2015/03/27 by Mu Yang, Yang, Mu, Choon Yik Tang +1
Computer Science · Physics and Astronomy · #Distributed #Distributed Control Multi-Agent Systems #FOS: Computer and information sciences #FOS: Electrical engineering #Neural Networks Stability and Synchronization #Opinion Dynamics and Social Influence #Parallel #Systems and Control (eess.SY) #and Cluster Computing (cs.DC) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1503.08192
openalex publication_date 2015/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this paper, we develop a two-stage distributed algorithm that enables nodes in a graph to cooperatively estimate the spectrum of a matrix W associated with the graph, which includes the adjacency and Laplacian matrices as special cases. In the first stage, the algorithm uses a discrete-time linear iteration and the Cayley-Hamilton theorem to convert the problem into one of solving a set of linear equations, where each equation is known to a node. In the second stage, if the nodes happen to know that W is cyclic, the algorithm uses a Lyapunov approach to asymptotically solve the equations with an exponential rate of convergence. If they do not know whether W is cyclic, the algorithm uses a random perturbation approach and a structural controllability result to approximately solve the equations with an error that can be made small. Finally, we provide simulation results that illustrate the algorithm.