Resilient consensus of second-order agent networks: Asynchronous update rules with delays

We study the problem of resilient consensus of sampled-data multi-agent networks with double-integrator dynamics. The term resilient points to algorithms considering the presence of attacks by faulty/malicious agents in the network. Each normal agent updates its state based on a predetermined control law using its neighbors' information which may be delayed while misbehaving agents make updates arbitrarily and might threaten the consensus within the network. Assuming that the maximum number of malicious agents in the system is known, we focus on algorithms where each normal agent ignores large and small state values among its neighbors to avoid being influenced by malicious agents. The malicious agents are assumed to be omniscient in that they know the updating times and delays and can collude with each other. We deal with both synchronous and partially asynchronous cases with delayed information and derive topological conditions in terms of graph robustness.