Prescribed-time control for impulsive systems with uncertainties via adaptive control

Chenrong Niu; Chunyan Zhang; Liping Du; Lichao Feng; Chenrong Niu; Chunyan Zhang; Liping Du; Lichao Feng

doi:10.3934/nhm.2025040

Networks and Heterogeneous Media

2025, Volume 20, Issue 3: 938-954. doi: 10.3934/nhm.2025040

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Research article

Prescribed-time control for impulsive systems with uncertainties via adaptive control

1.
College of Science, North China University of Science and Technology, Tangshan 063210, China
2.
Hebei Key Laboratory of Data Science and Application, North China University of Science and Technology, Tangshan 063210, China

Received: 15 July 2025 Revised: 15 August 2025 Accepted: 28 August 2025 Published: 05 September 2025

To present, there has been much research on prescribed-time stability (PTS) of uncertain systems, but the significant impulse factor has not been considered. Therefore, in this paper, the stability control problem of a class of impulsive systems with uncertainties within the prescribed time was studied by the Lyapunov functional approach. The comparison lemma was utilized and iteration was carried out for each impulsive interval to prove the PTS theorem for general impulsive systems with uncertainties. In addition, a time-varying adaptive controller in combination with the backstepping method was constructed for PTS of special impulsive strict-feedback systems with uncertainties, breaking through the dependence of traditional methods on uncertain parameters. Finally, a simulation example was used to verify the effectiveness and feasibility of the proposed method.
- impulsive systems,
- prescribed-time stability,
- adaptive control,
- backstepping method,
- Lyapunov functional approach
Citation: Chenrong Niu, Chunyan Zhang, Liping Du, Lichao Feng. Prescribed-time control for impulsive systems with uncertainties via adaptive control[J]. Networks and Heterogeneous Media, 2025, 20(3): 938-954. doi: 10.3934/nhm.2025040

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Abstract

To present, there has been much research on prescribed-time stability (PTS) of uncertain systems, but the significant impulse factor has not been considered. Therefore, in this paper, the stability control problem of a class of impulsive systems with uncertainties within the prescribed time was studied by the Lyapunov functional approach. The comparison lemma was utilized and iteration was carried out for each impulsive interval to prove the PTS theorem for general impulsive systems with uncertainties. In addition, a time-varying adaptive controller in combination with the backstepping method was constructed for PTS of special impulsive strict-feedback systems with uncertainties, breaking through the dependence of traditional methods on uncertain parameters. Finally, a simulation example was used to verify the effectiveness and feasibility of the proposed method.

References

[1]	S. P. Bhat, D. S. Bernstein, Finite-time stability of continuous autonomous systems, SIAM J. Control Optim., 38 (2000), 751–766. https://doi.org/10.1137/S0363012997321358 doi: 10.1137/S0363012997321358
[2]	Y. Guo, B. Huang, S. M. Song, A. J. Li, C. Q. Wang, Robust saturated finite-time attitude control for spacecraft using integral sliding mode, J. Guid. Control Dyn., 42 (2019), 440–446. https://doi.org/10.2514/1.G003520 doi: 10.2514/1.G003520
[3]	Z. Y. Sun, M. M. Yun, T. Li, A new approach to fast global finite-time stabilization of high-order nonlinear system, Automatica, 81 (2019), 455–463. https://doi.org/10.1016/j.automatica.2017.04.024 doi: 10.1016/j.automatica.2017.04.024
[4]	M. A. Z. Tajrishi, A. Akbarzadeh Kalat, Fast finite time fractional-order robust-adaptive sliding mode control of nonlinear systems with unknown dynamics, J. Comput. Appl. Math., 438 (2024), 115554. https://doi.org/10.1016/j.cam.2023.115554 doi: 10.1016/j.cam.2023.115554
[5]	C. C. Hua, Y. F. Li, X. P. Guan, Finite/fixed-time stabilization for nonlinear interconnected systems with dead-zone input, IEEE Trans. Autom. Control, 62 (2016), 2554–2560. https://doi.org/10.1109/TAC.2016.2600343 doi: 10.1109/TAC.2016.2600343
[6]	X. Y. Liu, D. W. C. Ho, Q. Song, J. D. Cao, Finite-/fixed-time robust stabilization of switched discontinuous systems with disturbances, Nonlinear Dyn., 90 (2017), 2057–2068. https://doi.org/10.1007/s11071-017-3782-9 doi: 10.1007/s11071-017-3782-9
[7]	H. Shen, X. Yu, H. C. Yan, J. H. Park, J. Wang, Robust fixed-time sliding mode attitude control for a 2-DOF helicopter subject to input saturation and prescribed performance, IEEE Trans. Transp. Electrif., 11 (2024), 1223–1233. https://doi.org/10.1109/TTE.2024.3402316 doi: 10.1109/TTE.2024.3402316
[8]	M. A. Jamal, R. Kumar, S. Mukhopadhyay, S. Das, Fixed-time stability of dynamical systems with impulsive effects, J. Franklin Inst., 359 (2022), 3164–3182. https://doi.org/10.1016/j.jfranklin.2022.02.016 doi: 10.1016/j.jfranklin.2022.02.016
[9]	Q. Lin, Y. Zhou, G. P. Jiang, S. Ge, S. Ye, Prescribed-time containment control based on distributed observer for multi-agent systems, Neurocomputing, 431 (2021), 69–77. https://doi.org/10.1016/j.neucom.2020.12.030 doi: 10.1016/j.neucom.2020.12.030
[10]	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 Heterog. Media, 10 (2024), 970–991. https://doi.org/10.3934/nhm.2024043 doi: 10.3934/nhm.2024043
[11]	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
[12]	H. Shen, W. Zhao, J. D. Cao, J. H. Park, J. Wang, Predefined-time event-triggered tracking control for nonlinear servo systems: A fuzzy weight-based reinforcement learning scheme, IEEE Trans. Fuzzy Syst., 32 (2024), 4557–4569. https://doi.org/10.1109/TFUZZ.2024.3403917 doi: 10.1109/TFUZZ.2024.3403917
[13]	A. Shakouri, N. Assadian, Prescribed-time control with linear decay for nonlinear systems, IEEE Control Syst. Lett., 6 (2021), 313–318. https://doi.org/10.1109/LCSYS.2021.3073346 doi: 10.1109/LCSYS.2021.3073346
[14]	L. Cui, N. Jin, Prescribed-time ESO-based prescribed-time control and its application to partial IGC design, Nonlinear Dyn., 106 (2021), 491–508. https://doi.org/10.21203/rs.3.rs-643681/v1 doi: 10.21203/rs.3.rs-643681/v1
[15]	X. Y. He, X. D. Li, S. J. Song, Prescribed-time stabilization of nonlinear systems via impulsive regulation, IEEE Trans. Syst. Man Cybern.: Syst., 53 (2022), 981–985. https://doi.org/10.1109/TSMC.2022.3188874 doi: 10.1109/TSMC.2022.3188874
[16]	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
[17]	K. K. Zhang, B. Zhou, G. R. Duan, Global prescribed-time output feedback control of a class of uncertain nonlinear systems by linear time-varying feedback, Automatica, 165 (2024), 111680. https://doi.org/10.1016/j.automatica.2024.111680 doi: 10.1016/j.automatica.2024.111680
[18]	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
[19]	C. C. Hua, P. J. 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
[20]	J. Wu, W. Wang, S. H. Ding, X. P. Xie, Y. Yi, Adaptive neural optimized control for uncertain strict-feedback systems with unknown control directions and pre-set performance, Commun. Nonlinear Sci. Numer. Simul., 126 (2023), 107506. https://doi.org/10.1016/j.cnsns.2023.107506 doi: 10.1016/j.cnsns.2023.107506
[21]	G. W. Zuo, Y. J. Wang, Adaptive prescribed finite time control for strict-feedback systems, IEEE Trans. Autom. Control, 68 (2022), 5729–5736. https://doi.org/10.1109/TAC.2022.3225465 doi: 10.1109/TAC.2022.3225465
[22]	B. Mao, X. Q. Xu, H. Liu, Y. H. Xu, J. H. Lu, Adaptive fuzzy tracking control with global prescribed-time prescribed performance for uncertain strict-feedback nonlinear systems, IEEE Trans. Cybern., 54 (2024), 5217–5230. https://doi.org/10.1109/TCYB.2024.3366177 doi: 10.1109/TCYB.2024.3366177
[23]	T. Wang, J. Wu, Y. J. Wang, M. Ma, Adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems with time-varying input delay and full state constraints, IEEE Trans. Fuzzy Syst., 28 (2019), 3432–3441. https://doi.org/10.1109/TFUZZ.2019.2952832 doi: 10.1109/TFUZZ.2019.2952832
[24]	T. Wang, N. Wang, J. B. Qiu, C. Buccella, C. Cecati, Adaptive event-triggered control of stochastic nonlinear systems with unknown dead zone, IEEE Trans. Fuzzy Syst., 31 (2022), 138–147. https://doi.org/10.1109/TFUZZ.2022.3183763 doi: 10.1109/TFUZZ.2022.3183763
[25]	B. Cui, Y. Q. Xia, K. Liu, G. H. Shen, Finite-time tracking control for a class of uncertain strict-feedback nonlinear systems with state constraints: a smooth control approach, IEEE Trans. Neural Networks Learn. Syst., 31 (2020), 4920–4932. https://doi.org/10.1109/TNNLS.2019.2959016 doi: 10.1109/TNNLS.2019.2959016
[26]	C. H. Zhang, L. Chang, L. T. Xing, X. F. Zhang, Fixed-time stabilization of a class of strict-feedback nonlinear systems via dynamic gain feedback control, IEEE/CAA J. Autom. Sinica, 10 (2023), 403–310. https://doi.org/10.1109/JAS.2023.123408 doi: 10.1109/JAS.2023.123408
[27]	H. Wang, W. Q. Li, M. Krstic, Prescribed-time stabilization and inverse optimality for strict-feedback nonlinear systems, Syst. Control Lett., 190 (2024), 105859. https://doi.org/10.1016/j.sysconle.2024.105859 doi: 10.1016/j.sysconle.2024.105859
[28]	W. H. Pan, W. J. Zhang, X. F. Zhang, Impulsive control for strict-feedback nonlinear systems based on discontinuous monitoring of system states, Nonlinear Dyn., 113 (2025), 13535–13551. https://doi.org/10.1007/s11071-025-11080-9 doi: 10.1007/s11071-025-11080-9
[29]	D. B. Fan, X. F. Zhang, W. H. Pan, Sliding mode control for strict-feedback nonlinear impulsive systems with matched disturbances, IEEE Trans. Circuits Syst. Ⅱ, 71 (2023), 787–791. https://doi.org/10.1109/TCSII.2023.3311920 doi: 10.1109/TCSII.2023.3311920
[30]	M. Bohner, G. Guseinov, Improper integrals on time scales, Dyn. Syst. Appl., 12 (2003), 45–66. https://doi.org/10.1007/s00454-002-0761-8 doi: 10.1007/s00454-002-0761-8
[31]	M. Kline, Calculus: An intuitive and physical approach, Courier Corp., (1998).
[32]	B. Zhou, Finite-time stability analysis and stabilization by bounded linear time-varying feedback, Automatica, 121 (2020), 109191. https://doi.org/10.1016/j.automatica.2020.109191 doi: 10.1016/j.automatica.2020.109191
[33]	A. A. Martynyuk, I. M. Stamova, V. A. Chernienko, Stability analysis of uncertain impulsive systems via fuzzy differential equations, Int. J. Syst. Sci., 51 (2020), 643–654. https://doi.org/10.1080/00207721.2020.1737265 doi: 10.1080/00207721.2020.1737265
[34]	G. Stamov, L. Stamova, Uncertain impulsive differential systems of fractional order: Almost periodic solutions, Int. J. Syst. Sci., 49 (2018), 631–638. https://doi.org/10.1080/00207721.2017.1416428 doi: 10.1080/00207721.2017.1416428
[35]	T. Wang, M. Ma, J. B. Qiu, H. J. Gao, Event-triggered adaptive fuzzy tracking control for pure-feedback stochastic nonlinear systems with multiple constraints, IEEE Trans. Fuzzy Syst., 29 (2020), 1496–1506. https://doi.org/10.1109/TFUZZ.2020.2979668 doi: 10.1109/TFUZZ.2020.2979668
[36]	H. Shen, C. J. Peng, H. C. Yan, S. Y. Xu, Data-driven near optimization for fast sampling singularly perturbed systems, IEEE Trans. Autom. Control., 69 (2024), 4689–4694. https://doi.org/10.1109/TAC.2024.3352703 doi: 10.1109/TAC.2024.3352703

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