Distributed consensus over directed networks with limited information communication

Existing works that deal with the problem of distributed average consensus with quantized information communication assume that the update matrices are doubly stochastic, which amounts to agents evolving on balanced directed networks. Thus, the resulting quantized average consensus protocols are not applicable to directed networks with unbalanced topology. This paper is concerned with the problem of seeking consensus via quantized information communication over a general unbalanced directed network. It is established that, by designing a protocol with a finite-level uniform quantized scheme, merely one bit quantized information transmitting along each connected directed channel suffices for achieving weighted average consensus with an exponential convergence rate, as long as the directed network is strongly connected. An explicit characterization of the convergence rate is also given.