On Sampled-Data Consensus: Divide and Concur

This note studies the consensus problem for integrator agents under intermittent information exchange between connected neighbours at asynchronous sampling time instances. It proposes a novel sampled-data protocol, based on emulating suitable global analog consensus dynamics at each agent and using sampled centroids of these emulators to convey information between agents. We show that the closed-loop dynamics can be divided into centroid and disagreement parts. The former is completely autonomous and evolves according to time-varying discrete consensus dynamics, independent of the sampling intervals. The disagreement part evolves according to conventional analog consensus dynamics for a constant network topology and is driven by the emulator centroids. The system then asymptotically converges to agreement under mild assumptions on the persistency of connectivity and the uniform boundedness of sampling intervals. A substantially simplified and scalable implementation under a special emulated topology, namely the complete graph, is also proposed.