Practical fixed-time consensus via intermittent dynamic event-based control

Nan Li; Na Li; Shuaibing Zhu; Jianwen Feng; Nan Li; Na Li; Shuaibing Zhu; Jianwen Feng

doi:10.3934/math.2026869

AIMS Mathematics

2026, Volume 11, Issue 7: 21441-21462. doi: 10.3934/math.2026869

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Practical fixed-time consensus via intermittent dynamic event-based control

1.
The School of Mathematics and Statistics, Henan University, Kaifeng 475004, China
2.
Henan Engineering Research Center for Industrial Internet of Things, Zhengzhou 450046, China
3.
The MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
4.
The School of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China

Received: 21 April 2026 Revised: 25 June 2026 Accepted: 01 July 2026 Published: 17 July 2026
MSC : 93C10, 93A16, 93C65, 93D40

This paper investigates the practical fixed-time consensus problem for multi-agent systems under intermittent dynamic event-triggered communication. First, unlike traditional fixed-time controllers that rely on linear and nonlinear power terms, the proposed controller incorporates an exponential function, resulting in a more concise and easily implementable control strategy. Next, two auxiliary functions are introduced to determine the working and resting intervals of intermittent control. Finally, we conduct a numerical simulation to validate the proposed method.
- intermittent control,
- dynamic event-triggered control,
- fixed-time consensus,
- Zeno behavior
Citation: Nan Li, Na Li, Shuaibing Zhu, Jianwen Feng. Practical fixed-time consensus via intermittent dynamic event-based control[J]. AIMS Mathematics, 2026, 11(7): 21441-21462. doi: 10.3934/math.2026869

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Abstract

This paper investigates the practical fixed-time consensus problem for multi-agent systems under intermittent dynamic event-triggered communication. First, unlike traditional fixed-time controllers that rely on linear and nonlinear power terms, the proposed controller incorporates an exponential function, resulting in a more concise and easily implementable control strategy. Next, two auxiliary functions are introduced to determine the working and resting intervals of intermittent control. Finally, we conduct a numerical simulation to validate the proposed method.

References

[1]	A. Abdessameud, A. Tayebi, Formation control of vtol unmanned aerial vehicles with communication delays, Automatica, 47 (2011), 2383–2394. https://doi.org/10.1016/j.automatica.2011.08.042} doi: 10.1016/j.automatica.2011.08.042
[2]	A. M. Zou, A. H. J. de Ruiter, K. D. Kumar, Distributed finite-time velocity-free attitude coordination control for spacecraft formations, Automatica, 67 (2016), 46–53. https://doi.org/10.1016/j.automatica.2015.12.029} doi: 10.1016/j.automatica.2015.12.029
[3]	M. N. Zhai, Q. Y. Sun, R. Wang, B. Y. Wang, J. Hu, H. G. Zhang, Distributed multiagent-based event-driven fault-tolerant control of islanded microgrids, IEEE T. Cybernetics, 53 (2023), 7251–7262. https://doi.org/10.1109/TCYB.2023.3266923 doi: 10.1109/TCYB.2023.3266923
[4]	M. N. Zhai, S. Liu, Q. Y. Sun, Fully distributed protocols for multiagent systems subject to actuator faults With intermittent communication, IEEE Syst. J., 19 (2025), 1181–1190. https://doi.org/10.1109/JSYST.2025.3624911 doi: 10.1109/JSYST.2025.3624911
[5]	X. W. Li, Y. Tang, H. R. Karimi, Consensus of multi-agent systems via fully distributed event-triggered control, Automatica, 116 (2020), 108898. https://doi.org/10.1016/j.automatica.2020.108898 doi: 10.1016/j.automatica.2020.108898
[6]	J. Liu, Y. B. Wu, L. Xue, J. Liu, A new intermittent control approach to practical fixed-time consensus with input delay, IEEE Trans. Circuits Syst. II-Express Briefs, 70 (2023), 2186–2190. https://doi.org/10.1109/TCSII.2022.3233794 doi: 10.1109/TCSII.2022.3233794
[7]	S. He, X. Liu, P. Lu, C. Du, H. Liu, Distributed finite-time consensus algorithm for multiagent systems via aperiodically intermittent protocol, IEEE Trans. Circuits Syst. II-Express Briefs, 69 (2022), 3229–3233. https://doi.org/10.1109/TCSII.2021.3135866 doi: 10.1109/TCSII.2021.3135866
[8]	W. C. Zou, J. Guo, C. K. Ahn, Z. R. Xiang, Sampled-data consensus protocols for a class of second-order switched nonlinear multiagent systems, IEEE T. Cybernetics, 53 (2023), 3726–373. https://doi.org/10.1109/TCYB.2022.3163157 doi: 10.1109/TCYB.2022.3163157
[9]	J. X. Chen, J. M. Li, X. X. Yuan, Global fuzzy adaptive consensus control of unknown nonlinear multiagent systems, IEEE Trans. Fuzzy Syst., 28 (2020), 510–522. https://doi.org/10.1109/TFUZZ.2019.2908771 doi: 10.1109/TFUZZ.2019.2908771
[10]	C. D. Li, G. Feng, X. F. Liao, Stabilization of nonlinear systems via periodically intermittent control, IEEE Trans. Circuits Syst. II-Express Briefs, 54 (2007), 1019–1023. https://doi.org/10.1109/TCSII.2007.903205 doi: 10.1109/TCSII.2007.903205
[11]	B. Y. Wang, Y. J. Zhang, M. Wei, Fixed-time leader-following consensus of multi-agent systems with intermittent control, Appl. Math. Comput., 438 (2023), 127524. https://doi.org/10.1016/j.amc.2022.127524 doi: 10.1016/j.amc.2022.127524
[12]	A. Azarbahram, A. Amini, Secure event-triggered tracking consensus under denial of service: A resilient periodically intermittent approach, IEEE Control Syst. Lett., 6 (2022), 2786–2791. https://doi.org/10.1109/LCSYS.2022.3177856 doi: 10.1109/LCSYS.2022.3177856
[13]	Q. Xiao, F. L. Lewis, Z. G. Zeng, Containment control for multiagent systems under two intermittent control schemes, IEEE Trans. Autom. Control, 64 (2019), 1236–1243. https://doi.org/10.1109/TAC.2018.2845675 doi: 10.1109/TAC.2018.2845675
[14]	S. C. He, X. D. Liu, P. L. Lu, C. K. Du, H. K. Liu, Distributed finite-time consensus algorithm for multiagent systems via aperiodically intermittent protocol, IEEE Trans. Circuits Syst. II-Express Briefs, 69 (2022), 3229–3233. https://doi.org/10.1109/TCSII.2021.3135866 doi: 10.1109/TCSII.2021.3135866
[15]	J. Liu, J. Liu, Y. B. Wu, C. X. Mu, C. Y. Sun, Aperiodically intermittent event-based fixed-time consensus tracking and its applications, IEEE Trans. Autom. Sci. Eng., 21 (2024), 5790–5801. https://doi.org/10.1109/TASE.2023.3318832 doi: 10.1109/TASE.2023.3318832
[16]	W. Zhu, Z. P. Jiang, G. Feng, Event-based consensus of multi-agent systems with general linear models, Automatica, 50 (2014), 552–558. https://doi.org/10.1016/j.automatica.2013.11.023 doi: 10.1016/j.automatica.2013.11.023
[17]	Y. L. Cai, J. Dai, H. G. Zhang, Y. C. Wang, Fixed-time leader-following/containment consensus of nonlinear multi-agent systems based on event-triggered mechanism, Appl. Math. Comput., 396 (2021), 125881. https://doi.org/10.1016/j.amc.2020.125881 doi: 10.1016/j.amc.2020.125881
[18]	Y. L. Zhang, G. G. Wen, A. Rahmani, X. Q. Zhai, Aperiodically intermittent adaptive event-triggered control for linear multi-agent systems, Int. J. Control Autom. Syst., 21 (2023), 94–108. http://dx.doi.org/10.1007/s12555-021-0713-9 doi: 10.1007/s12555-021-0713-9
[19]	P. F. Zhu, X. L. Wang, F. F. Li, S. Y. Qian, H. T. Li, Model-free optimal consensus control for multi-agent systems via DDPG-based event-triggered adaptive dynamic programming method, Math. Model. Control, 6 (2026), 97–110. https://doi.org/10.3934/mmc.2026008 doi: 10.3934/mmc.2026008
[20]	T. T. Chen, F. Y. Wang, M. L. Feng, C. Y. Xia, Z. Q. Chen, Fully distributed consensus of linear multi-agent systems via dynamic event-triggered control, Neurocomputing, 569 (2024), 127129. https://doi.org/10.1016/j.neucom.2023.127129 doi: 10.1016/j.neucom.2023.127129
[21]	L. L. Wang, S. M. Chen, Fully distributed observer-based leader-following consensus of linear multiagent systems by adaptive dynamic event-triggered schemes, IEEE T. Cybernetics, 55 (2025), 332–342. https://doi.org/10.1109/TCYB.2024.3485986 doi: 10.1109/TCYB.2024.3485986
[22]	L. Zhou, J. Hu, B. Li, Partial-nodes-based state estimation for complex networks under hybrid attacks: A dynamic event-triggered approach, Math. Model. Control, 5 (2025), 202–215. https://doi.org/10.3934/mmc.2025015 doi: 10.3934/mmc.2025015
[23]	Z. Y. Gao, H. G. Zhang, Y. L. Cai, Y. F. Mu, Finite-time event-triggered output consensus of heterogeneous fractional-order multiagent systems with intermittent communication, IEEE T. Cybernetics, 53 (2023), 2164–2176. https://doi.org/10.1109/TCYB.2021.3110964 doi: 10.1109/TCYB.2021.3110964
[24]	X. Wang, S. D. Wang, J. Liu, Y. B. Wu, C. Y. Sun, Bipartite finite-time consensus of multi-agent systems with intermittent communication via event-triggered impulsive control, Neurocomputing, 598 (2024), 127970. https://doi.org/10.1016/j.neucom.2024.127970 doi: 10.1016/j.neucom.2024.127970
[25]	M. Haripriya, A. Manivannan, S. Dhanasekar, S. Lakshmanan, Finite-time synchronization of delayed complex dynamical networks via sampled-data controller, Math. Model. Control, 5 (2025), 73–84. https://doi.org/10.3934/mmc.2025006 doi: 10.3934/mmc.2025006
[26]	A. Polyakov, Nonlinear feedback design for fixed-time stabilization of linear control systems, IEEE T. Automat. Control, 57 (2012), 2106–2110. https://doi.org/10.1109/TAC.2011.2179869} doi: 10.1109/TAC.2011.2179869
[27]	Z. Y. Zuo, R. Q. Ke, Q. L. Han, Fully distributed adaptive practical fixed-time consensus protocols for multi-agent systems, Automaica, 157 (2023), 111248. https://doi.org/10.1016/j.automatica.2023.111248 doi: 10.1016/j.automatica.2023.111248
[28]	D. Zhou, A. Zhang, P. Yang, Fixed-time event-triggered consensus of second-order multi-agent systems with fully continuous communication free, IET Control Theory A., 14 (2020), 2385–2394. https://doi.org/10.1049/iet-cta.2020.0401 doi: 10.1049/iet-cta.2020.0401
[29]	B. X. Liao, C. Hu, Y. Sheng, L. Feng, Z. G. Zeng, Fixed-time intra-/inter-layer output synchronization for multiplex networks under dynamic event-triggered control, IEEE Trans. Circuits Syst. I-Regul. Pap., 72 (2025), 8171–8183. https://doi.org/10.1109/TCSI.2025.3570536 doi: 10.1109/TCSI.2025.3570536
[30]	Z. Y. Yu, S. Z. Yu, H. J. Jiang, Finite/fixed-time event-triggered aperiodic intermittent control for nonlinear systems, Chaos Soliton. Fract., 173 (2023), 113735. https://doi.org/10.1016/j.chaos.2023.113735 doi: 10.1016/j.chaos.2023.113735
[31]	H. J. Liu, Z. Y. Yu, H. J. Jiang, Fixed-time consensus of nonlinear multi-agent systems via both event-triggered intermittent communication and sampled-data control, Commun. Nonlinear Sci., 140 (2025), 108391. https://doi.org/10.1016/j.cnsns.2024.108391 doi: 10.1016/j.cnsns.2024.108391
[32]	Y. B. Wu, Z. R. Guo, L. Xue, C. K. Ahn, J. Liu, Stabilization of complex networks under asynchronously intermittent event-triggered control, Automatica, 161 (2024), 111493. https://doi.org/10.1016/j.automatica.2023.111493 doi: 10.1016/j.automatica.2023.111493
[33]	N. Li, X. Q. Wu, J. W. Feng, J. H. Lü, Fixed-time synchronization of complex dynamical networks: A novel and economical mechanism, IEEE T. Cybernetics, 52 (2022), 4430–4440. https://doi.org/10.1109/TCYB.2020.3026996 doi: 10.1109/TCYB.2020.3026996
[34]	N. Li, X. Q. Wu, J. W. Feng, Y. H. Xu, J. H. Lü, Fixed-time synchronization of coupled neural networks with discontinuous activation and mismatched parameters, IEEE T. Neur. Net. Lear., 32 (2021), 2470–2482. https://doi.org/10.1109/TNNLS.2020.3005945 doi: 10.1109/TNNLS.2020.3005945
[35]	L. Y. Cheng, F. C. Tang, X. L. Shi, X. Y. Chen, J. L. Qiu, Finite-time and fixed-time synchronization of delayed memristive neural networks via adaptive aperiodically intermittent adjustment strategy, IEEE T. Neur. Net. Lear., 34 (2023), 8516–8530. https://doi.org/10.1109/TNNLS.2022.3151478 doi: 10.1109/TNNLS.2022.3151478
[36]	D. S. Xu, S. T. Song, H. Su, Fixed-time synchronization of large-scale systems via aperiodically intermittent control, Chaos Soliton. Fract., 173 (2023), 113613. https://doi.org/10.1016/j.chaos.2023.113613 doi: 10.1016/j.chaos.2023.113613
[37]	Y. B. Wu, Z. Y. Sun, G. T. Ran, L. Xue, Intermittent control for fixed-time synchronization of coupled networks, IEEE-CAA J. Autom. Sin., 10 (2023), 1488–1490. https://doi.org/10.1109/JAS.2023.123363 doi: 10.1109/JAS.2023.123363
[38]	F. Wang, C. Zhou, X. N. Lin, W. Liu, C. C. Hua, Adaptive dynamic event-triggered-based practical fixed-time optimal consensus of multiagent systems, IEEE T. Syst. Man Cyb.-S., 55 (2025), 2846–2858. https://doi.org/10.1109/TSMC.2025.3526969 doi: 10.1109/TSMC.2025.3526969
[39]	L. Xue, H. Y. Zhou, Y. B. Wu, J. Liu, D. C. Wunsch, Aperiodically intermittent dynamic event-triggered control for predefined-time synchronization of stochastic complex networks, IEEE T. Netw. Sci. Eng., 12 (2025), 970–981. https://doi.org/10.1109/TNSE.2024.3521598 doi: 10.1109/TNSE.2024.3521598
[40]	B. Hu, Z. H. Guan, M. Y. Fu, Distributed event-driven control for finite-time consensus, Automatica, 103 (2019), 88–95. https://doi.org/10.1016/j.automatica.2019.01.026 doi: 10.1016/j.automatica.2019.01.026
[41]	J. Liu, Y. L. Zhang, Y. Yu, C. Y. Sun, Fixed-time event-triggered consensus for nonlinear multiagent systems without continuous communications, IEEE T. Syst. Man Cyb.-S., 49 (2019), 2221–2229. https://doi.org/10.1109/TSMC.2018.2876334 doi: 10.1109/TSMC.2018.2876334

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