# Resilient Consensus Control for Multi-Agent Systems: A Comparative Survey
## 3 Resilient Control for MASs
### DoS Attack  
Network attacks can be divided into point attacks (agent dynamic behavior) and edge attacks (topology communication behavior) according to the attacked object. The former can be seen as the attacked agent being \"moved out\" of the topology [34], while the DoS attack belongs to the latter. That is, the control/measurement transmission channel is truncated by the attack, so that the target agent cannot obtain the signal, thereby damaging the availability of information, as shown in Figure 1. The DoS attack can be implemented by the attackers in several ways: filling buffers in a user or the kernal domain, blocking or jamming the communication among key components, and altering a routing protocol. Refs. [26; 27; 30; 35], respectively, analyze the DoS attack in the form of centralized control and distributed control. Due to the excellent robustness of the latter, it has a broader theoretical exploration prospect than the former, but there is less relevant research at present. Researchers usually simulate the impact of the attack on the system through packet loss, serious delay or communication interruption. With the gradual progress of research, the hypothetical limitation of DoS attack model has been issued from the period known in advance [36] and gradually relaxed to the random occurrence mechanism of [30; 31]. Generally speaking, the attack energy is always limited; that is, there is a period of energy accumulation time between adjacent attacks, which is called sleep time. During this period, communication can be carried out normally. If the sleep time is too short, the system will not be able to complete the transmission of control signals and the update of state values in time when the input information is lost for a long time, which may cause the irreparable loss of consensus. In existing studies, in order to avoid the above extreme attacks, the attack frequency \(F_{a}\) and attack duration \(T_{a}\) of DoS attacks are generally limited according to the designed control structure parameters [30; 31; 32; 33; 37; 38]. Their definitions in the time period \([T_{1},T_{2})\) are as follows:  
\[F_{a}(T_{1},\ T_{2})=\frac{N_{a}(T_{1},\ T_{2})}{T_{2}-T_{1}}, \tag{5}\]  
\[T_{a}(T_{1},\ T_{2})\leq T_{0}+\frac{T_{2}-T_{1}}{\tau_{0}}, \tag{6}\] \begin{table}
\begin{tabular}{c c} \hline \hline Limitations of information & DoS attack, Byzantine attack, spoofing attack, \\ interaction level & repay attack, police attack, communication attack \\ \hline Limitations of system level & Actuator attack \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Classification of common cyber attacks of MASs. Figure 1: Multi-agent systems under DoS attack. DoS attacks may occur on the sensor–controller channel or the controller–actuator channel, affecting the transmission of system output signals and control signals, respectively. Hacker can also launch DoS attacks that can be independent of each other on different agents. where \(N_{a}\) denotes the attack number in the time period \([T_{1},T_{2})\), \(T_{2}\geq T_{1}\geq t_{0}\); \(T_{0}>0\) and \(\tau_{0}>1\) are scalars. DoS attacks can paralyze the communication between agents, making the target agent unable to obtain the state information of the neighbor agents, thus, increasing the state error of the system. The trigger function of the event-triggered control mechanism is generally related to the state error, which can effectively judge the divergence of the system state error under the DoS attack, and can timely suppress the error divergence behavior. Therefore, the security control under DoS attack is mostly associated with the event-triggered mechanism [39]. While realizing flexible control, compared with periodic sampling control, it is more conducive to saving communication resources and avoiding network congestion. The event-triggered mechanism was proposed in [40,41] and then widely used in [31,42, 43, 44].