Event-triggered adaptive prescribed-time control of a class of uncertain nonlinear systems with time-varying parameters and disturbances

Litong Zhou; Ruicheng Zhang; Lichao Feng; Weizheng Liang; Litong Zhou; Ruicheng Zhang; Lichao Feng; Weizheng Liang

doi:10.3934/era.2026306

Electronic Research Archive

2026, Volume 34, Issue 10: 7071-7095. doi: 10.3934/era.2026306

Previous Article Next Article

Research article Special Issues

Event-triggered adaptive prescribed-time control of a class of uncertain nonlinear systems with time-varying parameters and disturbances

1.
College of Electrical Engineering, North China University of Science and Technology, Tangshan 063210, China
2.
College of Sciences, North China University of Science and Technology, Tangshan 063210, China

Received: 05 June 2026 Revised: 29 July 2026 Accepted: 07 August 2026 Published: 17 August 2026

For a class of strict-feedback nonlinear systems involving unknown time-varying parameters and external disturbances, an event-triggered adaptive prescribed-time control method is proposed. First, a prescribed-time adjustment function containing only a single reciprocal term is introduced to unify the multi-stage high-order scaling in conventional prescribed-time backstepping into a single first-order scaling, thereby simplifying the structure of the prescribed-time scaling term and reducing the complexity of the recursive controller design. Second, an adaptive law is developed to adaptively compensate for the effects of unknown time-varying parametric uncertainties, while a radial basis function neural network (RBFNN) is embedded into the backstepping framework to achieve real-time approximation and compensation of external disturbances. Moreover, an event-triggered mechanism is incorporated to operate synchronously with the controller, guaranteeing prescribed-time stability and substantially reducing the number of control updates compared with periodic sampling, thus saving communication and computational resources. Finally, numerical simulations demonstrate that the proposed control strategy achieves prescribed-time convergence and post-prescribed-time practical boundedness, while maintaining satisfactory robustness with significantly fewer control updates.
- time-varying parameters,
- uncertain nonlinear systems,
- prescribed-time stability,
- adaptive backstepping control,
- event-triggered control,
- neural network control
Citation: Litong Zhou, Ruicheng Zhang, Lichao Feng, Weizheng Liang. Event-triggered adaptive prescribed-time control of a class of uncertain nonlinear systems with time-varying parameters and disturbances[J]. Electronic Research Archive, 2026, 34(10): 7071-7095. doi: 10.3934/era.2026306

Related Papers:

Abstract

For a class of strict-feedback nonlinear systems involving unknown time-varying parameters and external disturbances, an event-triggered adaptive prescribed-time control method is proposed. First, a prescribed-time adjustment function containing only a single reciprocal term is introduced to unify the multi-stage high-order scaling in conventional prescribed-time backstepping into a single first-order scaling, thereby simplifying the structure of the prescribed-time scaling term and reducing the complexity of the recursive controller design. Second, an adaptive law is developed to adaptively compensate for the effects of unknown time-varying parametric uncertainties, while a radial basis function neural network (RBFNN) is embedded into the backstepping framework to achieve real-time approximation and compensation of external disturbances. Moreover, an event-triggered mechanism is incorporated to operate synchronously with the controller, guaranteeing prescribed-time stability and substantially reducing the number of control updates compared with periodic sampling, thus saving communication and computational resources. Finally, numerical simulations demonstrate that the proposed control strategy achieves prescribed-time convergence and post-prescribed-time practical boundedness, while maintaining satisfactory robustness with significantly fewer control updates.

References

[1]	W. M. Haddad, A. L'Afflitto, Finite-time stabilization and optimal feedback control, IEEE Trans. Autom. Control, 61 (2016), 1069–1074. https://doi.org/10.1109/TAC.2015.2454891 doi: 10.1109/TAC.2015.2454891
[2]	A. Polyakov, Nonlinear feedback design for fixed-time stabilization of linear control systems, IEEE Trans. Autom. Control, 57 (2012), 2106–2110. https://doi.org/10.1109/TAC.2011.2179869 doi: 10.1109/TAC.2011.2179869
[3]	Y. D. Song, Y. Wang, J. Holloway, M. Krstic, Time-varying feedback for regulation of normal-form nonlinear systems in prescribed finite time, Automatica, 83 (2017), 243–251. https://doi.org/10.1016/j.automatica.2017.06.008 doi: 10.1016/j.automatica.2017.06.008
[4]	Y. Wang, Y. Song, A general approach to precise tracking of nonlinear systems subject to non-vanishing uncertainties, Automatica, 106 (2019), 306–314. https://doi.org/10.1016/j.automatica.2019.05.008 doi: 10.1016/j.automatica.2019.05.008
[5]	F. Gao, Y. Wu, Z. Zhang, Global fixed-time stabilization of switched nonlinear systems: A time-varying scaling transformation approach, IEEE Trans. Circuits Syst. Ⅱ Express Briefs, 66 (2019), 1890–1894. https://doi.org/10.1109/TCSⅡ.2018.2890556 doi: 10.1109/TCSⅡ.2018.2890556
[6]	Y. D. Song, H. F. Ye, F. L. Lewis, Prescribed-time control and its latest developments, IEEE Trans. Syst. Man Cybern. : Syst., 53 (2023), 4102–4116. https://doi.org/10.1109/TSMC.2023.3240751 doi: 10.1109/TSMC.2023.3240751
[7]	B. Zhou, Y. Shi, Prescribed-time stabilization of a class of nonlinear systems by linear time-varying feedback, IEEE Trans. Autom. Control, 66 (2021), 6123–6130. https://doi.org/10.1109/TAC.2021.3061645 doi: 10.1109/TAC.2021.3061645
[8]	C. C. Hua, P. Ning, K. Li, Adaptive prescribed-time control for a class of uncertain nonlinear systems, IEEE Trans. Autom. Control, 67 (2022), 6159–6166. https://doi.org/10.1109/TAC.2021.3130883 doi: 10.1109/TAC.2021.3130883
[9]	P. J. Ning, C. C. Hua, K. Li, H. Li, A novel theorem for prescribed-time control of nonlinear uncertain time-delay systems, Automatica, 152 (2023), 111009. https://doi.org/10.1016/j.automatica.2023.111009 doi: 10.1016/j.automatica.2023.111009
[10]	B. Liu, J. Li, R. C. Ma, J. Fu, Adaptive prescribed-time tracking control for uncertain nonlinear systems with full state constraints, Int. J. Adapt. Control Signal Process., 38 (2024), 1262–1280. https://doi.org/10.1002/acs.3744 doi: 10.1002/acs.3744
[11]	Y. Zhang, M. Chadli, Z. Xiang, Prescribed-time adaptive fuzzy optimal control for nonlinear systems, IEEE Trans. Fuzzy Syst., 32 (2024), 2403–2412. https://doi.org/10.1109/TFUZZ.2024.3352590 doi: 10.1109/TFUZZ.2024.3352590
[12]	Y. Zhang, M. Chadli, Z. Xiang, Predefined-time adaptive fuzzy control for a class of nonlinear systems with output hysteresis, IEEE Trans. Fuzzy Syst., 31 (2023), 2522–2531. https://doi.org/10.1109/TFUZZ.2022.3228012 doi: 10.1109/TFUZZ.2022.3228012
[13]	L. C. Feng, M. Y. Dai, N. Ji, Y. L. Zhang, L. P. Du, Prescribed-time stabilization of nonlinear systems with uncertainties/disturbances by improved time-varying feedback control, AIMS Math., 9 (2024), 23859–23877. https://doi.org/10.3934/math.20241159 doi: 10.3934/math.20241159
[14]	C. C. Li, C. Y. Zhang, L. C. Feng, Z. H. Wu, Note on prescribed-time stability of impulsive piecewise-smooth differential systems and application in networks, Networks Heterogen. Media, 19 (2024), 970–991. https://doi.org/10.3934/nhm.2024043 doi: 10.3934/nhm.2024043
[15]	L. C. Feng, C. C. Li, M. Abdel-Aty, J. D. Cao, Prescribed-time stability of nonlinear impulsive piecewise systems and synchronization for dynamical networks, Qual. Theory Dyn. Syst., 24 (2025), 165. https://doi.org/10.1007/s12346-025-01302-1 doi: 10.1007/s12346-025-01302-1
[16]	F. L. Lewis, S. Jagannathan, A. Yesildirak, Neural Network Control of Robot Manipulators and Nonlinear Systems, London: Taylor & Francis, 1999.
[17]	M. Li, S. Li, C. K. Ahn, Z. Xiang, Adaptive fuzzy event-triggered command-filtered control for nonlinear time-delay systems, IEEE Trans. Fuzzy Syst., 30 (2022), 1025–1035. https://doi.org/10.1109/TFUZZ.2021.3052095 doi: 10.1109/TFUZZ.2021.3052095
[18]	S. Li, C. K. Ahn, J. Guo, Z. Xiang, Neural-network approximation-based adaptive periodic event-triggered output-feedback control of switched nonlinear systems, IEEE Trans. Cybern., 51 (2021), 4011–4020. https://doi.org/10.1109/TCYB.2020.3022270 doi: 10.1109/TCYB.2020.3022270
[19]	P. J. Ning, C. C. Hua, K. Li, R. Meng, Event-triggered control for nonlinear uncertain systems via a prescribed-time approach, IEEE Trans. Autom. Control, 68 (2023), 6975–6981. https://doi.org/10.1109/TAC.2023.3243863 doi: 10.1109/TAC.2023.3243863
[20]	P. J. Ning, C. C. Hua, K. Li, R. Meng, Event-triggered adaptive prescribed-time control for nonlinear systems with uncertain time-varying parameters, Automatica, 157 (2023), 111229. https://doi.org/10.1016/j.automatica.2023.111229 doi: 10.1016/j.automatica.2023.111229
[21]	W. Sun, J. Zhao, W. Sun, J. Xia, Z. Sun, Adaptive event-triggered global fast finite-time control for a class of uncertain nonlinear systems, Int. J. Robust Nonlinear Control, 30 (2020), 3773–3785. https://doi.org/10.1002/rnc.4966 doi: 10.1002/rnc.4966
[22]	K. Li, C. C. Hua, X. You, X. Guan, Output feedback-based consensus control for nonlinear time-delay multiagent systems, Automatica, 111 (2020), 108669. https://doi.org/10.1016/j.automatica.2019.108669 doi: 10.1016/j.automatica.2019.108669
[23]	J. Du, X. Hu, M. Krstic, Y. Sun, Robust dynamic positioning of ships with disturbances under input saturation, Automatica, 73 (2016), 207–214. https://doi.org/10.1016/j.automatica.2016.06.020 doi: 10.1016/j.automatica.2016.06.020
[24]	L. C. Feng, C. L. Zhang, M. Abdel-Aty, J. D. Cao, F. E. Alsaadi, Prescribed-time trajectory tracking control for a class of nonlinear system, Electron. Res. Arch., 32 (2024), 6535–6552. https://doi.org/10.3934/era.2024305 doi: 10.3934/era.2024305
[25]	L. T. Zhou, L. C. Feng, N. Ji, R. C. Zhang, Backstepping-sliding-mode-based prescribed-time control for a class of nonlinear systems with disturbances, AIMS Math., 10 (2025), 22791–22816. https://doi.org/10.3934/math.20251013 doi: 10.3934/math.20251013
[26]	Y. W. Wang, Y. Lei, T. Bian, Z. H. Guan, Distributed control of nonlinear multiagent systems with unknown and nonidentical control directions via event-triggered communication, IEEE Trans. Cybern., 50 (2020), 1820–1832. https://doi.org/10.1109/TCYB.2019.2908874 doi: 10.1109/TCYB.2019.2908874
[27]	Z. Li, J. Yan, W. Yu, J. Qiu, Adaptive event-triggered control for unknown second-order nonlinear multiagent systems, IEEE Trans. Cybern., 51 (2021), 6131–6140. https://doi.org/10.1109/TCYB.2020.2964430 doi: 10.1109/TCYB.2020.2964430
[28]	J. X. Zhang, G. H. Yang, Event-triggered prescribed performance control for a class of unknown nonlinear systems, IEEE Trans. Syst., Man, Cybern. : Syst., 51 (2021), 6576–6586. https://doi.org/10.1109/TSMC.2019.2963215 doi: 10.1109/TSMC.2019.2963215
[29]	J. X. Zhang, T. Chai, Proportional-integral funnel control of unknown lower-triangular nonlinear systems, IEEE Trans. Autom. Control, 69 (2024), 1921–1927. https://doi.org/10.1109/TAC.2023.3330900 doi: 10.1109/TAC.2023.3330900

Reader Comments

Your name:*

Email:*
© 2026 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)