A Distributed Strategy to Detect When to Stop the Continuous-Time Average Consensus Protocol

Continuous-time average consensus protocols have been deeply analyzed in recent years. This kind of protocols enable the network to reach the agreement on the average of the initial conditions in a fully distributed way. Moreover, the convergence of such protocols is proved to be asymptotic. However, several applications need the network to reach the agreement in finite time. On the other hand, often a convergence to a ball centered at the average value is sufficient in most application contexts. In this paper, a method for distributively detecting when the continuous-time average consensus protocol has reached the agreement within a given error margin is presented. This distributed detection takes finite time and occurs at each node simultaneously. Numerical results show the effectiveness of the proposed approach.