Almost sure average consensus of multi-agent systems with time-varying topologies and stochastic communication noises

This paper is concerned with the average-consensus problem of first-order discrete-time multi-agent networks with time-varying topologies. Each agent can only receive its neighbors' state information corrupted by stochastic communication noises. To attenuate the noises, a distributed stochastic approximation type protocol is used. By using probability limit theory and algebraic graph theory, sufficient conditions are given to ensure consensus to be achieved asymptotically. Especially, if the network switches between jointly-containing-spanning-tree instantaneously balanced graphs, then the designed protocol can guarantee that each individual state converges to a common random variable almost surely. The expectation of this common variable is right the average of the initial states of the whole system.