# Resilient Consensus Control for Multi-Agent Systems: A Comparative Survey
## 3 Resilient Control for MASs
### Spoofing Attack  
A MAS can be regarded as a special cyber-physical system. Its controller not only needs to obtain data from sensors, but also needs to send control information to actuators. Network attacks may occur on the channels from a sensor to a controller and from a controller to a actuator--even the controller itself may be attacked. For attackers, in addition to interrupting the information loop, tampering with the data being used for communication can also achieve destructive effects, which is a deception attack. A spoofing attack refers to an attack in which an attacker can obtain system information and perform arbitrary operations on measurement data and control instructions. It can bypass the detection device and make the agent adopt an error value. Common false data injection (FDI) [60] attacks also fall into the scope of spoofing attacks, as well as data replay [61], data change [12] and other types of attacks. Compared with DoS attacks, deception attacks are more difficult to detect. They exist in power networks [62], smart grids [63] and other fields, which greatly threaten the integrity of data [64]. Refs. [64; 65], respectively, consider the spoofing attack on the sensor-controller channel and the controller-actuator channel. Ref. [66] uses the indicator vector to model the deception attack and discusses the situation that the attack occurs on the sensor and actuator at the same time. Generally speaking, the establishment of attack model always revolves around the change of data. Similar to DoS attacks, the research of deception attacks is generally carried out in discrete-time systems, and the control methods adopted include periodic control, event-triggered control, pulse control, etc. Among them, pulse control is more commonly used because it allows discontinuous input and has the characteristics of instantaneous jump, which is very appropriate to deal with some deceptive attacks that implement state mutation. In [67], for a Lipschitz-type nonlinear MAS under deception attack, a mean-square bounded synchronization control scheme based on distributed impulse control is proposed. Given \(i=1,\ldots,N\), the Bernoulli distribution with parameter \(\beta\) is used to model the displacement type spoofing attack behavior on the controller-actuator channel, as shown in Figure 3.  
When the attack succeeds, replace the control input signal \(u_{i}\) with an error signal \(\psi_{i}\):  
\[u_{i}(t)=c\sum_{k=1}^{\infty}(-\sum_{j=1}^{N}l_{ij}x_{j}(t)-d_{i}(x_{i}(t)-x_{l} (t)))\delta(t-t_{k}), \tag{24}\]  
\[\hat{u}_{i}(t)=\sum_{k=1}^{\infty}[\beta_{i}(t)\psi_{i}(t)+(1-\beta_{i}(t))u_{ i}(t)]\delta(t-t_{k}), \tag{25}\]  
where \(\text{Prob}\{\beta_{i}(t)=1\}=\hat{\beta}\); \(\text{Prob}\{\beta_{i}(t)=0\}=1-\hat{\beta}\); \(\delta\) denotes the Dirac pulse; \(d_{i}\) is the corresponding element value of the \(i\)-th degree matrix; \(c\) is the coupling strength, and it is assumed that \(\beta_{i}\) is independent and the attack signal is bounded: \(\|\psi(t_{k})\|^{2}\leq\psi\). For the MASs with the following nonlinear dynamics:  
\[\dot{x}_{i}(t)=Ax_{i}(t)+Bf(x_{i}(t)+\hat{u}_{i}(t)),\ i=1,\ldots,N, \tag{26}\]  
\[\dot{x}_{l}(t)=Ax_{l}(t)+Bf(x_{i}(t)), \tag{27}\]  
where \(x_{i}\) is the state of the \(i\)-th follower, \(x_{l}\) is the state of the leader and \(f(\cdot)\) is a Lipschitz type nonlinear function. The protocol defines a parameter \(\mu\), which corresponds to the Laplace matrix, degree matrix, coupling strength and attack strength. By limiting the value range of \(\mu\), the communication topology can be appropriately designed according to the attack situation. At the same time, when \(\mu\) satisfies the linear matrix inequality condition of the pulse interval parameter \(h_{2}\)--that is, when the pulse interval as well as the topological coupling coefficient match the strength of the deception attack and the attack probability--the control protocols (24) and (25) can successfully defend the deception attack and the followers (26) track the leader (27) in the mean square sense.