The Approach of k-Leader Selection in Undirected Graphs on Maximizing the Consensus Convergence Rate - Shanshan Gao; Chao Ping; Xinzhuang Chen (IEEE Access)
This paper undertakes an in-depth study and detailed analysis of the problem of the optimal selection of k leaders for a first-order leader-follower multi-agent system (MAS) whose interaction topology is an undirected graph, with the aim of achieving the maximum consensus convergence rate. The consensus performance of the MAS, which is characterized by the convergence rate, is associated with the algebraic connectivity, which is the smallest nonzero eigenvalue of the interaction topology. Firstly, with the increase in the distance between the followers and the leaders, the entries corresponding to the Fielder vector (the Laplacian eigenvector determined by the algebraic connectivity) also increases. Subsequently, the upper and lower bounds of the algebraic connectivity are obtained with the leader-induced diameter (LID) and the order of the graph. For an interaction topology of leader-follower MAS, it is shown through experiments on generated graphs that the algebraic connectivity has a negative correlation with the LID. Thus, the optimal k-leader selection problem can be approximately transformed into a metric k-center problem, i.e., select k-leader in an undirected graph so that the LID is minimum. Finally, the accuracy of the results was validated through experiments conducted on real networks.