Consensus of two-layer multi-agent systems subjected to cyber-attack

doi:10.11772/j.issn.1001-9081.2020081159

Abstract

Abstract: The consensus problem of the two-layer multi-agent systems subjected to cyber-attacks was studied. Aiming at the two-layer multi-agent systems composed of the leaders' layer and the followers' layer, the situation as the following was given:the neighboring agents in the leaders' layer were cooperative, the adjacent agents in the followers' layer were cooperative or competitive, and there was a restraining relationship between some corresponding agents in the leaders' layer and the followers' layer. The consensus problem among the nodes of leaders' layer, followers' layer and two-layer multi-agent systems subjected to cyber-attack was discussed. Based on the related knowledge such as Linear Matrix Inequality (LMI), Lyapunov stability theory and graph theory, the sufficient criteria for consensus between the nodes in the leaders' layer multi-agent system, bipartite consensus between the nodes in the followers' layer multi-agent system and node-to-node bipartite consensus between the nodes in the two-layer multi-agent systems were given. Finally, the numerical simulation examples were given, and the consensus of the two-layer multi-agent systems subjected to cyber-attack was realized, which verified the validity of the proposed criteria.

Key words: multi-agent system, consensus, cyber-attack, sign graph, linear matrix inequality

摘要： 研究了遭受网络攻击的双层结构多智能体系统的一致性问题。针对包含领导层和跟随者层的双层网络结构的多智能体系统，考虑了如下情况：领导层相邻智能体之间为友好合作关系，跟随者层相邻智能体之间既包含友好合作也包含对抗竞争关系，同时领导层与跟随者层中部分对应智能体之间存在牵制关系。分析了受网络攻击的领导层多智能体系统、跟随者层多智能体系统和双层网络结构多智能体系统的节点之间的一致性关系。基于线性矩阵不等式（LMI）、李雅普诺夫稳定性理论和图论等相关知识给出了领导层多智能体系统节点间实现一致，跟随者层多智能体系统节点间实现二分一致，以及双层结构的多智能体系统之间实现点对点二分一致的充分性判据。最后，给出了具体的数值仿真例子，实现了遭受网络攻击的双层结构多智能体系统的一致性，验证了所给出的判据的有效性。

关键词: 多智能体系统, 一致性, 网络攻击, 符号图, 线性矩阵不等式

CLC Number:

TP18

WANG Yunyan, HU Aihua. Consensus of two-layer multi-agent systems subjected to cyber-attack[J]. Journal of Computer Applications, 2021, 41(5): 1399-1405.

王云燕, 胡爱花. 网络攻击下双层结构多智能体系统一致性[J]. 计算机应用, 2021, 41(5): 1399-1405.

References

[1] MOSTAFA S A,AHMAD M S,MUSTAPHA A,et al. Formulating layered adjustable autonomy for unmanned aerial vehicles[J]. International Journal of Intelligent Computing and Cybernetics, 2017,10(4):430-450.
[2] YAN C, FANG H, CHAO H. Energy-aware leader-follower tracking control for electric-powered multi-agent systems[J]. Control Engineering Practice,2018,79:209-218.
[3] MOROZOVA N S. Formation motion control for a multi-agent system simulating autonomous robots[J]. Moscow University Computational Mathematics and Cybernetics, 2015, 39(4):175-183.
[4] NGUYEN D H. A sub-optimal consensus design for multi-agent systems based on hierarchical LQR[J]. Automatica,2015,55:88-94.
[5] 王亚军, 张申, 胡青松, 等. 具有测量噪声的时滞多智能体系统的一致性问题[J]. 山东大学学报(理学版),2017,52(1):74-80.(WANG Y J,ZHANG S,HU Q S,et al. Consensus problem of time-delayed multi-agent system with measurement noise[J]. Journal of Shandong University(Natural Science),2017,52(1):74-80.)
[6] XUE A,HONG Y. Performance evaluation for damping controllers of power systems based on multi-agent models[J]. Journal of Systems Science and Complexity,2009,22(1):77-87.
[7] WANG B,CHEN W,WANG J,et al. Accurate cooperative control for multiple leaders multi-agent uncertain systems:a two-layer nodeto-node communication framework[J]. IEEE Transactions on Industrial Informatics,2018,14(6):2395-2405.
[8] WAN Y, WEN G, CAO J, et al. Distributed node-to-node consensus of multi-agent systems with stochastic sampling[J]. International Journal of Robust and Nonlinear Control,2016,26(1):110-124.
[9] 李玲, 胡爱花, 高海云. 事件触发控制多智能体网络点对点一致性[J]. 计算机工程与应用, 2018,54(17):50-55.(LI L,HU A H,GAO H Y. Node-to-node consensus of multi-agent networks under event-triggered control[J]. Computer Engineering and Applications,2018,54(17):50-55.)
[10] WEN G,WANG P,HUANG T,et al. Distributed consensus of layered multi-agent systems subject to attacks on edges[J]. IEEE Transactions on Circuits and Systems I:Regular Papers,2020,67(9):3152-3162.
[11] WANG P,WEN G,YU X,et al. Synchronization of multi-layer networks:from node-to-node synchronization to complete synchronization[J]. IEEE Transactions on Circuits and Systems I:Regular Papers,2019,66(3):1141-1152.
[12] WEN G,YU W,WANG J,et al. Distributed node-to-node consensus of multi-agent systems with time-varying pinning links[J]. Neurocomputing,2015,149(Pt C):1387-1395.
[13] JIA K, LI H, ZHENG W, et al. Distributed node-to-node consensus of multi-agent systems with delayed nonlinear dynamics and intermittent communications[J]. Mathematical Problems in Engineering,2015,2015:No. 268083.
[14] WANG P,YU W,YU X. Robust node-to-node consensus of linear multiagent systems with directed switching topologies subject to uncertain pinning communications[J]. International Journal of Robust and Nonlinear Control,2018,28(5):1886-1900.
[15] HE W,CHEN G,HAN Q L,et al. Multiagent systems on multilayer networks:synchronization analysis and network design[J]. IEEE Transactions on Systems, Man, and Cybernetics Systems,2017,47(7):1655-1667.
[16] TIAN L,JI Z,HU T,et al. Bipartite consensus of edge dynamics on coopetition multi-agent systems[J]. Science China Information Sciences,2019,62(12):No. 229201.
[17] MENG D, DU M, JIA Y. Interval bipartite consensus of networked agents associated with signed digraphs[J]. IEEE Transactions on Automatic Control,2016,61(12):3755-3770.
[18] QIN J,FU W,ZHENG W,et al. On the bipartite consensus for generic linear multi-agent systems with input saturation[J]. IEEE Transactions on Cybernetics,2017,47(8):1948-1958.
[19] MA C,ZHAO Y,SUN W. Event-triggered bipartite consensus of single-integrator multi-agent systems with measurement noise[J]. Journal of Control Science and Engineering, 2018, 2018:No. 7186737.
[20] HU J,WU Y,LIU L,et al. Adaptive bipartite consensus control of high-order multiagent systems on coopetition networks[J]. International Journal of Robust and Nonlinear Control,2018,28(7):2868-2886.
[21] ZHANG H,CHEN J. Bipartite consensus of multi-agent systems over signed graphs:state feedback and output feedback control approaches[J]. International Journal of Robust and Nonlinear Control,2017,27(1):3-14.
[22] LU M, LIU L. Leader-following consensus of second-order nonlinear multi-agent systems subject to disturbances[J]. Frontiers of Information Technology and Electronic Engineering, 2019,20(1):88-94.
[23] TEIXEIRA A,SANDBERG H,JOHANSSON K H. Networked control systems under cyber-attacks with applications to power networks[C]//Proceedings of the 2010 American Control Conference. Piscataway:IEEE,2010:3690-3696.
[24] SHARMA D D, SINGH S N, LIN J, et al. Agent-based distributed control schemes for distributed energy storage systems under cyber-attacks[J]. IEEE Journal on Emerging and Selected Topics in Circuits and Systems,2017,7(2):307-318.
[25] DING D,WANG Z,HO D W C,et al. Observer-based eventtriggering consensus control for multiagent systems with lossy sensors and cyber-attacks[J]. IEEE Transactions on Cybernetics, 2017,47(8):1936-1947.
[26] DIESTEL R. Graph Theory[M]. 4th ed. New York:Springer, 2000:67-128.
[27] CARTWRIGHT D, HARARY F. Structural balance:a generalization of Heider's theory[J]. Psychological Review, 1956,63(5):277-293.
[28] ALTAFINI C. Consensus problems on networks with antagonistic interactions[J]. IEEE Transactions on Automatic Control,2013, 58(4):935-946.
[29] YANG H,YE D. Adaptive fixed-time bipartite tracking consensus control for unknown nonlinear multi-agent systems:An information classification mechanism[J]. Information Sciences,2018,459:238-254.
[30] YAKUBOVICH V A. Book review of linear matrix inequalities in system and control theory by BOYD S,GHAOUI L E,FERON E, et al.[J]. SIAM Review,1995,37(3):479-481.