Self-triggered consensus for multi-agent systems with Zeno-free triggers

In this technical note, a self-triggered consensus algorithm for multi-agent systems has been proposed. Each agent receives the state information of its neighbors and computes the average state of its neighborhood. Based on this average state the event trigger is designed to determine when the agent updates its control input and transmits the average state to its neighbors. By specifying a strictly positive minimal inter-event time for each agent, Zeno behavior can be avoided. Then by solving quadratic equations related to the event condition, the self-triggered consensus algorithm is developed by directly computing the event time instants with a set of iterative procedures. It has been proved that with the proposed 'Zeno-free' algorithm the agent group can achieve consensus asymptotically. Compared with the existing works, the proposed algorithm is simpler in formulation and computation. Moreover, it has been showed that agents need less time to achieve consensus with considerable reduction of the number of triggering events, controller updates and information transmission. As a result, more energy can be saved using the proposed algorithm in practical multi-agent systems.