Average Consensus in the Presence of Dynamically Changing Directed Graph Topologies and Time Delays

We have recently proposed a robustified ratio consensus algorithm which achieves asymptotic convergence to the global average in a distributed fashion in static strongly connected digraphs, despite the possible presence of bounded but otherwise arbitrary delays. In this work, we propose a protocol which reaches asymptotic convergence to the global average in a distributed fashion under possible changes in the underlying interconnection topology (e.g., due to component mobility), as well as time-varying delays that might affect transmissions at different times. More specifically, we extend our previous work to also account for the case where, in addition to arbitrary but bounded delays, we may have time varying communication links. The proposed protocol requires that each component has knowledge of the number of its outgoing links, perhaps with some bounded delay, and that the digraphs formed by the switching communication topologies over a finite time window are jointly strongly connected.