Asymptotically unbiased average consensus under measurement noises and fixed topologies

This paper is concerned with average-consensus control under directed topologies and random measurement noises. To attenuate the measurement noises, time-varying consensus gains are introduced in the protocol. It is shown that under the protocol designed, all agents' states converge to a common Gaussian random variable, whose mathematical expectation is just the average of the initial states, and the mean square static error vanishes as the number of agents increases to infinity under certain topologies. In addition, for the noise-free case, necessary and sufficient conditions are given on the network topology and consensus gains to achieve average-consensus; and for the noisy measurement case, by combining algebraic graph theory and stochastic analysis, necessary and sufficient conditions are given on the consensus gains to achieve asymptotically unbiased mean square average-consensus.