Agreeing Asynchronously: Announcement of Results

This paper formulates and solves a continuoustime version of the widely studied Vicsek consensus problem in which each agent independently updates its heading at times determined by its own clock. It is not assumed that the agents’ clocks are synchronized or that the “event” times between which any one agent updates its heading are evenly spaced. Heading updates need not occur instantaneously. Using the concept of “analytic synchronization” together with several key results concerned with properties of “compositions” of directed graphs, it is shown that the conditions under which a consensus is achieved are essentially the same as those applicable in the synchronous discrete-time case provided the notion of an agent’s neighbor between its event times is appropriately defined