Adaptive Asymptotic Tracking Control for Stochastic Nonlinear Systems with Unknown Backlash-Like Hysteresis

doi:10.1007/s11424-022-1111-y

Journal of Systems Science and Complexity ›› 2022, Vol. 35 ›› Issue (5): 1824-1838.DOI: 10.1007/s11424-022-1111-y

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Adaptive Asymptotic Tracking Control for Stochastic Nonlinear Systems with Unknown Backlash-Like Hysteresis

WANG Le¹, SUN Wei¹, WU Yuqiang²

1. School of Mathematics Science, Liaocheng University, Liaocheng 252000, China;
2. School of Engineering, Qufu Normal University, Rizhao 276826, China

Received:2021-04-11 Revised:2021-07-05 Online:2022-10-25 Published:2022-10-12
Supported by:
This research was supported in part by the Natural Science Foundation of Shandong Province for Key Projects under Grant No.ZR2020KA010;in part by the National Natural Science Foundation of China under Grant No.62073187;in part by the Major Scientific and Technological Innovation Project in Shandong Province under Grant No.2019JZZY011111,and "Guangyue Young Scholar Innovation Team" of Liaocheng University under Grant No.LCUGYTD2022-01.

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WANG Le, SUN Wei, WU Yuqiang. Adaptive Asymptotic Tracking Control for Stochastic Nonlinear Systems with Unknown Backlash-Like Hysteresis[J]. Journal of Systems Science and Complexity, 2022, 35(5): 1824-1838.

In this study,an adaptive asymptotic tracking control problem is considered for stochastic nonlinear systems with unknown backlash-like hysteresis.By utilizing backstepping technology and bound estimation approach,an adaptive asymptotic tracking control scheme is designed,where fuzzy systems are applied to approximate unknown function terms,the effect of hysteresis and stochastic disturbances is compensated appropriately.The proposed scheme ensures that the tracking error can asymptotically converge to zero in probability and all signals of the closed-loop system are bounded almost surely.Finally,the effectiveness of the control scheme is verified by giving a simulation example.

Key words: Adaptive fuzzy control, asymptotic tracking, stochastic nonlinear systems, unknown backlash-like hysteresis

[1] Zou A M, Hou Z G, and Tan M, Adaptive control of a class of nonlinear pure-feedback systems using fuzzy backstepping approach, IEEE Transaction on Fuzzy Systems, 2008, 16(4):886-897.
[2] Li Y X, Finite time command filtered adaptive fault tolerant control for a class of uncertain nonlinear systems, Automatic, 2019, 106:117-123.
[3] Zhao K, Song Y D, Chen C L P, et al., Control of nonlinear systems under dynamic constraints:A unified barrier function-based approach, Automatic, DOI:10.1016/j.automatica.2020.109102.
[4] Yang H Y, Jiang Y C, and Yin S, Adaptive fuzzy fault-tolerant control for markov jump systems with additive and multiplicative actuator faults, IEEE Transaction on Fuzzy Systems, 2021, 29(4):772-785.
[5] Tong S C, Ming X, and Li Y X, 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.
[6] Wang L J, Basin M V, Li H Y, et al., Observer-based composite adaptive fuzzy control for nonstrictfeedback systems with actuator failures, IEEE Transactions on Fuzzy Systems, 2018, 26(4):2336-2347.
[7] Li R C and Zhang X F, Adaptive sliding mode observer design for a class of T-S fuzzy descriptor fractional order systems, IEEE Transactions on Fuzzy Systems, 2020, 28(9):1951-1960.
[8] Liu C X, Wen G L, Zhao Z J, et al., Neural-network-based lliding-mode control of an uncertain robot using dynamic model approximated switching gain, IEEE Transactions on Cybernetics, 2021, 51(5):2339-2346.
[9] Zhang Y Y and Li S, Adaptive near-optimal consensus of high-order nonlinear multi-agent systems with heterogeneity, Automatic, 2017, 85:426-432.
[10] Xie X P, Zhou Q, Yue D, et al., Relaxed control design of discrete-time takagi-sugeno fuzzy systems:An event-triggered real-time scheduling approach, IEEE Transactions on Systems, Man, and Cybernetics:Systems, 2018, 48(12):2251-2262.
[11] Lai G Y, Liu Z, Zhang Y, et al., Adaptive backstepping-based tracking control of a class of uncertain switched nonlinear systems, Automatic, 2019, 91:301-310.
[12] Xu N, Zao X D, Zong G D, et al., Adaptive control design for uncertain switched nonstrictfeedback nonlinear systems to achieve asymptotic tracking performance, Applied Mathematics and Computation, DOI:10.1016/j.amc.2021.126344.
[13] Guo J and Diao J D, Prediction-based event-triggered identification of quantized input FIR systems with quantized output observations, Science China-Information Sciences, 2020, 63(1):136-147.
[14] Diao S Z, Sun W, Su S F, et al., Adaptive fuzzy event-triggered control for single-link flexiblejoint robots with actuator failures, IEEE Transactions on Cybernetics, DOI:10.1109/TCYB. 2021.3049536.
[15] Chen Z Y, Nu B, Zhao X D, et al., Model-based adaptive event-triggered control of nonlinear continuous-time systems, Applied Mathematics and Computation, DOI:10.1016/j.amc.2021. 126330.
[16] Huo X, Karimi R H, Zhao X D, et al., Adaptive-critic design for decentralized event-triggered control of constrained nonlinear interconnected systems within an identifier-critic framework, IEEE Transactions on Cybernetics, DOI:10.1109/TCYB.2020.3037321.
[17] Wang T, Qiu J B, Yin S, et al., Performance-based adaptive fuzzy tracking control for networked industrial processes, IEEE Transactions on Cybernetics, 2016, 46(8):1760-1770.
[18] Wu Z J, Yang J, and Shi P, Adaptive tracking for stochastic nonlinear systems with markovian switching, IEEE Transactions on Automatic Control, 2010, 55(9):2135-2141.
[19] Sun K K, Mou S S, Qiu J B, et al., Adaptive fuzzy control for nontriangular structural stochastic switched nonlinear systems with full state constraints, IEEE Transactions on Fuzzy Systems, 2019, 27(8):1587-1601.
[20] Yang Y, Miao S T, Yue D, et al., Adaptive neural containment seeking of stochastic nonlinear strict-feedback multi-agent systems, Neurocomputing, 2020, 400:393-400.
[21] Wang F, Wang J M, Wang K, et al., Adaptive backstepping sliding mode control of uncertain semi-strict nonlinear systems and application to permanent magnet synchronous motor, Journal of Systems Science and Complexity, 2021, 34(2):552-571.
[22] Fu X X, Kang Y, Li P F, et al., Control for a class of stochastic mechanical systems based on the discrete-time approximate observer, Journal of Systems Science and Complexity, 2019, 32(2):526-541.
[23] Chen C, Liu Z, Zhang Y, et al., Asymptotic fuzzy tracking control for a class of stochastic strictfeedback systems, IEEE Transactions on Fuzzy Systems, 2017, 25(3):556-568.
[24] Sui S, Chen C L P, and Tong S C, Fuzzy adaptive finite-time control design for nontriangular stochastic nonlinear systems, IEEE Transactions on Fuzzy Systems, 2019, 27(11):172-184.
[25] Li T S, Li Z F, Wang D, et al., Output-feedback adaptive neural control for stochastic nonlinear time-varying delay systems with unknown control directions, IEEE Transactions on Neural Networks and Learning Systems, 2015, 26(6):1188-1201.
[26] Wu L B and Yang G H, Adaptive output neural network control for a class of stochastic nonlinear systems with dead-zone nonlinearities, IEEE Transactions on Neural Networks and Learning Systems, 2017, 28(3):726-739.
[27] Li P P and Shen Y J, Adaptive sampled-data observer design for a class of nonlinear systems with unknown hysteresis, Journal of Systems Science and Complexity, 2020, 52(1):561-579.
[28] Shen F, Wang X J, and Yin X H, Adaptive output-feedback control for a class of stochastic nonlinear systems with unknown control directions and hysteresis input, International Journal of Systems Science, 2020, 52(3):657-670.
[29] Huang L T, Li Y M, and Tong S C, Fuzzy adaptive output feedback control for MIMO switched nontriangular structure nonlinear systems with unknown control directions, IEEE Transactions on Systems, Man, and Cybernetics:Systems, 2020, 50(2):550-564.
[30] Qiu J B, Sun K K, Rudas I J, et al., Command filter-based adaptive NN control for MIMO nonlinear systems with full-state constraints and actuator hysteresis, IEEE Transactions on Cybernetics, 2020, 50(7):2905-2915.
[31] Lu K X, Liu Z, Chen C L P, et al., Event-triggered neural control of nonlinear systems with rate-dependent hysteresis input based on a new filter, IEEE Transactions on Neural Networks and Learning Systems, 2020, 31(4):1270-1284.
[32] Li Y M, Tong S C, and Li T S, Adaptive fuzzy output feedback control of MIMO nonlinear uncertain systems with time-varying delays and unknown backlash-like hysteresis, Neurocomputing, 2012, 93:56-66.
[33] Wang J H, 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.
[34] Wang H Q, Chen B, Liu K F, et al., Adaptive neural tracking control for a class of nonstrictfeedback stochastic nonlinear systems with unknown backlash-like hysteresis, IEEE Transactions on Neural Networks and Learning Systems, 2014, 25(5):947-958.
[35] Li Y X and Tong S C, A bound estimation approach for adaptive fuzzy asymptotic tracking of uncertain stochastic nonlinear systems, IEEE Transactions on Cybernetics, DOI:10.1109/TCYB.2020.3030276.
[36] Su C Y, Stepanenko Y, Svoboda J, et al., Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis, IEEE Transactions on Automatic Control, 2000, 45(12):2427-2432.
[37] Li H Y, Zhao S Y, He W, et al., Adaptive finite-time tracking control of full state constrained nonlinear systems with dead-zone, Automatica, 2019, 100:99-107.
[38] Liu Y J, Lu S, Tong S C, et al., Adaptive control-based barrier Lyapunov functions for a class of stochastic nonlinear systems with full state constraints, Automatica, 2018, 87:83-93.
[39] Jin X and Xu J X, Iterative learning control for output-constrained systems with both parametric and nonparametric uncertainties, Automatica, 2013, 49(8):2508-2516.
[40] Sun W, Su S F, Wu Y Q, et al., Adaptive fuzzy control with high-order barrier Lyapunov functions for high-order uncertain nonlinear systems with full-state constraints, IEEE Transactions on Cybernetics, 2020, 50(8):3424-3432.
[41] Yu X and Xie X J, Output feedback regulation of stochastic nonlinear systems with stochastic iISS inverse dynamics, IEEE Transactions on Automatic Control, 2010, 55(2):304-320.

[1]	Yongli ZHANG，Jiayin WANG， Hongxing LI. STABILIZATION OF THE QUADRUPLE INVERTED PENDULUM BY VARIABLE UNIVERSE ADAPTIVE H∞ REGULATOR [J]. Journal of Systems Science and Complexity, 2012, 25(5): 856-872.
[2]	Xiaowu MU;Haijun LIU. STABILIZATION FOR A CLASS OF LARGE-SCALE STOCHASTIC NONLINEAR SYSTEMS WITH DECENTRALIZED CONTROLLER DESIGN [J]. Journal of Systems Science and Complexity, 2007, 20(1): 127-134.

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