# Resilient Consensus Control for Multi-Agent Systems: A Comparative Survey
## 3 Resilient Control for MASs
### Spoofing Attack
When the \(F\)-local hypothesis is no longer satisfied--that is, when the number of attacks is uncertain--as long as \(\mathcal{G}_{T}(k)=(\mathcal{V},\mathcal{E}_{T}(k))\) has a spanning tree and the root node only has a trust entry edge, consensus can also be achieved. Since spoofing attacks involve the operation of communication data, they are generally more difficult to deal with than DoS attacks that truncate channels. On the one hand, according to the constraint conditions of the attack, the transmission frequency of the control signal and the coupling strength of the communication topology can be designed, and the distributed pulse control can be used to achieve the certain state synchronization. However, the restrictions on the attack situation are generally strong and conservative; On the other hand, a filtering algorithm can be designed to exclude data values suspected of tampering. After this, a secure state update can be carried out, but the corresponding topology needs to be specially constructed. At the same time, since the algorithm can only screen out problematic extreme values, it may be difficult to deal with more complex attacks. In addition, there are also methods performing security control through state observation [72]. Ref. [60] establishes an observer based on the Kalman filter and realizes the system mean square consensus under the influence of Gaussian white noise and FDI attack. Different from the former, while observing, it also proposes a threshold comparison scheme to decide whether to use the observed value as the input of the next time step, as shown in Figure 4:When the difference between the actual value of the state \(\tilde{x}_{j}(k)\) and the observed value \(\hat{x}_{j}^{i}(k)\) does not meet the preset threshold, observation will be enabled for control. That is,  
\[x_{i}(k+1)=x_{i}(k)-e\sum_{j=0}^{N}ll_{ij}(k)[\theta_{ij}(k)\tilde{x}_{j}(k)+(1- \theta_{ij}(k))\hat{x}_{j}^{i}(k))]+\omega_{i}(k), \tag{34}\]  
\[\theta_{ij}(k)=\left\{ \begin{array}{rl}&1,\;\text{if}\|\hat{x}_{j}(k)-\hat{x }_{j}^{i}(k)\|\leq\phi(k)\\ &0,\;\text{otherwise}.\end{array} \right. \tag{35}\]  
However, the observer embedded in each agent contains the information of system dynamics structure and communication topology. The control structure is thus not completely distributed. Ref. [73] studies the detection and identification of physical faults and FDI attacks and designs an exception handling mechanism with independent detector and cooperative detector through a \(H_{\text{so}}\) multi-objective optimization method. The former is used to judge whether faults and attacks exist, and the latter is used to distinguish the two kinds of anomalies. At the same time, it puts forward the concept of intermediary centrality, which well describes the possibility of different topological edges being attacked so that detection resources can be reasonably allocated. Then, sensitivity and accuracy can be improved. However, there is a compromise between the accuracy and the robustness of the system to disturbances. Ref. [74] obtains the necessary and sufficient conditions for the system under FDI attack to lose security consensus, according to which the prediction error can be set to an arbitrary value by bypassing the detection mechanism. Ref. [75] constructs a distributed filter against spoofing attacks by using a network composed of sensors of itself and of neighbors. Starting from the characteristic that both belong to opposite side attacks, ref. [76] studies the discrete-time stochastic system under DOS attack and deception attack and achieves consensus through event-triggered control. Ref. [77] gives a detection structure based on a neural network to judge whether the system is attacked by FDI. Ref. [78] proposes the concept of \"competitive interaction\" to design a flexible and cooperative control mechanism to achieve consensus under FDI attacks.