Focused First-Followers Accelerate Aligning Followers with the Leader in Reaching Network Consensus

Abstract This paper proposes and analyzes a new strategy to accelerate the process of reaching consensus in leader-follower networks. By removing or weakening specific directed couplings pointing to the first followers from the other followers, we prove that all the followers' states converge faster to that of the leader. This result is in sharp contrast to the well known fact that when the followers are coupled together through undirected links, removing or weakening links always decelerate the converging process. Simulation results are provided to illustrate this subtle, yet somewhat surprising, provably correct result.