Sufficient conditions for accelerated consensus over random networks

Multiple autonomous agents measuring the same phenomenon and communicating randomly among themselves may or may not reach an agreement in finite time depending on the system design and communication pattern. We exploit here the consensus concept for investigating if and how such a collective agreement among agents can be accelerated. Indeed an accelerated consensus has many benefits for situations where time is critical such as emergency response or surveillance teams made of geographically dispersed network agents. Specifically we look at accelerating consensus of random networks made of independent agents with unidirectional (one-way) communication capabilities. In particular we propose a sub-network consensus concept and show how the proposed scheme relates to a lower bound for the conventional network state variance. Also we derive sufficient conditions for accelerating consensus through the manipulation of information relevance, which can be associated to the edge weights of a directed graph.