Mean-square consensus of a semi-Markov jump multi-agent system based on event-triggered stochastic sampling

Duoduo Zhao; Fang Gao; Jinde Cao; Xiaoxin Li; Xiaoqin Ma; Duoduo Zhao; Fang Gao; Jinde Cao; Xiaoxin Li; Xiaoqin Ma

doi:10.3934/mbe.2023637

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 8: 14241-14259. doi: 10.3934/mbe.2023637

Previous Article Next Article

Theory article Special Issues

Mean-square consensus of a semi-Markov jump multi-agent system based on event-triggered stochastic sampling

1.
School of Big Data and Artificial Intelligence, Chizhou University, Chizhou 247000, Anhui, China
2.
School of Mathematics, Southeast University, Nanjing 211189, Jiangsu, China

Received: 27 April 2023 Revised: 10 June 2023 Accepted: 14 June 2023 Published: 28 June 2023

This paper focuses on achieving leader-follower mean square consensus in semi-Markov jump multi-agent systems. To effectively reduce communication costs and control updates, we propose an event-triggered protocol based on stochastic sampling. The stochastic sampling interval randomly switches between finite given values, while the event-triggered function depends on the stochastic sampled data from neighboring agents. Using the event-triggered strategy, we present sufficient conditions to ensure mean square consensus. Finally, we provide a numerical example demonstrating the effectiveness of the theoretical results.
- event-triggered,
- stochastic sampling,
- Lyapunov function,
- semi-Markovian switching,
- multi-agent systems,
- mean-square consensus
Citation: Duoduo Zhao, Fang Gao, Jinde Cao, Xiaoxin Li, Xiaoqin Ma. Mean-square consensus of a semi-Markov jump multi-agent system based on event-triggered stochastic sampling[J]. Mathematical Biosciences and Engineering, 2023, 20(8): 14241-14259. doi: 10.3934/mbe.2023637

Related Papers:

Abstract

This paper focuses on achieving leader-follower mean square consensus in semi-Markov jump multi-agent systems. To effectively reduce communication costs and control updates, we propose an event-triggered protocol based on stochastic sampling. The stochastic sampling interval randomly switches between finite given values, while the event-triggered function depends on the stochastic sampled data from neighboring agents. Using the event-triggered strategy, we present sufficient conditions to ensure mean square consensus. Finally, we provide a numerical example demonstrating the effectiveness of the theoretical results.

References

[1]	X. Ren, D. Li, Y. Xi, H. Shao, Distributed multi-agent optimization via coordination with second-order nearest neighbors, IET Control Theory Appl., 14 (2020), 1733–1743. https://doi.org/10.1049/iet-cta.2019.0708 doi: 10.1049/iet-cta.2019.0708
[2]	X. Tan, M. Cao, J. Cao, Distributed dynamic event-based control for nonlinear multi-agent systems, IEEE Trans. Circuits Syst. Ⅱ Exp. Briefs, 68 (2021), 687–691. https://doi.org/10.1109/TCSII.2020.3006125 doi: 10.1109/TCSII.2020.3006125
[3]	Y. L. Wang, Q. L. Han, M. R. Fei, C. Peng, Network-based ${\mathrm{t}}-s $ fuzzy dynamic positioning controller design for unmanned marine vehicles, IEEE Trans. Cybern., 48 (2018), 1–14. https://doi.org/10.1109/TCYB.2018.2829730 doi: 10.1109/TCYB.2018.2829730
[4]	Y. L. Wang, Q. L. Han, Network-based modelling and dynamic output feedback control for unmanned marine vehicles in network environments, Automatica, 91 (2018), 43–53. https://doi.org/10.1016/j.automatica.2018.01.026 doi: 10.1016/j.automatica.2018.01.026
[5]	W. He, C. Xu, Q. L. Han, F. Qian, Z. Lang, Finite-time ${\mathrm{L}} 2$ leader-follower consensus of networked euler-lagrange systems with external disturbances, IEEE Trans. Syst. Man Cybern. Syst., 48 (2017), 1–9. 10.1109/TSMC.2017.2774251 doi: 10.1109/TSMC.2017.2774251
[6]	X. Wang, H. Wu, J. Cao, Global leader-following consensus in finite time for fractional-order multi-agent systems with discontinuous inherent dynamics subject to nonlinear growth, Nonlinear Anal.-Hybri. Syst., 37 (2020), 100888. https://doi.org/10.1016/j.nahs.2020.100888 doi: 10.1016/j.nahs.2020.100888
[7]	S. V. Feofilov, A. Kozyr, Stability of periodic movements in sampled data relay feedback control systems, in 2019 1st International Conference on Control Systems, Mathematical Modelling, Automation and Energy Efficiency (SUMMA), (2019), 18–21. https://doi.org/10.1109/SUMMA48161.2019.8947604
[8]	E. Rosenwasser, W. Drewelow, T. Jeinsch, Synchronous sampled-data modal control of a linear periodic object with lti actuator, in 2020 International Russian Automation Conference (RusAutoCon), (2020), 49–56. https://doi.org/10.1109/RusAutoCon49822.2020.9208195
[9]	W. He, S. Lv, C. Peng, N. Kubota, F. Qian, Improved leaderless consenus criteria of networked multi-agent systems based on the sampled data, Int. J. Syst. Sci., 49 (2018), 2737–2752. https://doi.org/10.1080/00207721.2018.1505005 doi: 10.1080/00207721.2018.1505005
[10]	W. He, S. Lv, X. Wang, F. Qian, Leaderless consensus of multi-agent systems via an event-triggered strategy under stochastic sampling, J. Franklin I., 356 (2019), 6502–6524. https://doi.org/10.1016/j.jfranklin.2019.05.033 doi: 10.1016/j.jfranklin.2019.05.033
[11]	Y. C. Sun, G. H. Yang, Periodic event-triggered resilient control for cyber-physical systems under denial-of-service attacks, J. Franklin I., 355 (2018), 5613–5631. https://doi.org/10.1016/j.jfranklin.2018.06.009 doi: 10.1016/j.jfranklin.2018.06.009
[12]	H. Li, Y. Fan, G. Pan, C. Song, Event-triggered remote dynamic control for network control systems, in 2020 16th International Conference on Control, Automation, Robotics and Vision (ICARCV), (2020), 483–488. https://doi.org/10.1109/ICARCV50220.2020.9305348
[13]	D. Liu, G. H. Yang, Robust event-triggered control for networked control systems, Inform. Sci., 459 (2018), 186–197. https://doi.org/10.1016/j.ins.2018.02.057 doi: 10.1016/j.ins.2018.02.057
[14]	M. Hertneck, S. Linsenmayer, F. Allgower, Nonlinear dynamic periodic event-triggered control with robustness to packet loss based on non-monotonic lyapunov functions, in 2019 IEEE 58th Conference on Decision and Control (CDC), (2019), 1680–1685. https://doi.org/10.1109/CDC40024.2019.9029770
[15]	T. Y. Zhang, D. Ye, Distributed event-triggered control for multi-agent systems under intermittently random denial-of-service attacks, Inform. Sci., 542 (2021), 380–390. https://doi.org/10.1016/j.ins.2020.06.070 doi: 10.1016/j.ins.2020.06.070
[16]	Z. G. Wu, Y. Xu, R. Lu, Y. Wu, T. Huang, Event-triggered control for consensus of multiagent systems with fixed/switching topologies, IEEE Trans. Syst. Man Cybern. Syst., 48 (2018), 1736–1746. http://dx.doi.org/10.1109/TSMC.2017.2744671 doi: 10.1109/TSMC.2017.2744671
[17]	S. Lv, W. He, F. Qian, J. Cao, Leaderless synchronization of coupled neural networks with the event-triggered mechanism, Neural Netw., 105 (2018), 316–327. https://doi.org/10.1016/j.neunet.2018.05.012 doi: 10.1016/j.neunet.2018.05.012
[18]	D. Liu, G. H. Yang, Dynamic event-triggered control for linear time-invariant systems with ${\mathrm{L}} 2$-gain performance, Int. J. Robust Nonlin., 29 (2018), 507–518. https://doi.org/10.1002/rnc.4403 doi: 10.1002/rnc.4403
[19]	X. Yi, K. Liu, D. V. Dimarogonas, K. H. Johansson, Dynamic event-triggered and self-triggered control for multi-agent systems, IEEE Trans. Automat. Contr., 64 (2019), 3300–3307. https://doi.org/10.1109/TAC.2018.2874703 doi: 10.1109/TAC.2018.2874703
[20]	D. Liu, G. H. Yang, A dynamic event-triggered control approach to leader-following consensus for linear multiagent systems, IEEE Trans. Syst. Man, and Cybern. Syst., 50 (2020), 1–9. https://doi.org/10.1109/TSMC.2019.2960062 doi: 10.1109/TSMC.2019.2960062
[21]	S. L. Du, T. Liu, D. W. C. Ho, Dynamic event-triggered control for leader-following consensus of multiagent systems, IEEE Trans. Syst. Man Cybern. Syst., 50 (2018), 2168–2216. https://doi.org/10.1109/TSMC.2018.2866853 doi: 10.1109/TSMC.2018.2866853
[22]	W. He, B. Xu, Q. L. Han, F. Qian, Adaptive consensus control of linear multiagent systems with dynamic event-triggered strategies, IEEE Trans. Cybern., 50 (2019), 1–13. https://doi.org/10.1109/TCYB.2019.2920093 doi: 10.1109/TCYB.2019.2920093
[23]	X. M. Zhang, Q. L. Han, B. L. Zhang, An overview and deep investigation on sampled-data-based event-triggered control and filtering for networked systems, IEEE Trans. Ind. Inform., 13 (2016), 4–16. https://doi.org/10.1109/TII.2016.2607150 doi: 10.1109/TII.2016.2607150
[24]	L. Liu, S. Zhu, B. Wu, Asynchronous sampled-data consensus of singular multi-agent systems based on event-triggered strategy, Int. J. Syst. Sci., 50 (2019), 1530–1542. https://doi.org/10.1080/00207721.2019.1616232 doi: 10.1080/00207721.2019.1616232
[25]	H. Su, Z. Wang, Z. Song, X. Chen, Event-triggered consensus of nonlinear multi-agent systems with sampling data and time delay, IET Control Theory Appl., 11 (2016), 1715–1725. https://doi.org/10.1049/iet-cta.2016.0865 doi: 10.1049/iet-cta.2016.0865
[26]	H. Wangli, L. Siqi, W. Xiaoqiang and Q. Feng, Leaderless consensus of multi-agent systems via an event-triggered strategy under stochastic sampling, J. Franklin I., 356 (2019), 6502–6524. https://doi.org/10.1016/j.jfranklin.2019.05.033 doi: 10.1016/j.jfranklin.2019.05.033
[27]	X. Ruan, J. Feng, C. Xu, J. Wang, Observer-based dynamic event-triggered strategies for leader-following consensus of multi-agent systems with disturbances, IEEE Trans. Netw. Sci. Eng., 7 (2020), 3148–3158. https://doi.org/10.1109/TNSE.2020.3017493 doi: 10.1109/TNSE.2020.3017493
[28]	X. Li, H. Wu, J. Cao, Prescribed-time synchronization in networks of piecewise smooth systems via a nonlinear dynamic event-triggered control strategy, Math. Comput. Simulat., 203 (2023), 647–668. https://doi.org/10.1016/j.matcom.2022.07.010 doi: 10.1016/j.matcom.2022.07.010
[29]	A. Hu, J. Cao, M. Hu, L. Guo, Event-triggered consensus of Markovian jumping multi-agent systems via stochastic sampling, IET Control Theory Appl., 9 (2015), 1964–1972. https://doi.org/10.1049/iet-cta.2014.1164 doi: 10.1049/iet-cta.2014.1164
[30]	X. H. Ge, Q. L. Han, Consensus of multiagent systems subject to partially accessible and overlapping markovian network topologies, IEEE Trans. Cyberne., 47 (2017), 1807–1819. https://doi.org/10.1109/TCYB.2016.2570860 doi: 10.1109/TCYB.2016.2570860
[31]	L. Wang, Y. Dong, D. Xie, J. Cao, Robust passivity analysis of markov-type lotka–volterra model with time-varying delay and uncertain mode transition rates, Math. Methods Applied Sci., 43 (2020), 6976–6984. https://doi.org/10.1002/mma.6447 doi: 10.1002/mma.6447
[32]	J. Dai, G. Guo, Exponential consensus of nonlinear multi-agent systems with semi-markov switching topologies, IET Control Theory and Appl., 11 (2017), 3363–3371. https://doi.org/10.1049/iet-cta.2017.0562 doi: 10.1049/iet-cta.2017.0562
[33]	B. Wang, Q. Zhu, Mode dependent ${\mathrm{H}}_{\infty}$ filtering for semi-Markovian jump linear systems with sojourn time dependent transition rates, IET Control Theory Appl., 13 (2019), 3019–3025. https://doi.org/10.1049/iet-cta.2019.0141 doi: 10.1049/iet-cta.2019.0141
[34]	J. Dai, G. Guo, Event-triggered leader-following consensus for multi-agent systems with semi-markov switching topologies, Inform. Sci., 459 (2018), 290–301. https://doi.org/10.1016/j.ins.2018.04.054 doi: 10.1016/j.ins.2018.04.054
[35]	M. He, J. Mu, X. Mu, ${\mathrm{H}}_{\infty}$ leader-following consensus of nonlinear multi-agent systems under semi-markovian switching topologies with partially unknown transition rates, Inform. Sci., 513 (2020), 168–179. https://doi.org/10.1016/j.ins.2019.11.002 doi: 10.1016/j.ins.2019.11.002
[36]	X. Xie, Z. Yang, X. Mu, Observer-based consensus control of nonlinear multi-agent systems under semi-markovian switching topologies and cyber attacks, Int. J. Robust Nonlin., 30 (2020), 5510–5528. https://doi.org/10.1002/rnc.5088 doi: 10.1002/rnc.5088
[37]	Z. Zhang, H. Wu, Cluster synchronization in finite/fixed time for semi-markovian switching t-s fuzzy complex dynamical networks with discontinuous dynamic nodes, AIMS Math., 7 (2022), 11942–11971. http://dx.doi.org/10.3934/math.2022666 doi: 10.3934/math.2022666

Reader Comments

Your name:*

Email:*
© 2023 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)