Bipartite Consensus Tracking of Second-Order Multi-Agent Systems Under DoS Attacks

doi:10.3778/j.issn.1002-8331.2207-0192

Abstract

Abstract: The leader-following secure bipartite consensus problem is investigated for second-order nonlinear multi-agent systems under denial-of-service（DoS） attacks. A class of aperiodic DoS attacks based on time series is considered. Distributed bipartite consensus protocols are designed for multi-agent systems without and with communication delay, respectively. Lyapunov stability theory and graph theory are utilized to analyze the stability of bipartite error systems. Sufficient conditions are derived for ensuring the leader-following bipartite consensus of multi-agent systems, which involve the attack frequency, the length rate of DoS attacks, control parameters and so on. Finally, simulation examples demonstrate the correctness of the designed method.

Key words: second-order nonlinear multi-agent systems, communication delay, leader-following bipartite consensus, DoS attack

摘要： 针对拒绝服务（denial-of-service，DoS）攻击下的二阶非线性多智能体系统，研究了其领导跟随安全二分一致性问题。所考虑的DoS攻击是基于时间序列且非周期发生的攻击。针对无时滞和有通信时滞两种情形，分别设计了分布式二分一致性协议，利用李雅普诺夫稳定性理论和图论，分析了二分误差系统的稳定性，得到了多智能体系统实现二分跟踪一致性与DoS攻击频率、长度比率及控制参数等相关的充分条件。通过仿真实例验证了所设计方法的正确性。

关键词: 二阶非线性多智能体系统, 通信时滞, 领导跟随二分一致性, DoS攻击

LUO Xiang, FENG Yuanzhen. Bipartite Consensus Tracking of Second-Order Multi-Agent Systems Under DoS Attacks[J]. Computer Engineering and Applications, 2023, 59(12): 77-83.

罗香, 冯元珍. DoS攻击下二阶多智能体系统二分跟踪一致性[J]. 计算机工程与应用, 2023, 59(12): 77-83.

References

[1] 谢洋，王慧，陈国荣，等.分布式优化在智能电网经济调度问题中的应用[J].重庆工商大学学报（自然科学版），2020，37（2）：42-47.
XIE Y，WANG H，CHEN G R，et al.Application of distributed optimization method to economic dispatch in smart grid[J].Journal of Chongqing Technology and Business University（Natural Science Edition），2020，37（2）：42-47.
[2] LI X L，ER M J，YANG G，et al.Bearing-based formation manoeuvre control of nonholonomic multi-agent systems[J].International Journal of Systems Science，2019，50（16）：2993-3002.
[3] AKYILDIZ I F，SU W，SANKARASUBRAMANIAM Y，et al.A survey on sensor networks[J].IEEE Communications Magazine，2002，40（8）：102-114.
[4] REN W，BEARD R W.Consensus seeking in multiagent systems under dynamically changing interaction topologies[J].IEEE Transactions on Automatic Control，2005，50（5）：655-661.
[5] SINHA A，MISHRA R K.Consensus in first order nonlinear heterogeneous multi-agent systems with event-based sliding mode control[J].International Journal of Control，2020，93（4）：858-871.
[6] LI C G，LIU G D，LOU K.Quantized flocking control of multiple agents with second-order dynamics[J].Control and Decision，2015，30（3）：541-545.
[7] LI H Q，LIAO X F，HUANG T W，et al.Event-triggering sampling based leader-following consensus in second-order multi-agent systems[J].IEEE Transactions on Automatic Control，2014，60（7）：1998-2003.
[8] ALTAFINI C.Consensus problems on networks with antagonistic interactions[J].IEEE Transactions on Automatic Control，2012，58（4）：935-946.
[9] MENG D Y，DU M J，JIA Y M.Interval bipartite consensus of networked agents associated with signed digraphs[J].IEEE Transactions on Automatic Control，2016，61（12）：3755-3770.
[10] WANG H，YU W W，WEN G H，et al.Finite-time bipartite consensus for multi-agent systems on directed signed networks[J].IEEE Transactions on Circuits and Systems I：Regular Papers，2018，65（12）：4336-4348.
[11] LIU F，SONG Q，WEN G H，et al.Bipartite synchronization in coupled delayed neural networks under pinning control[J].Neural Networks，2018，108：146-154.
[12] ZHU W，JIANG Z P.Event-based leader-following consensus of multi-agent systems with input time delay[J].IEEE Transactions on Automatic Control，2014，60（5）：1362-1367.
[13] QIAN Y F，WU X Q，Lü J H，et al.Consensus of second-order multi-agent systems with nonlinear dynamics and time delay[J].Nonlinear Dynamics，2014，78（1）：495-503.
[14] FENG Z，HU G Q.Secure cooperative event-triggered control of linear multiagent systems under DoS attacks[J].IEEE Transactions on Control Systems Technology，2019，28（3）：741-752.
[15] 刘坤，马书鹤，马奥运，等.基于机器学习的信息物理系统安全控制[J].自动化学报，2021，47（6）：1273-1283.
LIU K，MA S H，MA A Y，et al.Secure control for cyber-physical systems based on machine learning[J].ACTA Automatica Sinica，2021，47（6）：1273-1283.
[16] YE D，YANG X.Distributed event-triggered consensus for nonlinear multi-agent systems subject to cyber attacks[J].Information Sciences，2019，473：178-189.
[17] HU A H，PARK J H，CAO J D，et al.Event-triggered bipartite consensus over cooperation-competition networks under DoS attacks[J].Science China Technological Sciences，2021，64（1）：157-168.
[18] XU Y，FANG M，SHI P，et al.Event-based secure consensus of multiagent systems against dos attacks[J].IEEE Transactions on Cybernetics，2020，50（8）：3468-3476.
[19] LU A Y，YANG G H.Distributed consensus control for multi-agent systems under denial-of-service[J].Information Sciences，2018，439：95-107.
[20] ZHANG X M，HAN Q L，GE X，et al.Resilient control design based on a sampled-data model for a class of networked control systems under denial-of-service attacks[J].IEEE Transactions on Cybernetics，2020，50（8）：3616-3626.
[21] LIU F，SONG Q，WEN G H，et al.Bipartite synchronization of Lur’e network under signed digraph[J].International Journal of Robust and Nonlinear Control，2018，28（18）：6087-6105.
[22] REN J，SONG Q，LU G P.Event-triggered bipartite leader-following consensus of second-order nonlinear multi-agent systems under signed digraph[J].Journal of the Franklin Institute，2019，356（12）：6591-6609.
[23] DONG T，GONG Y L.Leader-following secure consensus for second-order multi-agent systems with nonlinear dynamics and event-triggered control strategy under DoS attack[J].Neurocomputing，2020，416：95-102.
[24] SHANG Y，LIU C L，CAO K C.Event-triggered consensus control of second-order nonlinear multi-agent systems under denial-of-service attacks[J].Transactions of the Institute of Measurement and Control，2021，43（10）：2272-2281.
[25] HALE J K，LUNEL S M V.Introduction to functional differential equations[M].New York：Springer Science & Business Media，2013：151-161.