Reaching consensus in unbalanced networks with coarse information communication

Abstract

This paper is concerned with the problem of seeking consensus for a network of agents under a fixed or switching directed communication topology. Each agent is modeled as discrete-time first-order dynamics and interacts with its neighbors via logarithmically quantized information. We assume that the digraph is not necessarily balanced and, thus, avoiding the double stochasticity requirement for the adjacency matrix. For the case of a fixed topology that is strongly connected, it is shown that the proposed protocol is admissible for arbitrarily coarse logarithmic quantization and the β-asymptotic weighted-average consensus is achieved. For the case of a switching topology that is periodically strongly connected, it is shown that the proposed protocol is admissible for arbitrarily coarse quantization and the β-asymptotic consensus is achieved. Furthermore, for both cases, not only are the convergence rates for consensus specified but also the bounds on the consensus error that highlight their dependence on the sector bound β of the logarithmic quantizer are also provided. Copyright © 2015 John Wiley & Sons, Ltd.