A Resistance-Distance-Based Approach for Optimal Leader Selection in Noisy Consensus Networks

摘要

We study the performance of leader-follower noisy consensus networks and, in particular, the relationship between this performance and the locations of the leader nodes. Two types of dynamics are considered: 1) noise-free leaders, in which leaders dictate the trajectory exactly and followers are subject to external disturbances and 2) noise-corrupted leaders, in which both leaders and followers are subject to external perturbations. We measure the performance of a network by its coherence, an H-2 norm that quantifies how closely the followers track the leaders' trajectory. For both dynamics, there is a relationship between the coherence and resistance distances in an electrical network. Using this relationship, we derive closed-form expressions for coherence as a function of the locations of the leaders, and we give analytical solutions to the optimal leader selection problem for several classes of graphs.