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Event-Triggered Adaptive Fuzzy Finite Time Control of Fractional-Order Non-Strict Feedback Nonlinear Systems

XIN Chun1, LI Yuanxin1, NIU Ben2   

  1. 1. College of Science, Liaoning University of Technology, Jinzhou 121001, China;
    2. School of Information Science and Engineering, Shandong Normal University, Jinan 250014, China
  • Received:2021-07-06 Revised:2021-09-08 Online:2022-11-25 Published:2022-12-23
  • Contact: LI Yuanxin,Email:yxinly@126.com
  • Supported by:
    This work was supported in part by the Funds of National Science of China under Grant Nos. 61973146 and 61773188, and in part by the Distinguished Young Scientific Research Talents Plan in Liaoning Province under Grant Nos. XLYC1907077 and JQL201915402.

XIN Chun, LI Yuanxin, NIU Ben. Event-Triggered Adaptive Fuzzy Finite Time Control of Fractional-Order Non-Strict Feedback Nonlinear Systems[J]. Journal of Systems Science and Complexity, 2022, 35(6): 2166-2180.

In this article, the problem of event-triggered adaptive fuzzy finite time control of non-strict feedback fractional order nonlinear systems is investigated. By using the property of fuzzy basis function, the obstacle caused by algebraic loop problems is successfully circumvented. Moreover, a new adaptive event-triggered scheme is designed under the unified framework of backstepping control method, which can largely reduce the amount of communications. The stability of the closed-loop system is ensured through fractional Lyapunov stability analysis. Finally, the effectiveness of the proposed scheme is verified by simulation examples.
[1] Monje C A, Chen Y Q, Vinagre B M, et al., Fractional-Order Systems and Controls: Fundamentals and Applications, Springer, London, 2010.
[2] Wang L X, Stable adaptive fuzzy control of nonlinear systems, IEEE Transactions on Fuzzy Systems, 1993, 12: 46–155.
[3] He W, Chen Y, and Yin Z, Adaptive neural network control of an uncertain robot with full-state constraints, IEEE Transactions on Cybernetics, 2015, 46(3): 620–629.
[4] Wang F, Liu Z, and Lai G, Fuzzy adaptive control of nonlinear uncertain plants with unknown dead zone output, Fuzzy Sets and Systems, 2015, 263: 27–48.
[5] Wang M, Chen B, Liu X, et al., Adaptive fuzzy tracking control for a class of perturbed strictfeedback nonlinear time-delay systems, Fuzzy Sets and Systems, 2008, 159(8): 949–967.
[6] Chen M, Ge S S, and Ren B, Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints, Automatica, 2011, 47(3): 452–465.
[7] Muhammadhaji A and Teng Z, General decay synchronization for recurrent neural networks with mixed time delays, Journal of Systems Science and Complexity, 2020, 33(3): 672–684.
[8] Chaouki A, and El Abed A, Finite-time and fixed-time synchronization of inertial neural networks with mixed delays, Journal of Systems Science and Complexity, 2021, 34(1): 206–235.
[9] Wei Y, Chen Y, Liang S, et al., A novel algorithm on adaptive backstepping control of fractional order systems, Neurocomputing, 2015, 165: 395–402.
[10] Wei Y, Peter W T, Yao Z, et al., Adaptive backstepping output feedback control for a class of nonlinear fractional order systems, Nonlinear Dynamics, 2016, 86(2): 1047–1056.
[11] Liu H, Li S, Cao J, et al., Adaptive fuzzy prescribed performance controller design for a class of uncertain fractional-order nonlinear systems with external disturbances, Neurocomputing, 2017, 219: 422–430.
[12] Liu H, Li S, Wang H, et al., Adaptive fuzzy control for a class of unknown fractional-order neural networks subject to input nonlinearities and dead-zones, Information Sciences, 2018, 454: 30–45.
[13] Song S, Park J H, Zhang B, et al., Observer-based adaptive hybrid fuzzy resilient control for fractional-order nonlinear systems with time-varying delays and actuator failures, IEEE Transactions on Fuzzy Systems, 2021, 29(3): 471–485.
[14] Song S, Zhang B, Song X, et al., Neuro-fuzzy-based adaptive dynamic surface control for fractional-order nonlinear strict-feedback systems with input constraint, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2019, 51(6): 3575–3586.
[15] Liu H, Pan Y, and Cao J, Composite learning adaptive dynamic surface control of fractional-order nonlinear systems, IEEE Transactions on Cybernetics, 2019, 50(6): 2557–2567.
[16] Song S, Park J H, Zhang B, et al., Adaptive command filtered neuro-fuzzy control design for fractional-order nonlinear systems with unknown control directions and input quantization, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(11): 7238–7249.
[17] Ma Z and Ma H, Adaptive fuzzy backstepping dynamic surface control of strict-feedback fractional-order uncertain nonlinear systems, IEEE Transactions on Fuzzy Systems, 2019, 28(1): 122–133.
[18] Li Y X, Wang Q Y, and Tong S, Fuzzy adaptive fault-tolerant control of fractional-order nonlinear systems, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2021, 51(3): 1372– 1379.
[19] Liu H, Pan Y, Cao J, et al. Adaptive neural network backstepping control of fractional-order nonlinear systems with actuator faults, IEEE Transactions on Neural Networks and Learning Systems, 2020, 31(12): 5166–5177.
[20] Ma Z and Ma H, Reduced-order observer-based adaptive backstepping control for fractional-order uncertain nonlinear systems, IEEE Transactions on Fuzzy Systems, 2019, 28(12): 3287–3301.
[21] Chen B, Liu X P, Ge S S, et al., Adaptive fuzzy control of a class of nonlinear systems by fuzzy approximation approach, IEEE Transactions on Fuzzy Systems, 2012, 20(6): 1012–1021.
[22] Wang H, Liu X, Liu K, et al., Approximation-based adaptive fuzzy tracking control for a class of nonstrict-feedback stochastic nonlinear time-delay systems, IEEE Transactions on Fuzzy systems, 2014, 23(5): 1746–1760.
[23] Li Y, Liu L, and Feng G, Robust adaptive output feedback control to a class of non-triangular stochastic nonlinear systems, Automatica, 2018, 89: 325–332.
[24] Chen B, Zhang H, and Lin C, Observer-based adaptive neural network control for nonlinear systems in nonstrict-feedback form, IEEE Transactions on Neural Networks and Learning Systems, 2015, 27(1): 89–98.
[25] Mu X and Liu H, Stabilization for a class of large-scale stochastic nonlinear systems with decentralized controller design, Journal of Systems Science and Complexity, 2007, 20(1): 127–134.
[26] Tong S, Min X, and Li Y, Observer-based adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown control gain functions, IEEE Transactions on Cybernetics, 2020, 50(9): 3903–3913.
[27] Tabuada P, Event-triggered real-time scheduling of stabilizing control tasks, IEEE Transactions on Automatic Control, 2007, 52(9): 1680–1685.
[28] Liu T and Jiang Z P, Event-based control of nonlinear systems with partial state and output feedback, Automatica, 2015, 53: 10–22.
[29] Heemels W P M H, Donkers M C F, and Teel A R, Periodic event-triggered control for linear systems, IEEE Transactions on Automatic Control, 2012, 58(4): 847–861.
[30] Postoyan R, Tabuada P, Nesic D, et al., A framework for the event-triggered stabilization of nonlinear systems, IEEE Transactions on Automatic Control, 2014, 60(4): 982–996.
[31] Zhang J, Liu L, Li S, et al., Event-triggered L1-gain control of nonlinear positive switched systems, Journal of Systems Science and Complexity, 2021, 34(3): 873–898.
[32] Sun Y, Hu J, and Liu J, Periodic event-triggered control of flywheel energy storage matrix systems for wind farms, IET Control Theory & Applications, 2020, 14(11): 1467–1477.
[33] Hu J, Geng J, and Zhu H, An observer-based consensus tracking control and application to eventtriggered tracking, Communications in Nonlinear Science and Numerical Simulation, 2015, 20(2): 559–570.
[34] Xing L, Wen C, Liu Z, et al., Event-triggered adaptive control for a class of uncertain nonlinear systems, IEEE Transactions on Automatic Control, 2016, 62(4): 2071–2076.
[35] Xing L, Wen C, Liu Z, et al., Event-triggered output feedback control for a class of uncertain nonlinear systems, IEEE Transactions on Automatic Control, 2018, 64(1): 290–297.
[36] Li Y X and Yang G H, Model-based adaptive event-triggered control of strict-feedback nonlinear systems, IEEE Transactions on Neural Networks and Learning Systems, 2017, 29(4): 1033–1045.
[37] Li Y X and Yang G H, Event-triggered adaptive backstepping control for parametric strictfeedback nonlinear systems, International Journal of Robust and Nonlinear Control, 2018, 28(3): 976–1000.
[38] Qiu J, Sun K, Wang T, et al., Observer-based fuzzy adaptive event-triggered control for purefeedback nonlinear systems with prescribed performance, IEEE Transactions on Fuzzy Systems, 2019, 27(11): 2152–2162.
[39] Li H, Zhang Z, Yan H, et al., Adaptive event-triggered fuzzy control for uncertain active suspension systems, IEEE Transactions on Cybernetics, 2018, 49(12): 4388–4397.
[40] Wang J, Liu Z, Zhang Y, et al., Neural adaptive event-triggered control for nonlinear uncertain stochastic systems with unknown hysteresis, IEEE Transactions on Neural Networks and Learning Systems, 2019, 30(11): 3300–3312.
[41] Jia T, Pan Y, Liang H, et al., Event-based adaptive fixed-time fuzzy control for active vehicle suspension systems with time-varying displacement constraint, IEEE Transactions on Fuzzy Systems, 2021, DOI: 10.1109/TFUZZ.2021.3075490.
[42] Hong Y and Jiang Z P, Finite-time stabilization of nonlinear systems with parametric and dynamic uncertainties, IEEE Transactions on Automatic Control, 2006, 51(12): 1950–1956.
[43] Huang X, Lin W, and Yang B, Global finite-time stabilization of a class of uncertain nonlinear systems, Automatica, 2005, 41(5): 881–888.
[44] Wu Y, Hu J, Xiang L, et al., Finite-time output regulation of linear heterogeneous multi-agent systems, IEEE Transactions on Circuits and Systems II: Express Briefs, 2021, DOI: 10.1109/TCSII.2021.3098095.
[45] Li Y X, Finite time command filtered adaptive fault tolerant control for a class of uncertain nonlinear systems, Automatica, 2019, 106: 117–123.
[46] Gong P, Lan W, and Han Q L, Robust adaptive fault-tolerant consensus control for uncertain nonlinear fractional-order multi-agent systems with directed topologies, Automatica, 2020, 117: 109011.
[47] Podlubny I, Fractional Differential Equations: An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Elsevier, Amsterdam, Holland, 1998.
[48] Zhang Z, Park J H, Shao H, et al., Exact tracking control of uncertain non-linear systems with additive disturbance, IET Control Theory & Applications, 2015, 9(5): 736–744.
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