Distributed consensus over digital networks with limited bandwidth and time-varying topologies

In this paper, we consider discrete-time distributed average-consensus with limited communication data-rate and time-varying communication topologies. We design a distributed encoding-decoding scheme based on quantization of scaled innovations and a control protocol based on a symmetric compensation method. We develop an adaptive scheme to select the numbers of quantization levels according to whether the associated channel is active or not. We prove that if the network is jointly connected, then under the protocol designed, average-consensus can be asymptotically achieved, and the convergence rate is quantified. Especially, if the duration of any link failure in the network is bounded, then the control gain and the scaling function can be selected properly such that 5-level quantizers suffice for asymptotic average-consensus with an exponential convergence rate.