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Volume 8 Issue 6
Jun.  2021

IEEE/CAA Journal of Automatica Sinica

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J. X. Zhang, K. W. Li, and Y. M. Li, "Output-Feedback Based Simplified Optimized Backstepping Control for Strict-Feedback Systems with Input and State Constraints," IEEE/CAA J. Autom. Sinica, vol. 8, no. 6, pp. 1119-1132, Jun. 2021. doi: 10.1109/JAS.2021.1004018
Citation: J. X. Zhang, K. W. Li, and Y. M. Li, "Output-Feedback Based Simplified Optimized Backstepping Control for Strict-Feedback Systems with Input and State Constraints," IEEE/CAA J. Autom. Sinica, vol. 8, no. 6, pp. 1119-1132, Jun. 2021. doi: 10.1109/JAS.2021.1004018

Output-Feedback Based Simplified Optimized Backstepping Control for Strict-Feedback Systems with Input and State Constraints

doi: 10.1109/JAS.2021.1004018
Funds:  This work was supported by National Natural Science Foundation of China (61822307, 61773188)
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  • In this paper, an adaptive neural-network (NN) output feedback optimal control problem is studied for a class of strict-feedback nonlinear systems with unknown internal dynamics, input saturation and state constraints. Neural networks are used to approximate unknown internal dynamics and an adaptive NN state observer is developed to estimate immeasurable states. Under the framework of the backstepping design, by employing the actor-critic architecture and constructing the tan-type Barrier Lyapunov function (BLF), the virtual and actual optimal controllers are developed. In order to accomplish optimal control effectively, a simplified reinforcement learning (RL) algorithm is designed by deriving the updating laws from the negative gradient of a simple positive function, instead of employing existing optimal control methods. In addition, to ensure that all the signals in the closed-loop system are bounded and the output can follow the reference signal within a bounded error, all state variables are confined within their compact sets all times. Finally, a simulation example is given to illustrate the effectiveness of the proposed control strategy.

     

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  • [1]
    S. S. Ge and C. Wang, “Direct adaptive NN control of a class of nonlinear systems,” IEEE Trans. Neural Networks, vol. 13, no. 1, pp. 214–221, 2002. doi: 10.1109/72.977306
    [2]
    B. Chen, X. P. Liu, K. F. Liu, and C. Lin, “Direct adaptive fuzzy control of nonlinear strict-feedback systems,” Automatica, vol. 45, no. 6, pp. 1530–1535, 2009. doi: 10.1016/j.automatica.2009.02.025
    [3]
    Y. H. Li, S. Qiang, X. Y. Zhuang, and O. Kaynak, “Robust and adaptive backstepping control for nonlinear systems using RBF neural networks,” IEEE Trans. Neural Networks, vol. 15, no. 3, pp. 693–701, 2004. doi: 10.1109/TNN.2004.826215
    [4]
    R. Dong, S. G. Gao, B. Ning, T. Tang, Y. D. Li, and K. P. Valavanis, “Error-driven nonlinear feedback design for fuzzy adaptive dynamic surface control of nonlinear systems with prescribed tracking performance,” IEEE Trans. Systems,Man,and Cybernetics:Systems, vol. 50, no. 3, pp. 1013–1023, 2020. doi: 10.1109/TSMC.2017.2734698
    [5]
    B. Chen and C. Lin, “Finite-time stabilization-based adaptive fuzzy control design,” IEEE Trans. Fuzzy Systems, 2020. DOI: 10.1109/TFUZZ.2020.2991153
    [6]
    S. G. Gao, Y. H. Hou, H. R. Dong, Y. X. Yue, and S. Y. Li, “Global nested PID control of strict-feedback nonlinear systems with prescribed output and virtual tracking performance,” IEEE Trans. Circuits and Systems Ⅱ:Express Briefs, vol. 67, no. 2, pp. 325–329, 2020. doi: 10.1109/TCSII.2019.2907141
    [7]
    S. C. Tong, Y. M. Li, G. Feng, and T. S. Li, “Observer-based adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems,” IEEE Trans. Systems,Man,and Cybernetics,Part B, vol. 41, no. 4, pp. 1124–1135, 2011. doi: 10.1109/TSMCB.2011.2108283
    [8]
    D. R. Ding, Z. D. Wang, and Q. L. Han, “Neural-network-based output feedback control with stochastic communication protocols,” Automatica, vol. 106, pp. 221–229, 2019. doi: 10.1016/j.automatica.2019.04.025
    [9]
    S. C. Tong, X. Min, and Y. X. Li, “Observer-based adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown control gain functions,” IEEE Trans. Cybernetics, vol. 50, no. 9, pp. 3901–3913, 2020.
    [10]
    B. Chen, H. G. Zhang, X. P. Liu, and C. Lin, “Neural observer and adaptive neural control design for a class of nonlinear systems,” IEEE Trans. Neural Networks and Learning Systems, vol. 29, no. 9, pp. 4261–4271, 2018. doi: 10.1109/TNNLS.2017.2760903
    [11]
    K. P. Tee and S. S. Ge, “Control of nonlinear systems with partial state constraints using a Barrier Lyapunov function,” Int. J. Control, vol. 84, no. 12, pp. 2008–2023, 2011. doi: 10.1080/00207179.2011.631192
    [12]
    K. P. Tee and S. S. Ge, “Control of state-constrained nonlinear systems using integral Barrier Lyapunov functionals,” in Proc. IEEE Conf. Decision and Control, pp. 3239–3244, 2012.
    [13]
    Y. J. Liu and S. C. Tong, “Barrier Lyapunov functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints,” Automatica, vol. 64, pp. 70–75, 2016. doi: 10.1016/j.automatica.2015.10.034
    [14]
    T. Zhang, M. Xia, and Y. Yi, “Adaptive neural dynamic surface control of strict-feedback nonlinear systems with full state constraints and unmodeled dynamics,” Automatica, vol. 81, pp. 232–239, 2017. doi: 10.1016/j.automatica.2017.03.033
    [15]
    T. Gao, Y. J. Liu, L. Liu, and D. Li, “Adaptive neural network-based control for a class of nonlinear pure-feedback systems with time-varying full state constraints,” IEEE/CAA J. Autom. Sinica, vol. 5, no. 5, pp. 923–933, 2018. doi: 10.1109/JAS.2018.7511195
    [16]
    Y. J. Liu, M. Z. Gong, S. C. Tong, C. L. Philip. Chen, and D. J. Li, “Adaptive fuzzy output feedback control for a class of nonlinear systems with full state constraints,” IEEE Trans. Fuzzy System, vol. 26, no. 5, pp. 2607–2617, 2018. doi: 10.1109/TFUZZ.2018.2798577
    [17]
    K. Sun, S. Mou, J. Qiu, T. Wang, and H. Gao, “Adaptive fuzzy control for nontriangular structural stochastic switched nonlinear systems with full state constraints,” IEEE Trans. Fuzzy Systems, vol. 27, no. 8, pp. 1587–1601, 2019. doi: 10.1109/TFUZZ.2018.2883374
    [18]
    W. C. Meng, Q. M. Yang, J. Si, and Y. X. Sun, “Adaptive neural control of a class of output-constrained nonaffine systems,” IEEE Trans. Cybernetics, vol. 46, no. 1, pp. 85–95, 2016. doi: 10.1109/TCYB.2015.2394797
    [19]
    Y. M. Li, T. S. Li, and X. J. Jing, “Indirect adaptive fuzzy control for input and output constrained nonlinear systems using a barrier Lyapunov function,” Int. J. Adaptive Control and Signal Processing, vol. 28, no. 2, pp. 184–199, 2014. doi: 10.1002/acs.2410
    [20]
    X. Jin, “Adaptive fault tolerant control for a class of input and state constrained MIMO nonlinear systems,” Int. J. Robust and Nonlinear Control, vol. 26, no. 2, pp. 286–302, 2016. doi: 10.1002/rnc.3312
    [21]
    Q. Zhou, L. Wang, C. Wu, H. Li, and H. Du, “Adaptive fuzzy control for nonstrict-feedback systems with input saturation and output constraint,” IEEE Trans. Systems,Man,and Cybernetics:Systems, vol. 47, no. 1, pp. 1–12, 2017. doi: 10.1109/TSMC.2016.2557222
    [22]
    S. G. Gao, H. R. Dong, B. Ning, and Q. Zhang, “Cooperative prescribed performance tracking control for multiple high-speed trains in moving block signaling system,” IEEE Trans. Intelligent Transportation Systems, vol. 20, no. 7, pp. 2740–2749, 2019. doi: 10.1109/TITS.2018.2877171
    [23]
    R. E. Bellman, “Dynamic programming,” Princeton University Press, Princeton, NJ, USA, 1957.
    [24]
    M. L. Chambers, “The mathematical theory of optimal processes,” J. Operational Research Society, vol. 16, no. 4, pp. 493–494, 1965. doi: 10.1057/jors.1965.92
    [25]
    D. R. Liu, X. Yang, D. Wang, and Q. Wei, “Reinforcement-learningbased robust controller design for continuous-time uncertain nonlinear systems subject to input constraints,” IEEE Trans. Cybernetics, vol. 45, no. 7, pp. 1372–1385, 2015. doi: 10.1109/TCYB.2015.2417170
    [26]
    X. Yang, D. R. Liu, and D. Wang, “Reinforcement learning for adaptive optimal control of unknown continuous-time nonlinear systems with input constraints,” Int. J. Control, vol. 87, no. 3, pp. 553–566, 2013.
    [27]
    X. Yang and B. Zhao, “Optimal neuro-control strategy for nonlinear systems with asymmetric input constraints,” IEEE/CAA J. Autom. Sinica, vol. 7, no. 2, pp. 575–583, 2020. doi: 10.1109/JAS.2020.1003063
    [28]
    H. Modares, F. L. Lewis, and M. Naghibi-Sistani, “Integral reinforcement learning and experience replay for adaptive optimal control of partially unknown constrained-input continuous-time systems,” Automatica, vol. 50, no. 1, pp. 193–202, 2014. doi: 10.1016/j.automatica.2013.09.043
    [29]
    Y. M. Li, T. T. Yang, and S. C. Tong, “Adaptive neural networks finite-time optimal control for a class of nonlinear systems,” IEEE Trans. Neural Networks and Learning Systems, vol. 31, no. 11, pp. 4451–4460, 2020. doi: 10.1109/TNNLS.2019.2955438
    [30]
    G. X. Wen, S. S. Ge, and F. W. Tu, “Optimized backstepping for tracking control of strict-feedback systems,” IEEE Trans. Neural Networks and Learning Systems, vol. 29, no. 8, pp. 3850–3862, 2018. doi: 10.1109/TNNLS.2018.2803726
    [31]
    W. W. Bai, T. S. Li, and S. C. Tong, “NN reinforcement learning adaptive control for a class of nonstrict-feedback discrete-time systems,” IEEE Trans. Cybernetics, vol. 50, no. 11, pp. 4573–4584, 2020. doi: 10.1109/TCYB.2020.2963849
    [32]
    G. X. Wen, C. Chen, and S. S. Ge, “Simplified optimized backstepping control for a class of nonlinear strict-feedback systems with unknown dynamic functions,” IEEE Trans. Cybernetics, 2020. DOI: 10.1109/TCYB.2020.3002108
    [33]
    W. Sun, S. F. Su, Y. Q. Wu, J. W. Xia, and V. T. Nguyen, “Adaptive fuzzy control with high-order barrier Lyapunov functions for highorder uncertain nonlinear systems with full-state constraints,” IEEE Trans. Cybernetics, vol. 50, no. 8, pp. 3424–3432, 2019.
    [34]
    H. G. Zhang, L. L. Cui, and Y. H. Luo, “Near-optimal control for nonzerosum differential games of continuous-time nonlinear systems using single network ADP,” IEEE Trans. Cybernetics, vol. 43, no. 1, pp. 206–216, 2013. doi: 10.1109/TSMCB.2012.2203336
    [35]
    X. Yang, D. R. Liu, and Q. L. Wei, “Online approximate optimal control for affine non-linear systems with unknown internal dynamics using adaptive dynamic programming,” IET Control Theory and Applications, vol. 8, no. 16, pp. 1676–1688, 2014. doi: 10.1049/iet-cta.2014.0186
    [36]
    T. C. Wang, S. Sui, and S. C. Tong, “Data-based adaptive neural network optimal output feedback control for nonlinear systems with actuator saturation,” Neurocomputing, vol. 247, pp. 192–201, 2017. doi: 10.1016/j.neucom.2017.03.053

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    Highlights

    • An adaptive NN optimal control scheme is developed for nonlinear systems with input saturation.
    • The Barrier type of optimal cost functions are constructed to solve the optimal control problem for nonlinear system.
    • By using the actor-critic architecture with tan-type BLF, the optimal controllers are designed by the backstepping recursive design.
    • Simplified RL algorithm is designed by deriving the updating laws from the simple positive function.

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