Distributed Finite-Time Average Consensus Over Unbalanced Digraphs via Broadcast Mode

This article addresses the average consensus problem in multiagent system (MAS) with directed communication links. Existing finite-time average consensus algorithms for unbalanced digraphs require each agent to have at least knowledge of its out-degree (due to the requirement of column-stochastic weights). In contrast, our broadcast-based algorithm only requires the weight matrix (i.e., the update matrix of the diffusively coupled MAS) with equal row sums, but at the expense of additional iterations for the left eigenvector computation. The algorithm leverages the notion of "minimal polynomial of a matrix pair" associated with the graph node. We prove the reachable condition of average consensus, which ensures that agents find the average of initial values in a finite time on arbitrary strongly connected digraphs. A distributed synchronous termination principle is proposed and embedded in two calculation stages (including left eigenvector calculation and average value calculation) to terminate the iterative process. In addition, we present the extensions of our algorithm in switching networks and noisy networks.