Consensus control of multi-agent systems with delays

Yi Gong; Yi Gong

doi:10.3934/era.2024224

Electronic Research Archive

2024, Volume 32, Issue 8: 4887-4904. doi: 10.3934/era.2024224

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Research article

Consensus control of multi-agent systems with delays

Yi Gong ^,

Department of Basic Courses, Shanghai Customs College, Shanghai 201204, China

Received: 13 June 2024 Revised: 16 July 2024 Accepted: 05 August 2024 Published: 14 August 2024

This paper concerns the consensus problem of linear time-invariant multi-agent systems (MASs) with multiple state delays and communicate delays. Consensus control is widely applied in spacecraft formation, sensor networks, robotic manipulators, autonomous vehicles, and others. By introducing a linear transformation, the consensus problem of the delayed MAS under an undirected network was converted into a robust asymptotic stability problem associated with the eigenvalues of the normalized Laplacian matrix of the network. By means of the argument principle and optimization technologies, a numerical controller design method was presented for the delayed MAS to reach consensus. The effectiveness of the proposed approach was illustrated by some numerical examples. The proposed approach may be applied to multi-agent systems with distributed delays.
- multi-agent systems,
- optimization,
- argument principle,
- time delay
Citation: Yi Gong. Consensus control of multi-agent systems with delays[J]. Electronic Research Archive, 2024, 32(8): 4887-4904. doi: 10.3934/era.2024224

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Abstract

This paper concerns the consensus problem of linear time-invariant multi-agent systems (MASs) with multiple state delays and communicate delays. Consensus control is widely applied in spacecraft formation, sensor networks, robotic manipulators, autonomous vehicles, and others. By introducing a linear transformation, the consensus problem of the delayed MAS under an undirected network was converted into a robust asymptotic stability problem associated with the eigenvalues of the normalized Laplacian matrix of the network. By means of the argument principle and optimization technologies, a numerical controller design method was presented for the delayed MAS to reach consensus. The effectiveness of the proposed approach was illustrated by some numerical examples. The proposed approach may be applied to multi-agent systems with distributed delays.

References

[1]	Z. Li, Z. Duan, G. Chen, L. Huang, Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint, IEEE Trans. Circuits Syst. I, 57 (2009), 213–224. https://doi.org/10.1109/TCSI.2009.2023937 doi: 10.1109/TCSI.2009.2023937
[2]	M. Wooldridge, An Introduction to Multiagent Systems, John Wiley & Sons, 2009.
[3]	E. Fridman, Introduction to Time-delay Systems: Analysis and Control, Springer, 2014. https://doi.org/10.1007/978-3-319-09393-2
[4]	Y. P. Tian, C. L. Liu, Consensus of multi-agent systems with diverse input and communication delays, IEEE Trans. Autom. Control, 53 (2008), 2122–2128. https://doi.org/10.1109/TAC.2008.930184 doi: 10.1109/TAC.2008.930184
[5]	P. A. Bliman, G. Ferrari-Trecate, Average consensus problems in networks of agents with delayed communications, Automatica, 44 (2008), 1985–1995. https://doi.org/10.1016/j.automatica.2007.12.010 doi: 10.1016/j.automatica.2007.12.010
[6]	J. Xu, H. Zhang, L. Xie, Input delay margin for consensusability of multi-agent systems, Automatica, 49 (2013), 1816–1820. https://doi.org/10.1016/j.automatica.2013.02.044 doi: 10.1016/j.automatica.2013.02.044
[7]	W. Hou, M. Fu, H. Zhang, Z. Wu, Consensus conditions for general second-order multi-agent systems with communication delay, Automatica, 75 (2017), 293–298. https://doi.org/10.1016/j.automatica.2016.09.042 doi: 10.1016/j.automatica.2016.09.042
[8]	L. Li, M. Fu, H. Zhang, R. Lu, Consensus control for a network of high order continuous-time agents with communication delays, Automatica, 89 (2018), 144–150. https://doi.org/10.1016/j.automatica.2017.12.006 doi: 10.1016/j.automatica.2017.12.006
[9]	D. Ma, Delay range for consensus achievable by proportional and PD feedback protocols with time-varying delays, IEEE Trans. Autom. Control, 67 (2021), 3212–3219. https://doi.org/10.1109/TAC.2021.3096899 doi: 10.1109/TAC.2021.3096899
[10]	T. Qi, L. Qiu, J. Chen, MAS consensus and delay limits under delayed output feedback, IEEE Trans. Autom. Control, 62 (2016), 4660–4666. https://doi.org/10.1109/TAC.2016.2625422 doi: 10.1109/TAC.2016.2625422
[11]	X. Yu, F. Yang, C. Zou, L. Ou, Stabilization parametric region of distributed PID controllers for general first-order multi-agent systems with time delay, IEEE/CAA J. Autom. Sin., 7 (2019), 1555–1564. https://doi.org/10.1109/JAS.2019.1911627 doi: 10.1109/JAS.2019.1911627
[12]	T. Qi, R. Lu, J. Chen, Consensus of continuous-time multiagent systems via delayed output feedback: Delay versus connectivity, IEEE Trans. Autom. Control, 66 (2020), 1329–1336. https://doi.org/10.1109/TAC.2020.2991131 doi: 10.1109/TAC.2020.2991131
[13]	J. Luo, W. Tian, S. Zhong, K. Shi, H. Chen, X. M. Gu, et al., Non-fragile asynchronous H$\infty$ control for uncertain stochastic memory systems with Bernoulli distribution, Appl. Math. Comput., 312 (2017), 109–128. https://doi.org/10.1016/j.amc.2017.05.003 doi: 10.1016/j.amc.2017.05.003
[14]	J. Luo, W. Tian, S. Zhong, K. Shi, X. M. Gu, W. Wang, Improved delay-probability-dependent results for stochastic neural networks with randomly occurring uncertainties and multiple delays, Int. J. Syst. Sci., 49 (2018), 2039–2059. https://doi.org/10.1080/00207721.2018.1483044 doi: 10.1080/00207721.2018.1483044
[15]	Y. G. Sun, L. Wang, G. Xie, Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays, Syst. Control Lett., 57 (2008), 175–183. https://doi.org/10.1016/j.sysconle.2007.08.009 doi: 10.1016/j.sysconle.2007.08.009
[16]	P. Lin, Y. Jia, Consensus of a class of second-order multi-agent systems with time-delay and jointly-connected topologies, IEEE Trans. Autom. Control, 55 (2010), 778–784. https://doi.org/10.1109/TAC.2010.2040500 doi: 10.1109/TAC.2010.2040500
[17]	J. Chen, D. Xie, M. Yu, Consensus problem of networked multi-agent systems with constant communication delay: Stochastic switching topology case, Int. J. Control, 85 (2012), 1248–1262. https://doi.org/10.1080/00207179.2012.682262 doi: 10.1080/00207179.2012.682262
[18]	W. Hou, M. Y. Fu, H. Zhang, Consensusability of linear multi-agent systems with time delay, Int. J. Robust Nonlinear Control, 26 (2016), 2529–2541. https://doi.org/10.1002/rnc.3458 doi: 10.1002/rnc.3458
[19]	Y. Chen, X. Huang, J. Zhan, Gain-scheduled robust control for multi-agent linear parameter-varying systems with communication delays, Int. J. Robust Nonlinear Control, 32 (2022), 792–806. https://doi.org/10.1002/rnc.5854 doi: 10.1002/rnc.5854
[20]	Z. Wang, J. Xu, H. Zhang, Consensusability of multi-agent systems with time-varying communication delay, Syst. Control Lett., 65 (2014), 37–42. https://doi.org/10.1016/j.sysconle.2013.12.011 doi: 10.1016/j.sysconle.2013.12.011
[21]	Z. Meng, W. Ren, Y. Cao, Z. You, Leaderless and leader-following consensus with communication and input delays under a directed network topology, IEEE Trans. Syst. Man Cybern. Part B, 41 (2010), 75–88. https://doi.org/10.1109/TSMCB.2010.2045891 doi: 10.1109/TSMCB.2010.2045891
[22]	D. Wang, W. Wang, Necessary and sufficient conditions for containment control of multi-agent systems with time delay, Automatica, 103 (2019), 418–423. https://doi.org/10.1016/j.automatica.2018.12.029 doi: 10.1016/j.automatica.2018.12.029
[23]	W. Qin, Z. Liu, Z. Chen, Impulsive observer-based consensus control for multi-agent systems with time delay, Int. J. Control, 88 (2015), 1789–1804. https://doi.org/10.1080/00207179.2015.1017738 doi: 10.1080/00207179.2015.1017738
[24]	Y. Li, H. Li, X. Ding, G. Zhao, Leader–follower consensus of multiagent systems with time delays over finite fields, IEEE Trans. Cybern., 49 (2018), 3203–3208. https://doi.org/10.1109/TCYB.2018.2839892 doi: 10.1109/TCYB.2018.2839892
[25]	B. Cui, Y. Xia, K. Liu, J. Zhang, Cooperative tracking control for general linear multiagent systems with directed intermittent communications: An artificial delay approach, Int. J. Robust Nonlinear Control, 29 (2019), 3063–3077. https://doi.org/10.1002/rnc.4540 doi: 10.1002/rnc.4540
[26]	D. Ma, Delay range for consensus achievable by proportional and PD feedback protocols with time-varying delays, IEEE Trans. Autom. Control, 67 (2021), 3212–3219. https://doi.org/10.1109/TAC.2021.3096899 doi: 10.1109/TAC.2021.3096899
[27]	K. Li, X. Mu, Predictor-based $H_{\infty}$ leader-following consensus of stochastic multi-agent systems with random input delay, Optimal Control Appl. Methods, 42 (2021), 1349-1364. https://doi.org/10.1002/oca.2731 doi: 10.1002/oca.2731
[28]	G. Hu, R. Hu, Numerical optimization for feedback stabilization of linear systems with distributed delays, J. Comput. Appl. Math., 371 (2020), 112706. https://doi.org/10.1016/j.cam.2019.112706 doi: 10.1016/j.cam.2019.112706
[29]	J. Nocedal, S. Wright, Numerical Optimization, Springer Science & Business Media, 2006.
[30]	M. Fiedler, Algebraic connectivity of graphs, Czech. Math. J., 23 (1973), 298–305. https://doi.org/10.21136/CMJ.1973.101168 doi: 10.21136/CMJ.1973.101168

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