Average consensus with limited data rate and switching topologies

This paper is concerned with discrete-time distributed average-consensus with limited communication data-rate and switching communication topologies. We design a distributed encoding-decoding scheme based on difference quantization with dynamic scaling and a control protocol based on a symmetric compensation method. We develop an adaptive scheme to select the numbers of quantization levels. The number of quantization levels of each quantizer is tuned on-line according to whether the associated communication channel is active or not at the last step. We prove that if the network is jointly connected, then under the protocol designed, average-consensus can be asymptotically achieved without steady-state error, and the convergence rate is quantified. Especially, if the duration of link failures of all communication channels 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.