A Resistance Distance-Based Approach for Optimal Leader Selection in Noisy Consensus Networks
Provides theoretical insights and analytical solutions for optimal leader placement in noisy consensus networks, relevant to control and network theory.
The paper studies leader-follower consensus networks, showing that coherence (an H2 norm measuring tracking performance) relates to electrical resistance distances. It provides closed-form expressions for coherence and analytical solutions for optimal leader selection in special graph classes.
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, we show a relationship between the coherence and resistance distances in an a electrical network. Using this relationship, we derive closed-form expressions for coherence as a function of the locations of the leaders. Further, we give analytical solutions to the optimal leader selection problem for several special classes of graphs.