2014/07/28 by Angelia Nedich, Ji Liu, Nedich, Angelia +1 · 1 citation
Computer Science · Mathematics · #Distributed Control Multi-Agent Systems #FOS: Mathematics #Neural Networks Stability and Synchronization #Optimization and Control (math.OC) #Optimization and Variational Analysis #math.OC
paper · pdf · doi:10.48550/arxiv.1407.7585
arxiv created 2014/07/28 · openalex publication_date 2014/07/28 · arxiv updated 2014/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper investigates the weighted-averaging dynamic for unconstrained and constrained consensus problems. Through the use of a suitably defined adjoint dynamic, quadratic Lyapunov comparison functions are constructed to analyze the behavior of weighted-averaging dynamic. As a result, new convergence rate results are obtained that capture the graph structure in a novel way. In particular, the exponential convergence rate is established for unconstrained consensus with the exponent of the order of 1-O(1/(mlog2m)). Also, the exponential convergence rate is established for constrained consensus, which extends the existing results limited to the use of doubly stochastic weight matrices.