Consensus seeking 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 with digital channels. This paper is concerned with the problem of seeking consensus via quantized information communication over a general unbalanced directed digital network. It is established that, by designing a protocol with a finite-level uniform quantization scheme, merely one bit quantized information transmitted along each connected digital channel suffices for achieving weighted average consensus with an exponential convergence rate, as long as the directed unbalanced network is strongly connected. An explicit characterization of the convergence rate of consensus is also given. By avoiding the double stochasticity assumption on the update matrix, the proposed quantized protocol is particularly suitable for the scenarios where no bidirectional and/or balanced information communication among agents is available.