SCIENCE CHINA Information Sciences, Volume 63 , Issue 5 : 150208(2020) https://doi.org/10.1007/s11432-019-2687-7

Event-trigger-based consensus secure control of linear multi-agent systems under DoS attacks over multiple transmission channels

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  • ReceivedMar 26, 2019
  • AcceptedSep 23, 2019
  • PublishedMar 13, 2020


This paper proposes a consensus secure control scheme in the presence of denial-of-service (DoS) attacks based on an event-trigger mechanism.In contrast to a scenario in which attacks are the same and simultaneously paralyze all channels, the DoS attack addressed in this paper occurs aperiodically and results in the independent interruption of multiple transmission channels.A sufficient condition for the attack duration is designed and a distributed event-triggered control scheme is proposed,where the updated instants are triggered aperiodically to reduce the required communication resources.It is shown that the overall system is stable with the proposed scheme according to the Lyapunov stability theory and that Zeno behavior is excluded.Finally, a numerical example is presented to verify the effectiveness of the proposed scheme.


This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61873130, 61833008, 61833011, 61803210), Natural Science Foundation of Jiangsu Province (Grant No. BK20191377), Jiangsu Government Scholarship for Overseas Studies (Grant No. 2017-037), and 1311 Talent Project of the Nanjing University of Posts and Telecommunications.


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  • Figure 1

    (Color online) A schematic of DoS attacks.

  • Figure 2

    (Color online) Time sequences of the DoS attacks.

  • Figure 3

    Communication graph.

  • Figure 4

    (Color online) DoS attacks.

  • Figure 5

    (Color online) Internal states $x_{i,j}$, $i=1,2,3$ and $j=1,2$.

  • Figure 6

    (Color online)Control inputs $u_{i}$, $i=1,2,3$.

  • Figure 7

    (Color online) Triggered events.

  • Table 1   Decay rates $\alpha_{\Omega}$ under different attack conditions
    Attack conditionAlgebra condition$\alpha_{\Omega}$
    $|\Omega|=0,1$$L_{\Omega}\neq~L$, $\lambda_{\min}(\Lambda_{L_{0}}-\Lambda_{L_{\Omega}})\!\neq\!0$$-$0.141
    $|\Omega|=2$$L_{\Omega}\neq~L$, $\lambda_{\min}(\Lambda_{L_{0}}-\Lambda_{L_{\Omega}})\!=\!0$ 0.407
  • Table 2   Performance comparison for different triggered functions
    Function Control Updated numbers of agentsMinimum Maximum
    cmidrule3-5 scheme 1 2 3 inter-event timeinter-event time
    [27,28,40-42] $\varpi~_{i}~(t)=0,~\psi~_{i}(t)~=0$1822 1899 1643 0.01 1.49
    [38,39] $\varpi_{i}~(t)\neq~0,~\psi~_{i}(t)~=0$ 709 688 676 0.02 1.54
    [35] $\varpi~_{i}~(t)=0,~\psi~_{i}(t)~\neq~0$1364 1271 1122 0.01 1.49
    Our paper $\varpi~_{i}~(t)\neq~0,~\psi~_{i}(t)~\neq~0$ 611 570 560 0.02 1.54

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