# An Overview on Denial-of-Service Attacks in Control Systems: Attack Models and Security Analyses
## 5 An Overview of Attack-Resilient Control and Communication Techniques
### Resilient Communication Techniques
#### 5.2.1 Self-Triggered and Randomized Communication Techniques in Multi-Agent Consensus  
In [71; 73], the authors explored the multi-agent consensus problem in Section 2.3, where the network is subject to jamming attacks. In those works, one of the deterministic attack models discussed in Section 3.1 is utilized, and a self-triggered communication rule is developed. The utility of the self-triggered approach is that with self-triggering, inter-agent communications are asynchronous and agents are not required to possess synchronized clocks. Furthermore, the self-triggered communication technique provides resiliency against a large class of attack strategies.  
In the self-triggered communication technique, the \((k+1)\)th communication attempt time \(t^{i}_{k+1}\) for the agent \(i\) is determined based on the information available to agent \(i\) at time \(t^{i}_{k}\). If the \(i\) agent knows its neighbors' values at time \(t^{i}_{k}\), then it uses this information in designing the next communication attempt time \(t^{i}_{k+1}\). If, on the other hand, no information is available at \(t^{i}_{k}\) (due to jamming attacks), the \(i\)th agent sets the waiting time until \(t^{i}_{k+1}\) to be a fixed duration.  
The minimum interval between consecutive communication attempts of all agents is given in [71] by \(\Delta^{*}>0\). It is noted in [71] that consensus can be achieved under any attack strategy subject to the constraints in Equations (15) and (16) with scalars \(\rho_{\mathrm{D}}\) and \(\rho_{\mathrm{F}}\) that satisfy  
\[\rho_{\mathrm{D}}+\Delta^{*}\rho_{\mathrm{F}}<1. \tag{31}\]  
The inequality in Equation (31) guarantees that the average duration and the average frequency of attacks are sufficiently small. Note that, if the attacker can attack at a frequency that is larger than the frequency of communication attempts (i.e., \(\rho_{\mathrm{F}}>\frac{1}{\Delta^{*}}\)), then the attacker may be able to block all attempts of communication by the agents. The reason is that the attacker may actually be knowledgeable on the self-triggered mechanism used by the agents for deciding the times \(t_{k}^{i}\). This would allow the attacker to attack the network directly at those instants for very short durations. In such cases, the attacker can preserve energy and satisfy Equation (15) for arbitrarily small \(\rho_{\mathrm{D}}\).  
To achieve resilient consensus against attacks with high frequency, [72] proposed a randomized communication strategy. The key idea in the randomized setting is that the agents pick their communication times randomly (see Figure 9). In particular, each agent \(i\), first picks a deterministic interval length \(\Delta^{i}>0\). Then, for each \(k\in\mathbb{N}_{0}\), the communication attempt time \(t_{k}^{i}\) is selected as a random variable that is uniformly distributed in the interval \([k\Delta^{i},(k+1)\Delta^{i})\).  
Randomized transmissions prevent the attacker to know about future communication attempt times of agents. It is shown in [72] that consensus in the randomized communication setting is achieved if the attack constraint in Equation (15) holds with \(\rho_{\mathrm{D}}\) that satisfy  
\[\rho_{\mathrm{D}}<1. \tag{32}\]  
In other words, the randomized communication approach guarantees consensus under any attack strategy that is only constrained in its average duration as in Equation (15) regardless of its frequency.