Average Consensus Over Time-Varying Directed Graphs With Broadcast Communication

This paper proposes a novel protocol for achieving arithmetic average consensus over time-varying directed graphs using broadcast-only communication, where agents cannot selectively address out-neighbors. The proposed approach extends existing methods to compute the dominant left eigenvector of an infinite product of time-varying row-stochastic matrices in a fully distributed manner. By leveraging a local rescaling strategy, our algorithm ensures that agents autonomously compute correction offsets that drive the consensus value toward the arithmetic average of their initial states. The method circumvents the impractical requirement of point-to-point communication and eliminates the need for column stochastic normalization of the weights, which requires each node to know its local out-neighborhood; the proposed method only imposes a mild requirement on knowing an upper bound on the total number of agents. Theoretical convergence guarantees are provided, and simulations confirm the solution’s effectiveness.