2018/01/23 by Masaki Ogura, Junpei Tagawa, Naoki Masuda
Computer Science · Mathematics · #Class (philosophy) #Convergence (economics) #Cooperative Communication and Network Coding #Distributed Control Multi-Agent Systems #Eigenvalues and eigenvectors #Exponential growth #Matrix (chemical analysis) #Neural Networks Stability and Synchronization #Protocol (science) #Rate of convergence #cs.SI #math.OC
paper · pdf · doi:10.23919/acc.2018.8431658
arxiv created 2018/01/23 · openalex created_date 2018/02/02 · openalex publication_date 2018/06/01 · arxiv updated 2019/03/19 · openalex updated_date 2026/08/05
In this paper, we investigate asymptotic properties of a consensus protocol taking place in a class of temporal (i.e., time-varying) networks called the activity driven network. We first show that a standard methodology provides us with an estimate of the convergence rate toward the consensus, in terms of the eigenvalues of a matrix whose computational cost grows exponentially fast in the number of nodes in the network. To overcome this difficulty, we then derive alternative bounds involving the eigenvalues of a matrix that is easy to compute. Our analysis covers the regimes of 1) sparse networks and 2) fast-switching networks. We numerically confirm our theoretical results by numerical simulations.