  We consider resilient versions of discrete-time multi-agent consensus in the
presence of faulty or even malicious agents in the network. In particular, we
develop event-triggered update rules which can mitigate the influence of the
malicious agents and at the same time reduce the necessary communication. Each
regular agent updates its state based on a given rule using its neighbors'
information. Only when the triggering condition is satisfied, the regular
agents send their current states to their neighbors. Otherwise, the neighbors
will continue to use the state received the last time. Assuming that a bound on
the number of malicious nodes is known, we propose two update rules with
event-triggered communication. They follow the so-called mean subsequence
reduced (MSR) type algorithms and ignore values received from potentially
malicious neighbors. We provide full characterizations for the necessary
connectivity in the network for the algorithms to perform correctly, which are
stated in terms of the notion of graph robustness. A numerical example is
provided to demonstrate the effectiveness of the proposed approach.
