Adaptive control with time-varying disturbance observation and saturation compensation based on event-triggered mechanism and phased error constraints

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  • (1.School of Navigation and Shipping, Shandong Jiaotong University, Weihai 264200, China; 2.Navigation College, Dalian Maritime University, Dalian 116026, China)

Online published: 2026-07-13

Abstract

Aiming at the robust control problem of control systems under unknown nonlinear dynamics, time-varying disturbances, input saturation and Gaussian noise, an adaptive sliding mode control method deeply integrating event-triggered mechanism and dynamic coupling strategy was proposed. Firstly, the dynamic surface control (DSC) technique combined with radial basis function neural network (RBFNN) was adopted to approximate the unknown dynamics of the system, and a staged error constraint strategy was designed to achieve dynamic collaborative optimization of convergence speed and steady-state accuracy. Secondly, a time-varying disturbance observer was introduced to estimate disturbances such as wave disturbances online, and an intelligent smoothing processing mechanism driven by Gaussian error function was used to handle the problem of asymmetric input saturation. Furthermore, by combining the event-triggered mechanism, the adaptive dynamic threshold control was used to reduce the control update frequency and decrease the consumption of computing resources. Based on the Lyapunov stability theory, it is proved that all signals of the closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error can converge to a preset neighborhood. Simulation results show that the proposed method significantly improves the system’s anti-interference ability and control efficiency, providing theoretical support for the application of related control theories in engineering practice.

Cite this article

LI Xinyi, HU Yancai, BAI Weiwei .

Adaptive control with time-varying disturbance observation and saturation compensation based on event-triggered mechanism and phased error constraints
[J]. Journal of Dalian Maritime University, 2026 , 52(2) : 46 -56 . DOI: 10.16411/j.cnki.issn1006-7736.2026.02.005

References

[1]ZHAO C, WANG D Y, XUE W C. Beyond linear limits: design of robust nonlinear PID control[J]. Automatica, 2025, 173:112075. doi:10.1016/j.automatica.2024.112075.
[2]FOSSEN T I. Handbook of marine craft hydrodynamics and motion control[M].[S.l.]: John Wiley & Sons Ltd,2021. 
[3]LIU S, LI P W. A novel chattering-free PI sliding mode control for a class of nonlinear underactuated systems[J]. International Journal of Modelling, Identification and Control, 2019, 32(1): 54. doi:10.1504/IJMIC.2019.101965.
[4]YANG B, TAO Y, SHU H C, et al. Robust sliding-mode control of wind energy conversion systems for optimal power extraction via nonlinear perturbation observers[J].Applied Energy,2017: 210711-210723.doi:10.1016/j.apenergy.2017.08.027.
[5]CHEN C L P, WEN G X, LIU Y J, et al. Observer-based adaptive backstepping consensus tracking control for high-order nonlinear semi-strict-feedback multiagent systems[J]. IEEE Transactions on Cybernetics, 2017, 46(7): 1591-1601. doi:10.1109/TCYB.2015.2452217.
[6]LI K, LI Y M. Adaptive neural network finite-time dynamic surface control for nonlinear systems[J]. IEEE Transactions on Neural Networks and Learning Systems, 2020,32(12): 5688-5697. doi:10.1109/TNNLS.2020.3027335.
[7]WANG J, WANG D, SHEN Y H. Composite antidisturbance H∞ control for hidden Markov jump systems with multi-sensor against replay attacks[J]. IEEE Transactions on Automatic Control, 2024, 69(3): 1760-1766.
[8]CHEN W H, YANG J, GUO L, et al. Disturbance-observer-based control and related methods—an overview[J]. IEEE Transactions on Industrial Electronics, 2016, 63(2): 1083-1095. doi:10.1109/TIE.2015.2478397.
[9]QIU J B, GAO H J, DING S X. Recent advances on fuzzy model based nonlinear networked control systems: a survey[J]. IEEE Transactions on Industrial Electronics, 2016, 63(2): 1207-1217. doi:10.1109/TIE.2015.2504351.
[10]CHEN Q, LIU G H, ZHAO W X, et al. Asymmetrical SVPWM fault-tolerant control of five phase PM brushless motors[J].IEEE Transactions on Energy Conversion, 2016, 32(1): 12-22. doi:10.1109/TEC.2016.2611620.
[11]YANG X, PAN Y, SUN J, et al. Optimized adaptive event-triggered tracking control for multi-agent systems with full-state constraints[J]. International Journal of Robust and Nonlinear Control, 2022, 32: 10101-10124. doi:10.1002/rnc.6378.
[12]MADEIRA D D S, CORREIA W B. Data-driven saturated state feedback design for polynomial systems using noisy data[J]. IEEE Transactions on Automatic Control, 2024,69(11):7932-7939. doi:10.1109/TAC.2024.3402499.
[13]GE Q B, BAI X F, ZENG P L. Gaussian-Cauchy mixture kernel function based maximum correntropy criterion Kalman filter for linear non-Gaussian systems[J]. IEEE Transactions on Signal Processing, 2025,73:158-172. doi:10.1109/TSP.2024.3479723.
[14]XIA X N, LI C, ZHANG T P, et al. Finite-time optimal control for uncertain strict-feedback nonlinear systems with input saturation and output constraints[J]. International Journal of Adaptive Control and Signal Processing,2023,38(2):580-603. doi:10.1002/acs.3714.
[15]SUN Z Y, ZHOU C, WEN C Y, et al. Adaptive event-triggered prescribed time stabilization of uncertain nonlinear systems with asymmetric time-varying output constraint[J].IEEE Transactions on Automatic Control, 2024,69(8):5454-5461.doi:10.1109/TAC.2024.3361803.
[16]HE X, WANG Z, GAO C,et al. Consensus control for multiagent systems under asymmetric actuator saturations with applications to mobile train lifting jack systems[J].IEEE Transactions on Industrial Informatics, 2023, 19(10): 10224-10232. doi:10.1109/TII.2022.3229138.
[17]KOODZIEJ R, HOFFMANN P. Determination of propeller-rudder-hull interaction coefficients in ship manoeuvring prediction[J].Polish Maritime Research, 2024, 31(3): 15-24. doi:10.2478/POMR-2024-0032.
[18]FENG Z X, WANG H B, ZHANG J Y, et al. Dynamics of wave powered boat considering the heave and pitch motion excited by waves[J]. Ocean Engineering, 2025, 335: 121541.doi:10.1016/J.OCEANENG.2025.121541.
[19]CHANDRA A D, ANANTHA V S, JAGADEESH K. Steering model identification and control design of autonomous ship: a complete experimental study[J]. Ships and Offshore Structures, 2022, 17(5): 992-1004. doi:10.1080/17445302.2021.1889193.
[20]LI Y, TONG S, LI T. Hybrid fuzzy adaptive output feedback control design for uncertain MIMO nonlinear systems with time-varying delays and input saturation[J]. IEEE Transactions on Fuzzy Systems, 2016, 24(4): 841-853. doi:10.1109/TFUZZ.2015.2486811.
[21]ZHANG K, REN Y F, ZHAO J M, et al. Fixed-time active disturbance rejection control scheme for hybrid energy storage system based on cascaded extended state observer[J]. Energies, 2025, 18(22): 5917. doi:10.3390/EN18225917.
[22]HOSSEINABADI A P, ABADI S S A, MEKHILEF S. Fuzzy adaptive finite-time sliding mode controller for trajectory tracking of ship course systems with mismatched uncertainties[J]. International Journal of Automation and Control, 2022, 16(3-4): 255-271. doi:10.1504/IJAAC.2022.122596.
[23]ZHOU Z, YU H Y, YANG Y. Distributed model predictive formation control with event-triggered mechanism and on-demand addition of collision avoidance constraints[J].Intelligent Service Robotics, 2025, 19(1): 12. doi:10.1007/S11370-025-00659-1.
[24]ZHANG F L, WANG T, ZHANG L, et al. Sliding-mode control based on prescribed performance function and its application to a SEA-based lower limb exoskeleton[J]. Frontiers in Robotics and AI, 2025,12. doi:10.3389/FROBT.2025.1534040.
[25]WU S C, LI X D. Finite-time synchronization of complex dynamical networks with input saturation[J]. IEEE Transactions on Cybernetics, 2024, 54(1): 364-372. doi:10.1109/TCYB.2022.3228325.
[26]LIU G P, ZHANG Y, HUA C C, et al. Adaptive fuzzy tracking control for nonlinear time-delay systems with performance constrained by deferred monotone tube boundaries[J]. IEEE Transactions on Fuzzy Systems, 2024,32(11):6136-6148. doi:10.1109/TFUZZ.2024.3441614.
[27]刘金华, 王远, 张智轩, 等. 基于RBF网络的四旋翼无人机姿态鲁棒自适应反步滑模控制[J]. 江苏大学学报(自然科学版), 2025, 46(1): 36-42.LIU J H, WANG Y, ZHANG Z X, et al. Robust adaptive backstepping sliding mode control of quadcopter UAV based on RBF network[J]. Journal of Jiangsu University (Natural Science Edition), 2025, 46(1): 36-42. (in Chinese)
[28]宁君, 刘子涵, 李伟, 等. 自适应量化神经网络滑模无人船编队控制[J]. 上海海事大学学报, 2024, 45(2): 7-13.NING J, LIU Z H, LI W, et al. Adaptive quantized neural network sliding mode control for unmanned surface vehicle formation[J]. Journal of Shanghai Maritime University, 2024, 45(2): 7-13. (in Chinese)
[29]宁君, 王二月, 李铁山, 等. 基于事件触发的船舶编队有限时间控制[J]. 船舶工程, 2023, 45(6): 130-139. doi:10.13788/j.cnki.cbgc.2023.06.19.NING J, WANG E Y, LI T S, et al. Event-triggered finite-time control for ship formation[J]. Ship Engineering, 2023, 45(6): 130-139. (in Chinese)
[30]TRAN T T, GE S S Z, HE W. Adaptive control for a robotic manipulator with uncertainties and input saturations[C]// IEEE International Conference on Mechatronics & Automation. Beijing:IEEE, 2015. doi:10.1109/ICMA.2015.7237711.
[31]DU H, YU X, CHEN M Z Q, et al. Chattering free discrete time sliding mode control[J]. Automatica, 2016, 68: 87-91. doi:10.1016/j.automatica.2016.01.047.
[32]苏文学, 孟祥飞, 张强. 输入饱和约束下自适应RBF神经网络非线性反馈船舶航向控制[J]. 上海海事大学学报, 2024, 45(2): 14-19. SU W X, MENG X F, ZHANG Q. Nonlinear feedback ship heading control based on adaptive RBF neural network under input saturation constraints[J]. Journal of Shanghai Maritime University, 2024, 45(2): 14-19. (in Chinese)
[33]LIU T F, JIANG Z P. A small-gain approach to robust event-triggered control of nonlinear systems[J].IEEE Transactions on Automatic Control, 2015, 60(8):2072-2085. doi:10.1109/TAC.2015.2396645.
[34]焦建芳, 包端华, 胡正中. 基于神经网络滑模控制的船舶事件触发预设性能跟踪控制[J]. 控制工程, 2025, 32(2): 193-200.JIAO J F, BAO R H, HU Z Z. Neural network sliding mode control-based event-triggered prescribed performance tracking control for ships[J]. Control Engineering, 2025, 32(2): 193-200. (in Chinese)
[35] CHEN H, LIU Y J, LIU L, et al. Anti-saturation based adaptivesliding-mode control for active suspension systems with time-varying vertical displacement and speed constraints[J]. IEEE Transactions on Cybernetics, 2021, 52(7): 6244-6254. doi:10.1109/TCYB.2020.3042613.
[36]GARONE E, DI CAIRANO S, KOLMANOVSKY I. Reference and command governors for systems with constraints: a survey on theory and applications[J]. Automatica, 2017, 75: 306-328. doi:10.1016/j.automatica.2016.08.013.
[37]李俊方, 李铁山. 考虑输入饱和的直接自适应神经网络跟踪控制[J]. 应用科学学报, 2013, 31(3): 294-302.LI J F, LI T S. Direct adaptive neural network tracking control considering input saturation[J]. Journal of Applied Science, 2013, 31(3): 294-302. (in Chinese)
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