Almost Sure Resilient Consensus Under Stochastic Interaction: Links Failure and Noisy Channels

The resilient consensus problem over a class of discrete-time linear multiagent systems is addressed. Because of external cyber-attacks, some agents are assumed to be malicious and not following a desired cooperative behavior. Thus, the objective consists in designing a control strategy for the healthy agents to reach consensus upon their state vectors, while due to interaction among the agents, the malicious agents try to prevent them to achieve consensus. Although this problem has been investigated by some researchers, under the existing approaches in the literature, achieving consensus is only guaranteed when the information exchange among the agents is deterministic. Based on this motivation, the main contribution of the paper is on almost sure resilient consensus control of a network of healthy agents in the presence of stochastic links failure and communication noises. We design a discrete-time protocol for the set of the healthy agents, and we show that under some probabilistic conditions on interaction among the agents, achieving almost sure consensus among the healthy agents can be guaranteed. The results also are verified by numerical examples.