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Volume 8 Issue 2
Feb.  2021

IEEE/CAA Journal of Automatica Sinica

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Yongliang Yang, Zhijie Liu, Qing Li and Donald C. Wunsch, "Output Constrained Adaptive Controller Design for Nonlinear Saturation Systems," IEEE/CAA J. Autom. Sinica, vol. 8, no. 2, pp. 441-454, Feb. 2021. doi: 10.1109/JAS.2020.1003524
Citation: Yongliang Yang, Zhijie Liu, Qing Li and Donald C. Wunsch, "Output Constrained Adaptive Controller Design for Nonlinear Saturation Systems," IEEE/CAA J. Autom. Sinica, vol. 8, no. 2, pp. 441-454, Feb. 2021. doi: 10.1109/JAS.2020.1003524

Output Constrained Adaptive Controller Design for Nonlinear Saturation Systems

doi: 10.1109/JAS.2020.1003524
Funds:  This work was supported in part by the National Natural Science Foundation of China (61903028, 62073030), in part by the China Post-Doctoral Science Foundation (2019M660463), in part by the Fundamental Research Funds for the China Central Universities of University of Science and Technology Beijing (FRF-TP-18-031A1, FRF-BD-19-002A), and in part by the Postdoctor Research Foundation of Shunde Graduate School of University of Science and Technology Beijing (2020BH002)
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  • This paper considers the adaptive neuro-fuzzy control scheme to solve the output tracking problem for a class of strict-feedback nonlinear systems. Both asymmetric output constraints and input saturation are considered. An asymmetric barrier Lyapunov function with time-varying prescribed performance is presented to tackle the output-tracking error constraints. A high-gain observer is employed to relax the requirement of the Lipschitz continuity about the nonlinear dynamics. To avoid the “explosion of complexity”, the dynamic surface control (DSC) technique is employed to filter the virtual control signal of each subsystem. To deal with the actuator saturation, an additional auxiliary dynamical system is designed. It is theoretically investigated that the parameter estimation and output tracking error are semi-global uniformly ultimately bounded. Two simulation examples are conducted to verify the presented adaptive fuzzy controller design.

     

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  • [1]
    L. H. Kong, W. He, C. G. Yang, Z. J. Li, and C. Y. Sun, “Adaptive fuzzy control for coordinated multiple robots with constraint using impedance learning,” IEEE Trans. Cybern., vol. 49, no. 8, pp. 3052–3063, Aug. 2019. doi: 10.1109/TCYB.2018.2838573
    [2]
    Z. J. Liu, J. K. Liu, and W. He, “Dynamic modeling and vibration control for a nonlinear 3-dimensional flexible manipulator,” Int. J. Robust Nonlinear Control, vol. 28, no. 13, pp. 3927–3945, Sep. 2018. doi: 10.1002/rnc.4113
    [3]
    Q. L. Wei, D. R. Liu, Y. Liu, and R. Z. Song, “Optimal constrained self-learning battery sequential management in microgrid via adaptive dynamic programming,” IEEE/CAA J. Autom. Sinica, vol. 4, no. 2, pp. 168–176, Apr. 2017. doi: 10.1109/JAS.2016.7510262
    [4]
    Q. L. Wei, G. Shi, R. Z. Song, and Y. Liu, “Adaptive dynamic programming-based optimal control scheme for energy storage systems with solar renewable energy,” IEEE Trans. Ind. Electron., vol. 64, no. 7, pp. 5468–5478, Jul. 2017. doi: 10.1109/TIE.2017.2674581
    [5]
    Q. L. Wei, F. L. Lewis, G. Shi, and R. Z. Song, “Error-tolerant iterative adaptive dynamic programming for optimal renewable home energy scheduling and battery management,” IEEE Trans. Ind. Electron., vol. 64, no. 12, pp. 9527–9537, Dec. 2017. doi: 10.1109/TIE.2017.2711499
    [6]
    S. H. Luo and Y. D. Song, “Chaos analysis-based adaptive backstepping control of the microelectromechanical resonators with constrained output and uncertain time delay,” IEEE Trans. Ind. Electron., vol. 63, no. 10, pp. 6217–6225, Oct. 2016. doi: 10.1109/TIE.2016.2569462
    [7]
    Q. L. Wei and D. R. Liu, “Data-driven neuro-optimal temperature control of water–gas shift reaction using stable iterative adaptive dynamic programming,” IEEE Trans. Ind. Electron., vol. 61, no. 11, pp. 6399–6408, Nov. 2014. doi: 10.1109/TIE.2014.2301770
    [8]
    S. Sui and C. L. Philip Chen, “Adaptive output-feedback finite-time stabilisation of stochastic non-linear systems with application to a two-stage chemical reactor,” IET Control Theory Appl., vol. 13, no. 4, pp. 534–542, Mar.−May. 2019. doi: 10.1049/iet-cta.2018.5431
    [9]
    J. Na, Q. Chen, X. M. Ren, and Y. Guo, “Adaptive prescribed performance motion control of servo mechanisms with friction compensation,” IEEE Trans. Ind. Electron., vol. 61, no. 1, pp. 486–494, Jan. 2014. doi: 10.1109/TIE.2013.2240635
    [10]
    L. Liu, Y. J. Liu, D. P. Li, S. C. Tong, and Z. S. Wang, “Barrier Lyapunov function-based adaptive fuzzy FTC for switched systems and its applications to resistance-inductance-capacitance circuit system,” IEEE Trans. Cybern., vol. 50, no. 8, pp. 3491–3502, Aug. 2020. doi: 10.1109/TCYB.2019.2931770
    [11]
    L. Liu, Y. J. Liu, and S. C. Tong, “Neural networks-based adaptive finite-time fault-tolerant control for a class of strict-feedback switched nonlinear systems,” IEEE Trans. Cybern., vol. 49, no. 7, pp. 2536–2545, Jul. 2019. doi: 10.1109/TCYB.2018.2828308
    [12]
    Y. Yang, K. G. Vamvoudakis, H. Modares, Y. X. Yin, and D. C. Wunsch, “Safe intermittent reinforcement learning with static and dynamic event generators, ” IEEE Trans. Neural Netw. Learn. Syst., to be published, DOI: 10.1109/TNNLS.2020.2967871.
    [13]
    Z. J. Liu, Z. J. Zhao, and C. K. Ahn, “Boundary constrained control of flexible string systems subject to disturbances,” IEEE Trans. Circuits Syst. II Express Briefs, vol. 67, no. 1, pp. 112–116, Jan. 2020. doi: 10.1109/TCSII.2019.2901283
    [14]
    Y. Yang, D. W. Ding, H. Y. Xiong, Y. X. Yin, and D. C. Wunsch, “Online barrier-actor-critic learning for H control with full-state constraints and input saturation,” J. Franklin Inst., vol. 357, no. 6, pp. 3316–3344, Apr. 2020. doi: 10.1016/j.jfranklin.2019.12.017
    [15]
    J. Na, “Adaptive prescribed performance control of nonlinear systems with unknown dead zone,” Int. J. Adapt. Control Signal Process., vol. 27, no. 5, pp. 426–446, May 2013. doi: 10.1002/acs.2322
    [16]
    H. Q. Wang, P. X. Liu, and S. C. Liu, “Adaptive neural synchronization control for bilateral teleoperation systems with time delay and backlash-like hysteresis,” IEEE Trans. Cybern., vol. 47, no. 10, pp. 3018–3026, Oct. 2017. doi: 10.1109/TCYB.2016.2644656
    [17]
    M. Krstić, I. Kanellakopoulos, and P. Kokotović, Nonlinear and Adaptive Control Design, New York, USA: John Wiley and Sons, 1995.
    [18]
    J. A. Farrell, M. Polycarpou, M. Sharma, and W. J. Dong, “Command filtered backstepping,” IEEE Trans. Automat. Control, vol. 54, no. 6, pp. 1391–1395, Jun. 2009. doi: 10.1109/TAC.2009.2015562
    [19]
    W. J. Dong, J. A. Farrell, M. M. Polycarpou, V. Djapic, and M. Sharma, “Command filtered adaptive backstepping,” IEEE Trans. Control Syst. Technol., vol. 20, no. 3, pp. 566–580, May 2012. doi: 10.1109/TCST.2011.2121907
    [20]
    D. Wang and J. Huang, “Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form,” IEEE Trans. Neural Netw., vol. 16, no. 1, pp. 195–202, Jan. 2005. doi: 10.1109/TNN.2004.839354
    [21]
    J. P. Yu, P. Shi, W. J. Dong, and H. S. Yu, “Observer and command-filter-based adaptive fuzzy output feedback control of uncertain nonlinear systems,” IEEE Trans. Ind. Electron., vol. 62, no. 9, pp. 5962–5970, Sep. 2015. doi: 10.1109/TIE.2015.2418317
    [22]
    W. J. Si and X. D. Dong, “Adaptive neural DSC for nonlinear switched systems with prescribed performance and input saturation, ” IEEE/CAA J. Autom. Sinica, to be published, DOI: 10.1109/JAS.2017.7510661.
    [23]
    S. Ling, H. Q. Wang, and P. X. Liu, “Adaptive fuzzy dynamic surface control of flexible-joint robot systems with input saturation,” IEEE/CAA J. Autom. Sinica, vol. 6, no. 1, pp. 97–107, Jan. 2019. doi: 10.1109/JAS.2019.1911330
    [24]
    S. Sui, S. C. Tong, and C. L. Philip Chen, “Finite-time filter decentralized control for nonstrict-feedback nonlinear large-scale systems,” IEEE Trans. Fuzzy Syst., vol. 26, no. 6, pp. 3289–3300, Dec. 2018. doi: 10.1109/TFUZZ.2018.2821629
    [25]
    S. Sui, C. L. Philip Chen, and S. C. Tong, “Neural network filtering control design for nontriangular structure switched nonlinear systems in finite time,” IEEE Trans. Neural Netw. Learn. Syst., vol. 30, no. 7, pp. 2153–2162, Jul. 2019. doi: 10.1109/TNNLS.2018.2876352
    [26]
    C. W. Wu, J. X. Liu, Y. Y. Xiong, and L. G. Wu, “Observer-based adaptive fault-tolerant tracking control of nonlinear nonstrict-feedback systems,” IEEE Trans. Neural Netw. Learn. Syst., vol. 29, no. 7, pp. 3022–3033, Jul. 2018.
    [27]
    S. C. Tong, S. Sui, and Y. M. Li, “Fuzzy adaptive output feedback control of MIMO nonlinear systems with partial tracking errors constrained,” IEEE Trans. Fuzzy Syst., vol. 23, no. 4, pp. 729–742, Aug. 2015. doi: 10.1109/TFUZZ.2014.2327987
    [28]
    Y. M. Li, S. C. Tong, and T. S. Li, “Observer-based adaptive fuzzy tracking control of MIMO stochastic nonlinear systems with unknown control directions and unknown dead zones,” IEEE Trans. Fuzzy Syst., vol. 23, no. 4, pp. 1228–1241, Aug. 2015. doi: 10.1109/TFUZZ.2014.2348017
    [29]
    H. K. Khalil, Nonlinear Systems. 3rd ed. New Jersey, USA: Prentice Hall, 2002.
    [30]
    S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, UK: Cambridge University Press, 2004.
    [31]
    K. B. Ngo, R. Mahony, and Z. P. Jiang, “Integrator backstepping using barrier functions for systems with multiple state constraints, ” in Proc. 44th IEEE Conf. on Decision and Control, Seville, Spain, 2005, pp. 8306−8312.
    [32]
    K. P. Tee, S. S. Ge, and E. H. Tay, “Barrier Lyapunov functions for the control of output-constrained nonlinear systems,” Automatica, vol. 45, no. 4, pp. 918–927, Apr. 2009. doi: 10.1016/j.automatica.2008.11.017
    [33]
    Y. Yang, K. G. Vamvoudakis, and H. Modares, “Safe reinforcement learning for dynamical games,” Int. J. Robust Nonlinear Control, vol. 30, no. 9, pp. 3706–3726, Jun. 2020. doi: 10.1002/rnc.4962
    [34]
    W. He, Y. H. Chen, and Z. Yin, “Adaptive neural network control of an uncertain robot with full-state constraints,” IEEE Trans. Cybern., vol. 46, no. 3, pp. 620–629, Mar. 2016. doi: 10.1109/TCYB.2015.2411285
    [35]
    T. T. Gao, Y. J. Liu, L. Liu, and D. P. 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, Sep. 2018. doi: 10.1109/JAS.2018.7511195
    [36]
    Y. J. Liu and S. C. Tong, “Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems,” Automatica, vol. 76, pp. 143–152, Feb. 2017. doi: 10.1016/j.automatica.2016.10.011
    [37]
    K. P. Tee, B. B. Ren, and S. S. Ge, “Control of nonlinear systems with time-varying output constraints,” Automatica, vol. 47, no. 11, pp. 2511–2516, Nov. 2011. doi: 10.1016/j.automatica.2011.08.044
    [38]
    C. P. Bechlioulis and G. A. Rovithakis, “Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems,” Automatica, vol. 45, no. 2, pp. 532–538, Feb. 2009. doi: 10.1016/j.automatica.2008.08.012
    [39]
    X. D. Ye and J. P. Jiang, “Adaptive nonlinear design without a priori knowledge of control directions,” IEEE Trans. Autom. Control, vol. 43, no. 11, pp. 1617–1621, Nov. 1998. doi: 10.1109/9.728882
    [40]
    J. A. Farrell and M. M. Polycarpou, Adaptive Approximation Based Control: Unifying Neural, Fuzzy and Traditional Adaptive Approximation Approaches. Hoboken, USA: Wiley-Interscience, 2006.
    [41]
    S. S. Ge, C. C. Hang, and T. Zhang, “Adaptive neural network control of nonlinear systems by state and output feedback,” IEEE Trans. Syst. Man Cybern. Part B Cybern., vol. 29, no. 6, pp. 818–828, Dec. 1999. doi: 10.1109/3477.809035
    [42]
    L. Praly, “Asymptotic stabilization via output feedback for lower triangular systems with output dependent incremental rate,” IEEE Trans. Autom. Control, vol. 48, no. 6, pp. 1103–1108, Jun. 2003. doi: 10.1109/TAC.2003.812819
    [43]
    B. B. Ren, S. S. Ge, K. P. Tee, and T. H. Lee, “Adaptive neural control for output feedback nonlinear systems using a barrier Lyapunov function,” IEEE Trans. Neural Netw., vol. 21, no. 8, pp. 1339–1345, Aug. 2010. doi: 10.1109/TNN.2010.2047115
    [44]
    S. C. Tong, X. L. He, and Y. M. Li, “Direct adaptive fuzzy backstepping robust control for single input and single output uncertain nonlinear systems using small-gain approach,” Inf. Sci., vol. 180, no. 9, pp. 1738–1758, May 2010. doi: 10.1016/j.ins.2009.12.033
    [45]
    S. C. Tong, K. K. Sun, and S. Sui, “Observer-based adaptive fuzzy decentralized optimal control design for strict-feedback nonlinear large-scale systems,” IEEE Trans. Fuzzy Syst., vol. 26, no. 2, pp. 569–584, Apr. 2018. doi: 10.1109/TFUZZ.2017.2686373
    [46]
    C. Y. Wen, J. Zhou, Z. T. Liu, and H. Y. Su, “Robust adaptive control of uncertain nonlinear systems in the presence of input saturation and external disturbance,” IEEE Trans. Autom. Control, vol. 56, no. 7, pp. 1672–1678, Jul. 2011. doi: 10.1109/TAC.2011.2122730
    [47]
    D. P. Li, Y. J. Liu, S. C. Tong, C. L. Philip Chen, and D. J. Li, “Neural networks-based adaptive control for nonlinear state constrained systems with input delay,” IEEE Trans. Cybern., vol. 49, no. 4, pp. 1249–1258, Apr. 2019. doi: 10.1109/TCYB.2018.2799683
    [48]
    W. He, H. F. Huang, and S. S. Ge, “Adaptive neural network control of a robotic manipulator with time-varying output constraints,” IEEE Trans. Cybern., vol. 47, no. 10, pp. 3136–3147, Oct. 2017. doi: 10.1109/TCYB.2017.2711961
    [49]
    Y. D. Song and S. Y. Zhou, “Tracking control of uncertain nonlinear systems with deferred asymmetric time-varying full state constraints,” Automatica, vol. 98, pp. 314–322, Dec. 2018. doi: 10.1016/j.automatica.2018.09.032
    [50]
    S. S. Ge and J. Wang, “Robust adaptive tracking for time-varying uncertain nonlinear systems with unknown control coefficients,” IEEE Trans. Autom. Control, vol. 48, no. 8, pp. 1463–1469, Aug. 2003. doi: 10.1109/TAC.2003.815049
    [51]
    H. J. Liang, X. Y. Guo, Y. N. Pan, and T. W. Huang, “Event-triggered fuzzy bipartite tracking control for network systems based on distributed reduced-order observers (revised manuscript of tfs-2019–1049), ” IEEE Trans. Fuzzy Syst., to be published, DOI: 10.1109/TFUZZ.2020.2982618
    [52]
    E. P. Ryan, “A universal adaptive stabilizer for a class of nonlinear systems,” Syst. Control Lett., vol. 16, no. 3, pp. 209–218, Mar. 1991. doi: 10.1016/0167-6911(91)90050-O

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    Highlights

    • A barrier Lyapunov function with an asymmetric time-varying constraint is presented to ensure the prescribed transient performance on the output tracking error.
    • To estimate the unmeasured states, the high-gain observer with adaptive feedback gain is designed with a relaxed continuity assumption.
    • The input saturation is solved by introducing an additional auxiliary system, of which the stability analysis is based on the Nussbaum function-based method.

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