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

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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.

Keywords

time-varying parameters / uncertain nonlinear systems / prescribed-time stability / adaptive backstepping control / event-triggered control / neural network control

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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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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