# Resilient Consensus Control for Multi-Agent Systems: A Comparative Survey
## 3 Resilient Control for MASs
### Byzantine Attack
If the research object of scheme three is a heterogeneous system, it needs to use adaptive control structure or output feedback control structure to adjust under the premise of considering sensor error. The introduction of the concept of topology robustness gradually extends the deployment conditions of attack coping strategies to the communication structure, which can be achieved by modifying on the original topology [79] or constructing a special k-cycle graph [80]. Most of the existing research refers to the mean subsequence reduction (MSR) algorithm under the branch of distributed fault-tolerant control algorithm in the computer field to screen out the state values. However, it can only screen out the state variables with extreme values and has no ability to detect abnormal state values. In order to ensure that the screened state sequence still retains enough state quantity to maintain normal operation, the MSR algorithm generally needs to be applied in combination with graph robustness theory. At the same time, the concept of \"\(F\)-total\" and \"\(F\)-local\" should be used to limit the maximum number of malicious agents in the system [71]. In fact, the \(F\)-local type Byzantine model can be transformed into the above \(F\)-local type deception attack model as long as the outgoing edge of the Byzantine node is regarded as suffering from a substitution type deception attack. Otherwise, it is not true. In the absence of external input, the final state value of the consensus achieved by this method always falls in a convex hull composed of the initial state value of the normal agents [81]; this final value will be affected by the behavior of the malicious agent. For the leadership system, the ideal situation is to track the leader's state reference value by followers while shielding the impact of attacks. However, since the reference value may not fall into the above convex hull, further improvement is required. Ref. [82] uses the modified sliding window MSR algorithm to solve the problem of elastic inclusion control in multi-leader systems and successfully makes followers track  
Figure 5: The diagram of a Byzantine attack. When the communication topology of agent \(i\) meets certain conditions, each follower \(x_{i}\) can not only directly receive the data of neighbor agent \(x_{j}\) (\(a_{ij}\
eq 0\)), but also directly receive data from leaders \(x_{l}\) (\(l_{ij}\
eq 0\)) and adversarial agents \(x_{k}\) (\(h_{ik}\
eq 0\)). It is worth noting that the abnormal state information sent by \(x_{k}\) may lead the system to an unexpected direction or even cause the system to crash. leaders whose state values are outside the convex hull. The parameter \(F\) in the algorithm is the corresponding parameter \(F\) in the \(F\)-local model to limit the maximum number of malicious agents. The time window loosens the robustness requirements of the topology map and no longer requires robustness to be maintained at every time step. It can be proved that, under the condition that graph \(\mathcal{G}(T)\) has strong \((T,t_{0},2F+1)\) robustness to the leader set \(\mathcal{L}\), the system can track the leader state values outside the upper convex hull. This is because the robustness of the topology ensures that there is at least one state value of a normal leader in the filtered state value sequence. Since the design of MSR algorithm needs to obtain the maximum number \(F\) of malicious agents in advance, the control protocol is not completely distributed. At the same time, the controller puts forward robustness requirements for communication topology, which makes the controller unsuitable for large-scale MASs. In the context of the security consensus of MAS on network attacks, in [83] for Byzantine attacks, two improved schemes based on MSR algorithm which relax the strict restrictions of the algorithm on network topology, improve the convergence speed of the system and solve the compatibility problem with clock synchronization are proposed. Ref.