A data-driven approach for influencing consensus networks

In this paper, we examine data-driven aspects of consensus networks influenced by a stubborn agent. In particular we show that the judicious placement of the stubborn agent can be achieved based on snapshots of the data generated by the network through estimating the appropriate eigenvector of the perturbed Laplacian matrix. The exact dynamic mode decomposition algorithm is employed for estimating the spectral properties of the network and we show that the dominant eigenvector can be determined if the rank of data snapshots is equal to the number of eigenvalue clusters of the perturbed Laplacian. Lastly, for large-scale networks, we provide a simple data-driven algorithm for approximating the spectral properties of the network.