Edge-event-based multi-agent consensus with Zeno-free triggers under synchronized/unsynchronized clocks

In this paper, we present novel edge-event-based triggering algorithms to achieve multi-agent consensus with Zeno-free triggers. The control inputs and triggering conditions for each agent are designed based only on relative state measurements in each agent's own local coordinate system. The existence of strictly positive minimal inter-event times guarantees the elimination of Zeno behaviour. Two cases, namely the synchronized clock case and the unsynchronized clock case, are studied. In the synchronized clock case, all agents are activated simultaneously to measure the relative state information over edge links under a global clock. Edge events are defined and their occurrences trigger the update of control inputs for the two agents sharing the link. We show that average consensus can be achieved with our proposed algorithm. In the unsynchronized clock case, each agent executes control algorithms under its own clock which is not synchronized with other agents' clocks. An edge event only triggers control input update for an individual agent. Detailed explanations and analysis are provided to show that all agents will reach consensus in a totally asynchronous manner. Numerical simulations are given to verify the effectiveness of the proposed algorithms.