Resilient consensus of second-order agent networks: Asynchronous update rules over robust graphs

In this paper, we study the problem of resilient consensus of sampled-data multi-agent networks with doubleintegrator dynamics. The term resilient points to the presence of faulty agents in the network. Each normal agent updates its state based on a predetermined control law using its neighbors´ information while misbehaving agents make updates arbitrarily and might threaten the consensus within the network. Assuming that the maximum number of malicious agents in the network is known, we focus on an algorithm where each normal agent ignores large and small position values among its neighbors to avoid being influenced by malicious agents. We address this problem in both synchronous and asynchronous cases with an emphasis on networks of vehicles and present topological conditions in terms of graph robustness.