Mean square average consensus of multi-agent systems with time-varying topologies and stochastic communication noises

This paper investigates the average-consensus problem of first-order discrete-time multi-agent networks in uncertain communication environments. Each agent can only use its own and neighbors’ information with stochastic communication noises to design its control input. To attenuate the noises, a distributed stochastic approximation type protocol is proposed. By using probability limit theory and algebraic graph theory, consensus conditions for this kind of protocols are obtained. A necessary and sufficient condition for mean square average-consensus is given for the case of fixed topologies; and sufficient conditions are given for the case of time-varying topologies. Especially, if the network switches between jointly-containing-spanning-tree, balanced graphs, then the designed protocol can guarantee that each individual state converges in mean square to a common random variable, whose expectation is right the average of the initial states of the whole system.