Average consensus on arbitrary strongly connected digraphs with dynamic topologies

We have recently proposed a “surplus-based” algorithm which solves the multi-agent average consensus problem on general strongly connected and static digraphs. The essence of that algorithm is to employ an additional variable to keep track of the state changes of each agent, thereby achieving averaging even though the state sum is not preserved. In this paper, we extend this approach to the more challenging case of dynamic digraphs, and consider both deterministic and randomized (of the gossip type) time-varying scenarios. For each scenario, we design an extended surplus-based algorithm and derive a necessary and sufficient graphical condition which guarantees state averaging. In the deterministic time-varying case, the digraphs should be strongly connected in a joint sense; and in the randomized gossip case, the digraphs in the mean should be strongly connected. In particular, these conditions do not impose “balanced” or “symmetric” requirements on the network topology, and are therefore more general than those previously reported in the literature.