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Adaptive Barrier-Lyapunov-Functions Based Control Scheme of Nonlinear Pure-Feedback Systems with Full State Constraints and Asymptotic Tracking Performance

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Abstract

In this paper, the authors propose an adaptive Barrier-Lyapunov-Functions (BLFs) based control scheme for nonlinear pure-feedback systems with full state constraints. Due to the coexist of the non-affine structure and full state constraints, it is very difficult to construct a desired controller for the considered system. According to the mean value theorem, the authors transform the pure-feedback system into a system with strict-feedback structure, so that the well-known backstepping method can be applied. Then, in the backstepping design process, the BLFs are employed to avoid the violation of the state constraints, and neural networks (NNs) are directly used to online approximate the unknown packaged nonlinear terms. The presented controller ensures that all the signals in the closed-loop system are bounded and the tracking error asymptotically converges to zero. Meanwhile, it is shown that the constraint requirement on the system will not be violated during the operation. Finally, two simulation examples are provided to show the effectiveness of the proposed control scheme.

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References

  1. Bi S, Wang L, and Han C, Robust control of nonlinear system with input and output nonlinear constraints, Journal of Robotics and Mechatronics, 2017, 29(6): 1073–1081.

    Article  Google Scholar 

  2. Yu J, Shi P, and Zhao L, Finite-time command filtered backstepping control for a class of nonlinear systems, Automatica, 2018, 92: 173–180.

    Article  MathSciNet  Google Scholar 

  3. Jia X, Xu S, Qi Z, et al., Adaptive output feedback tracking of nonlinear systems with uncertain nonsymmetric dead-zone input, ISA Transactions, 2019, 95: 35–44.

    Article  Google Scholar 

  4. Liu G, Networked learning predictive control of nonlinear cyber-physical systems, Journal of Systems Science & Complexity, 2020, 33(6): 1719–1732.

    Article  MathSciNet  Google Scholar 

  5. Li Y, Barrier Lyapunov function-based adaptive asymptotic tracking of nonlinear systems with unknown virtual control coefficients, Automatica, 2020, 121: 109181.

    Article  MathSciNet  Google Scholar 

  6. Niu B, Zhao P, Liu J, et al., Global adaptive control of switched uncertain nonlinear systems: An improved MDADT method, Automatica, 2020, 115: 108872.

    Article  MathSciNet  Google Scholar 

  7. Qi W, Zong G, and Zheng W, Adaptive event-triggered SMC for stochastic switching systems with semi-Markov process and application to boost converter circuit model, IEEE Transactions on Circuits and Systems I: Regular Papers, 2021, 68(2): 786–796.

    Article  MathSciNet  Google Scholar 

  8. Li Y, Hu X, Che W, et al., Event-based adaptive fuzzy asymptotic tracking control of uncertain nonlinear systems, IEEE Transactions on Fuzzy Systems, 2021, 29(10): 3003–3013.

    Article  Google Scholar 

  9. Niu B, Liu J, Wang D, et al., Adaptive decentralized asymptotic tracking control for large-scale nonlinear systems with unknown strong interconnections, IEEE/CAA Journal of Automatica Sinica, 2022, 9(1): 173–186.

    Article  MathSciNet  Google Scholar 

  10. Sofianos N and Boutalis Y, Stable indirect adaptive switching control for fuzzy dynamical systems based on TCS multiple models, International Journal of Systems Science, 2013, 44(8): 1546–1565.

    Article  MathSciNet  Google Scholar 

  11. Yoo S, Distributed consensus tracking for multiple uncertain nonlinear strict-feedback systems under a directed graph, IEEE Transactions on Neural Networks and Learning Systems, 2013, 24(4): 666–672.

    Article  Google Scholar 

  12. Li Y, Tong S, and Li T, Adaptive fuzzy output feedback dynamic surface control of interconnected nonlinear pure-feedback systems, IEEE Transactions on Cybernetics, 2015, 45(1): 138–149.

    Article  Google Scholar 

  13. Li H, Wang Y, Yao D, et al., A sliding mode approach to stabilization of nonlinear Markovian jump singularly perturbed systems, Automatica, 2018, 97: 404–413.

    Article  MathSciNet  Google Scholar 

  14. Wu C, Wu L, Liu J, et al., Active defense-based resilient sliding mode control under denial-of-service attacks, IEEE Transactions on Information Forensics and Security, 2019, 15: 237–249.

    Article  Google Scholar 

  15. Chen Z, Han Q, Yan Y, et al., How often should one update control and estimation: Review of networked triggering techniques, Science China-Information Sciences, 2020, 63(5): 150–201.

    Article  MathSciNet  Google Scholar 

  16. Jiang K, Niu B, Wang X, et al., Adaptive approximation-based design mechanism for non-strict-feedback nonlinear MIMO systems with application to continuous stirred tank reactor, ISA Transactions, 2020, 100: 92–102.

    Article  Google Scholar 

  17. Li X, Liu Y, Li J, et al., Adaptive output-feedback stabilization for PDE-ODE cascaded systems with unknown control coefficient and spatially varying parameter, Journal of Systems Science & Complexity, 2021, 34(1): 298–313.

    Article  MathSciNet  Google Scholar 

  18. Zhu Q, Niu B, Zhang G, et al., Adaptive fixed-time tracking control for a class of nonlinear pure-feedback systems: A relative threshold event-triggered strategy, ISA Transactions, 2021, 122: 346–356.

    Article  Google Scholar 

  19. Niu B, Chen W, Su W, et al., Switching event-triggered adaptive resilient dynamic surface control for stochastic nonlinear CPSs with unknown deception attacks, IEEE Transactions on Cybernetics, 2022, DOI: https://doi.org/10.1109/TCYB.2022.3209694.

  20. Wu Z, Xie X, and Zhang S, Adaptive backstepping controller design using stochastic small-gain theorem, Automatica, 2007, 43(4): 608–620.

    Article  MathSciNet  Google Scholar 

  21. Zhou J, Wen C, and Wang W, Adaptive backstepping control of uncertain systems with unknown input time-delay, Automatica, 2009, 45(6): 1415–1422.

    Article  MathSciNet  Google Scholar 

  22. Chiang M and Fu L, Adaptive stabilization of a class of uncertain switched nonlinear systems with backstepping control, Automatica, 2014, 50(8): 2128–2135.

    Article  MathSciNet  Google Scholar 

  23. He W, Kong L, Dong Y, et al., Fuzzy tracking control for a class of uncertain MIMO nonlinear systems with state constraints, IEEE Transactions on Systems, Man and Cybernetics: Systems, 2019, 49(3): 543–554.

    Article  Google Scholar 

  24. Zhou Q, Zhao S, Li H, et al., Adaptive neural network tracking control for robotic manipulators with dead zone, IEEE Transactions on Neural Networks and Learning Systems, 2019, 30(12): 3611–3620.

    Article  MathSciNet  Google Scholar 

  25. Wang X, Niu B, Zhao P, et al., Neural networks-based adaptive finite-time prescribed performance fault-tolerant control of switched nonlinear systems, International Journal of Adaptive Control and Signal Processing, 2021, 35(4): 532–548.

    Article  MathSciNet  Google Scholar 

  26. Li Y and Tong S, Fuzzy adaptive control design strategy of nonlinear switched large-scale systems, IEEE Transactions on Systems, Man and Cybernetics: Systems, 2018, 48(12): 2209–2218.

    Article  Google Scholar 

  27. Qi W, Yang X, Park J, et al., Fuzzy SMC for quantized nonlinear stochastic switching systems with semi-Markovian process and application, IEEE Transactions on Cybernetics, 2021, 52(9): 9316–9325.

    Article  Google Scholar 

  28. Li X, Zhang B, Li P, et al., Finite-horizon H-infinity state estimation for periodic neural networks over fading channels, IEEE Transactions on Neural Networks and Learning Systems, 2020, 31(5): 1450–1460.

    Article  MathSciNet  Google Scholar 

  29. Niu B, Liu J, Duan P, et al., Reduced-order observer-based adaptive fuzzy tracking control scheme of stochastic switched nonlinear systems, IEEE Transactions on Systems, Man and Cybernetics: Systems, 2020, 42(7): 1345–1357.

    Google Scholar 

  30. Du P, Liang H, Zhao S, et al., Neural-based decentralized adaptive finite-time control for nonlinear large-scale systems with time-varying output constraints, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(5): 3136–3147.

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  32. Niu B, Kong J, Zhao X, et.al., Event-triggered adaptive output-feedback control of switched stochastic nonlinear systems with actuator failures: A modified MDADT method, IEEE Transactions on Cybernetics, 2022, DOI: https://doi.org/10.1109/TCYB.2022.3169142.

  33. Li D, Liu Y, Tong S, et al., Neural networks-based adaptive control for nonlinear state constrained systems with input delay, IEEE Transactions on Cybernetics, 2018, 49(4): 1249–1258.

    Article  Google Scholar 

  34. Ma L, Huo X, Zhao X, et al., Adaptive fuzzy tracking control for a class of uncertain switched nonlinear systems with multiple constraints: A small-gain approach, International Journal of Fuzzy Systems, 2019, 21(8): 2609–2624.

    Article  MathSciNet  Google Scholar 

  35. Chang Y, Wang Y, Alsaadi F, et al., Adaptive fuzzy output-feedback tracking control for switched stochastic pure-feedback nonlinear systems, International Journal of Adaptive Control and Signal Processing, 2019, 33(10): 1567–1582.

    Article  MathSciNet  Google Scholar 

  36. Niu B, Wang D, Alotaibi N D, et al., Adaptive neural state-feedback tracking control of stochastic nonlinear switched systems: An average dwell-time method, IEEE Transactions on Neural Networks and Learning Systems, 2019, 30(4): 1076–1087.

    Article  MathSciNet  Google Scholar 

  37. Gao C, Liu X, Yang Y, et al., Event-triggered finite-time adaptive neural control for nonlinear non-strict-feedback time-delay systems with disturbances, Information Sciences, 2020, 536: 1–24.

    Article  MathSciNet  Google Scholar 

  38. Tabatabaei S M, Kamali S, Arefi M M, et al., Prescribed performance adaptive DSC for a class of time-delayed switched nonlinear systems in nonstrict-feedback form: Application to a two-stage chemical reactor, Journal of Process Control, 2020, 89: 85–94.

    Article  Google Scholar 

  39. Niu B, Liu Y, W Zhou, et al., Multiple lyapunov functions for adaptive neural tracking control of switched nonlinear nonlower-triangular systems, IEEE Transactions on Cybernetics, 2020, 50(5): 1877–1886.

    Article  Google Scholar 

  40. Liang Y, Zhang H, Zhang K, et al., A novel neural network discrete-time optimal control design for nonlinear time-delay systems using adaptive critic designs, Optimal Control Applications and Methods, 2020, 41(3): 748–764.

    Article  MathSciNet  Google Scholar 

  41. Niu B, Wang D, Liu M, et al., Adaptive neural output-feedback controller design of switched nonlower triangular nonlinear systems with time delays, IEEE Transactions on Neural Networks and Learning Systems, 2020, 31(10): 4084–4093.

    Article  MathSciNet  Google Scholar 

  42. Sun H, Hou L, Zong G, et al., Adaptive decentralized neural network tracking control for uncertain interconnected nonlinear systems with input quantization and time delay, IEEE transactions on Neural Networks and Learning Systems, 2020, 31(4): 2593–2610.

    Article  MathSciNet  Google Scholar 

  43. Niu B, Zhang Y, Zhao X, et al., Adaptive predefined-time bipartite consensus tracking control of constrained nonlinear MASs: An improved nonlinear mapping function method, IEEE Transactions on Cybernetics, 2023, DOI: https://doi.org/10.1109/TCYB.2022.3231900.

  44. Gao T, Liu Y, Liu L, et al., Adaptive neural network-based control for a class of nonlinear pure-feedback systems with time-varying full state constraints, IEEE/CAA Journal of Automatica Sinica, 2018, 5(5): 923–933.

    Article  MathSciNet  Google Scholar 

  45. Y Wu and Yue D, Robust adaptive neural network control for a class of multiple-input-multiple-output nonlinear time delay system with hysteresis inputs and dynamic uncertainties, Asian Journal of Control, 2019, 21(5): 796–812.

    Article  MathSciNet  Google Scholar 

  46. Na J, Wang S, Liu Y, et al., Finite-time convergence adaptive neural network control for nonlinear servo systems, IEEE Transactions on Cybernetics, 2020, 50(6): 2568–2579.

    Article  Google Scholar 

  47. Tee K and Ge S, Control of state-constrained nonlinear systems using integral barrier Lyapunov functionals, IEEE 51 st IEEE Conference on Decision and Control, 2012, 51: 3239–3244.

    Google Scholar 

  48. Xu J, Adaptive fault-tolerant control for a class of output-constrained nonlinear systems, International Journal of Robust and Nonlinear Control, 2014, 14: 3732–3745.

    MathSciNet  Google Scholar 

  49. Qiu Y, Liang X, Dai Z, et al., Backstepping dynamic surface control for a class of non-linear systems with time-varying output constraints, IET Control Theory and Applications, 2015, 9(15): 2312–2319.

    Article  MathSciNet  Google Scholar 

  50. Xu J, Adaptive fault tolerant control for a class of input and state constrained MIMO nonlinear systems, International Journal of Robust and Nonlinear Control, 2015, 26: 286–302.

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  52. Liu Y and Tong S, Barrier Lyapunov functions for nussbaum gain adaptive control of full state constrained nonlinear systems, Automatica, 2017, 76: 143–152.

    Article  MathSciNet  Google Scholar 

  53. Na J, Chen Q, Ren X, et al., Adaptive prescribed performance motion control of servo mechanisms with friction compensation, IEEE Transactions on Industrial Electronics, 2013, 61(1): 486–494.

    Article  Google Scholar 

  54. Dehaan D and Guay M, Extremum-seeking control of state-constrained nonlinear systems, IFAC Proceedings Volumes, 2005, 37(13): 663–668.

    Article  Google Scholar 

  55. Bemporad A, Reference governor for constrained nonlinear systems, IEEE Transactions on Automatic Control, 1998, 43(3): 415–419.

    Article  MathSciNet  Google Scholar 

  56. Mayne D, Rawlings J, Rao C, et al., Constrained model predictive control: Stability and optimality, Automatica, 2000, 36(6): 789–814.

    Article  MathSciNet  Google Scholar 

  57. Wang C, Wu Y, and Zhang Z, Tracking control for strict-feedback nonlinear systems with time-varying full state constraints, Transactions of the Institute of Measurement and Control, 2018, 14: 3964–3977.

    Article  Google Scholar 

  58. Liu J, Niu B, Zhao P, et al., Almost fast finite-time adaptive tracking control for a class of full-state constrained pure-feedback nonlinear systems, International Journal of Robust and Nonlinear Control, 2020, 30(17): 7517–7532.

    Article  MathSciNet  Google Scholar 

  59. Zhang J, Integral barrier Lyapunov functions-based neural control for strict-feedback nonlinear systems with multi-constraint, International Journal of Control Automation and Systems, 2018, 16: 2002–2010.

    Article  Google Scholar 

  60. Yang Z, Zhang X, Zong X, et al., Adaptive fuzzy control for non-strict feedback nonlinear systems with input delay and full state constraints, Journal of the Franklin Institute, 2020, 357(11): 6858–6881.

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  62. Tee K and Ge S, Control of nonlinear systems with partial state constraints using a barrier Lyapunov function, International Journal of Control, 2011, 84(12): 2008–2023.

    Article  MathSciNet  Google Scholar 

  63. Zhang C, Wang L, Gao C, et al., Adaptive neural tracking control for a class of pure-feedback systems with output constraints based on event-triggered strategy, IEEE Access, 2020, 8: 61593–61603.

    Article  Google Scholar 

  64. Ge S and Wang C, Adaptive NN control of uncertain nonlinear pure-feedback systems, Automatica, 2002, 38(4): 671–682.

    Article  MathSciNet  Google Scholar 

  65. Song J, Yan M, and Yang P, Neural adaptive dynamic surface asymptotic tracking control for a class of uncertain nonlinear system, Circuits Systems and Signal Processing, 2020, 40: 1673–1698.

    Article  Google Scholar 

  66. Krstic M, Kokotovic P, and Kanellakopoulos I, Nonlinear and Adaptive Control Design, Springer, Berlin Heidelberg, 2003.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, 116024, China

    Ben Niu

  2. School of Information Science and Engineering, Shandong Normal University, Jinan, 250014, China

    Ben Niu, Xiaomei Wang & Xinjun Wang

  3. School of Mathematics, Southeast University, Nanjing, 211189, China

    Xiaoan Wang

  4. School of Automation, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Tao Li

Authors
  1. Ben Niu
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  2. Xiaoan Wang
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  3. Xiaomei Wang
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  4. Xinjun Wang
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  5. Tao Li
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Corresponding author

Correspondence to Ben Niu.

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The authors declare no conflict of interest.

Additional information

This research was supported in part by the National Natural Science Foundation of China under Grant No. 62303278, and in part by the Taishan Scholar Project of Shandong Province of China under Grant No. tsqn201909078.

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Niu, B., Wang, X., Wang, X. et al. Adaptive Barrier-Lyapunov-Functions Based Control Scheme of Nonlinear Pure-Feedback Systems with Full State Constraints and Asymptotic Tracking Performance. J Syst Sci Complex 37, 965–984 (2024). https://doi.org/10.1007/s11424-024-1259-8

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  • DOI: https://doi.org/10.1007/s11424-024-1259-8

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