Graph Filter Design for Multi-Agent System Consensus

This paper revisits the problem of multi-agent consensus from a graph signal processing perspective. By defining the graph filter from the consensus protocol, we establish the direct relation between average consensus of multi-agent systems and filtering of graph signals. This relation not only provides new insights of the average consensus, it also turns out to be a powerful tool to design effective consensus protocols for uncertain networks, which is difficult to deal with by existing time-domain methods. In this paper, we consider two cases, one is uncertain networks modeled by an estimated Laplacian matrix, the other is connected graphs with unknown topology. The consensus protocols are designed by interpolation methods for both cases based on the protocol filter. Several numerical examples are given to demonstrate the effectiveness of our methods.