Recent advances of finite-field networks

Yunsi Yang; Jun-e Feng; Lei Jia; Yunsi Yang; Jun-e Feng; Lei Jia

doi:10.3934/mmc.2023021

Mathematical Modelling and Control

2023, Volume 3, Issue 3: 244-255. doi: 10.3934/mmc.2023021

Previous Article Next Article

Review Special Issues

Recent advances of finite-field networks

Yunsi Yang ¹,
Jun-e Feng ^{2
,
,},
Lei Jia ^{1
,
,}

1.
Institute of Marine Science and Technology, Shandong University, Jinan, China
2.
School of Mathematics, Shandong University, Jinan, China

Received: 28 December 2022 Revised: 25 February 2023 Accepted: 12 March 2023 Published: 14 September 2023

Finite-field networks (FFNs) are a class of multi-agent systems over finite fields with sensing, computing, and communication capabilities. FFNs have been investigated extensively to save computing and communication resources. This paper summarizes the current research results to provide a direction for future research. First, different models of FFNs are reviewed, including FFNs with time-delays, switching topology, and leader-following structures. Then, the consensus and synchronization problems of multi-agent systems over finite fields are analyzed, and the necessary and sufficient conditions for consensus and synchronization of some autonomous systems have been derived in recent research. Finally, the distributed control of multi-agent systems over finite fields has been developed by many scholars based on various approaches.
- multi-agent system,
- finite-field network,
- controllability,
- consensus,
- semi-tensor product (STP) of matrices
Citation: Yunsi Yang, Jun-e Feng, Lei Jia. Recent advances of finite-field networks[J]. Mathematical Modelling and Control, 2023, 3(3): 244-255. doi: 10.3934/mmc.2023021

Related Papers:

Abstract

Finite-field networks (FFNs) are a class of multi-agent systems over finite fields with sensing, computing, and communication capabilities. FFNs have been investigated extensively to save computing and communication resources. This paper summarizes the current research results to provide a direction for future research. First, different models of FFNs are reviewed, including FFNs with time-delays, switching topology, and leader-following structures. Then, the consensus and synchronization problems of multi-agent systems over finite fields are analyzed, and the necessary and sufficient conditions for consensus and synchronization of some autonomous systems have been derived in recent research. Finally, the distributed control of multi-agent systems over finite fields has been developed by many scholars based on various approaches.

References

[1]	A. Jadbabaie, J. Lin, A. S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE T. Automat. Contr., 48 (2003), 988–1001. https://doi.org/10.1109/TAC.2003.812781 doi: 10.1109/TAC.2003.812781
[2]	A. Ligtenberg, M. Wachowicz, A. K. Bregt, A.Beulensb, D. L. Kettenis, A design and application of a multiagent system for simulation of multi-actor spatial planning, J. Environ. Manage., 72 (2004), 43–55. https://doi.org/10.1016/j.jenvman.2004.02.007 doi: 10.1016/j.jenvman.2004.02.007
[3]	R. Olfati-Saber, R. M. Murray, Consensus problems in networks of agents with switching topology and time-delays, IEEE T. Automat. Contr., 49 (2004), 1520–1533. https://doi.org/10.1109/TAC.2004.834113 doi: 10.1109/TAC.2004.834113
[4]	W. Ren, R. W. Beard, Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE T. Automat. Contr., 50 (2005), 655–661. https://doi.org/10.1109/TAC.2005.846556 doi: 10.1109/TAC.2005.846556
[5]	R. E. Kalman, Contributions to the theory of optimal control, Bol. soc. mat. mexicana, 5 (1960), 102–119.
[6]	Z. Ji, Z. Wang, H.Lin, Controllability of multi-agent systems with time-delay in state and switching topology, Int. J. Control, 83 (2010), 371–386. https://doi.org/10.1080/00207170903171330 doi: 10.1080/00207170903171330
[7]	H. Kim, H. Shim, J. Back, J. Seo, in 2011 50th IEEE Conference on Decision and Control and European Control Conference, (2011), 4829–4834. https://doi.org/10.1109/CDC.2011.6161139
[8]	Y. Guan, Z. Ji, L. Zhang, L. Wang, Decentralized stabilizability of multi-agent systems under fixed and switching topologies, Syst. Control Lett., 62 (2013), 438–446. https://doi.org/10.1016/j.sysconle.2013.02.010 doi: 10.1016/j.sysconle.2013.02.010
[9]	R. Olfati-Saber, J. A. Fax, R. M. Murray, Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95 (2007), 215–233. https://doi.org/10.1109/JPROC.2006.887293 doi: 10.1109/JPROC.2006.887293
[10]	H. Su, M. Chen, J. Lam, Z. Lin, Semi-Global Leader-following consensus of linear multi-agent systems with input saturation via low gain feedback, IEEE Transactions on Circuits and Systems I Regular Papers, 60 (2013), 1881–1889. https://doi.org/10.1109/TCSI.2012.2226490 doi: 10.1109/TCSI.2012.2226490
[11]	D. Guo, G. Yan, Z. Lin, Distributed verification of controllability for weighted out-tree based topology, 2012 American Control Conference, (2012), 1507–1512. https://doi.org/10.1109/ACC.2012.6315624 doi: 10.1109/ACC.2012.6315624
[12]	B. Liu, G. Xie, T. Chu, L. Wang, Controllability of interconnected systems via switching networks with a leader, 2006 IEEE International Conference on Systems, Man and Cybernetics, 5 (2006), 3912–3916. https://doi.org/10.1109/ICSMC.2006.384742 doi: 10.1109/ICSMC.2006.384742
[13]	B. Liu, H. Su, R. Li, D. Sun, W. Hu, Switching controllability of discrete-time multi-agent systems with multiple leaders and time-delays, Appl. Math. Comput., 228 (2014), 571–588. https://doi.org/10.1016/j.amc.2013.12.020 doi: 10.1016/j.amc.2013.12.020
[14]	H. Tanner, On the controllability of nearest neighbor interconnections, 2004 43rd IEEE Conference on Decision and Control, 3 (2004), 2467–2472. https://doi.org/10.1109/CDC.2004.1428782 doi: 10.1109/CDC.2004.1428782
[15]	C. Lin, Structural controllability, IEEE T. Automat. Contr., 19 (1974), 201–208. https://doi.org/10.1109/TAC.1974.1100557 doi: 10.1109/TAC.1974.1100557
[16]	L. Wang, F. Jiang, G. Xie, Controllability of multi-agent systems based on agreement protocols, Science in China Series F: Information Sciences, 52 (2009), 2074–2088. https://doi.org/10.1007/s11432-009-0185-7 doi: 10.1007/s11432-009-0185-7
[17]	Y. Lou, Y. Hong, Controllability analysis of multi-agent systems with directed and weighted interconnection, Int. J. Control, 85 (2012), 1486–1496. https://doi.org/10.1080/00207179.2012.690162 doi: 10.1080/00207179.2012.690162
[18]	F. Pasqualetti, D. Borra, F. Bullo, Consensus networks over finite fields, Automatica, 50 (2014), 349–358. https://doi.org/10.1016/j.automatica.2013.11.011 doi: 10.1016/j.automatica.2013.11.011
[19]	S. Shreyas, H. Christoforos, Structural controllability and observability of linear systems over finite fields with applications to multi-agent systems, IEEE T. Automat. Contr., 58 (2013), 60–73. https://doi.org/10.1109/TAC.2012.2204155 doi: 10.1109/TAC.2012.2204155
[20]	Z. Lu, L. Zhang, L. Wang, Structural controllability of multi-agent systems with general linear dynamics over finite fields, 2016 35th Chinese Control Conference, (2016), 8230–8235. https://doi.org/10.1109/ChiCC.2016.7554667 doi: 10.1109/ChiCC.2016.7554667
[21]	X. Li, H. Su, M. Chen, Consensus networks with time-delays over finite fields, Int. J. Control, 89 (2016), 1000–1008. https://doi.org/10.1080/00207179.2015.1110755 doi: 10.1080/00207179.2015.1110755
[22]	X. Li, M. Chen, H. Su, C. Li, Consensus networks with switching topology and time-delays over finite fields, Automatica, 68 (2016), 39–43. https://doi.org/10.1016/j.automatica.2016.01.033 doi: 10.1016/j.automatica.2016.01.033
[23]	M. Meng, X. Li, G. Xiao, Synchronization of networks over finite fields, Automatica, 115 (2020), 108877. https://doi.org/10.1016/j.automatica.2020.108877 doi: 10.1016/j.automatica.2020.108877
[24]	W. Zhu, J. Cao, X. Shi, L. Rutkowski, Synchronization of finite-field networks with time delays, IEEE T. Netw. Sci. Eng., 9 (2022), 347–355. https://doi.org/10.1109/TNSE.2021.3115891 doi: 10.1109/TNSE.2021.3115891
[25]	X. Xu, Y. Hong, Leader-following consensus of multi-agent systems over finite fields, 53rd IEEE Conference on Decision and Control, (2014), 2999–3004. https://doi.org/10.1109/CDC.2014.7039850 doi: 10.1109/CDC.2014.7039850
[26]	Z. Lu, L. Zhang, L. Wang, Controllability analysis of multi-agent systems with switching topology over finite fields, Science China Information Sciences, 62 (2019), 1–15. https://doi.org/10.1007/s11432-017-9284-4 doi: 10.1007/s11432-017-9284-4
[27]	H. Li, Y. Wang, P. Guo, Consensus of finite-field networks with switching topologies and linear protocols, Proceedings of the 33rd Chinese Control Conference, (2014), 2475–2480. https://doi.org/10.1109/ChiCC.2014.6897023 doi: 10.1109/ChiCC.2014.6897023
[28]	H. Li, Z. Dong, P. Guo, Z. Liu, Analysis and Control of Finite-Value Systems, Boca Raton: CRC Press, 2018.
[29]	Y. Li, H. Li, Controllability of multi-agent systems over finite fields via semi-tensor product method, 2019 Chinese Control Conference, (2019), 5606–5611. https://doi.org/10.23919/ChiCC.2019.8866482 doi: 10.23919/ChiCC.2019.8866482
[30]	Y. Li, H. Li, X. Ding, G. Zhao, Leader-follower consensus of multiagent systems with time delays over finite fields, IEEE T. Cybernetics, 49 (2019), 3203–3208. https://doi.org/10.1109/TCYB.2018.2839892 doi: 10.1109/TCYB.2018.2839892
[31]	Y. Li, H. Li, X. Ding, Set stability of switched delayed logical networks with application to finite-field consensus, Automatica, 113 (2020), 108768. https://doi.org/10.1016/j.automatica.2019.108768 doi: 10.1016/j.automatica.2019.108768
[32]	Y. Li, H. Li, S. Wang, Finite-time consensus of finite field networks with stochastic time delays, IEEE Transactions on Circuits and Systems II: Express Briefs, 67 (2020), 3128–3132. https://doi.org/10.1109/TCSII.2020.2966377 doi: 10.1109/TCSII.2020.2966377
[33]	Y. Liu, M. Song, H. Li, Y. Li, W. Hou, Containment problem of finite-field networks with fixed and switching topology, Appl. Math. Comput., 411 (2021), 126519. https://doi.org/10.1016/j.amc.2021.126519 doi: 10.1016/j.amc.2021.126519
[34]	A. Roger, C. R. Johnson, Topics in matrix analysis, Cambridege: Cambridge University Press, 1991.
[35]	L. Ljung, T. Söderström, Theory and practice of recursive identification, Cambridege: MIT press, 1983.
[36]	D. Cheng, H. Qi, Z. Li, W. Hou, Analysis and Control of Boolean Networks: A Semi-tensor Product Approach, London: Springer, 2011.

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)