On Average Consensus Over Stochastically Switching Directed Topologies
Average consensus is a canonical problem in wireless sensor networks. Wireless communication channels exhibit stochastic data loss due to multiple reasons including fading and interference. This note considers average consensus algorithms executed over communication topologies that vary probabilistically due to such effects. It is known that even in this case the state values will reach consensus under fairly weak conditions. However, if the communication graph at every time step is not balanced, the consensus value is a random variable. The primary contribution of this note is to provide concentration bounds for the distance of the state vector from the consensus subspace and for the asymptotic distribution of the consensus value.