Distributed Event-triggered Consensus for Multi-agent Systems with Directed Topologies

In this paper, we study consensus problem of multi-agent system in networks with directed topology by event-triggered feedback control. We propose three distributed criteria to determine the next observation time of each agent triggered by its in-neighbours' information and its own states. We prove that if the network topology has a spanning tree, then under these event-triggered principles, the multi-agent system reaches consensus with the consensus value equals to a weighted average of all agents' initial values. These principles do not need any a priori knowledge of any global parameters for each agent, and the Zeno Behaviours can be excluded in the last two principles. In addition, these results are extended to the case of self-triggered control, in terms of that the next triggering time of each agent is predicted based on the states at the last event time, which implies that the system states are not be monitored in a simultaneous way. The effectiveness of the theoretical results is illustrated by a numerical example.