/10.1007/s00521-022-07247-9

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  • DOI: https://doi.org/10.1007/s00521-022-07247-9

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