标题：Convergence rates of discrete-time stochastic approximation consensus algorithms: Graph-related limit bounds
作者：Tang, Huaibin; Li, Tao
作者机构：[Tang, Huaibin] Shandong Univ, Sch Microelect, Jinan 250100, Shandong, Peoples R China.; [Tang, Huaibin] Chinese Acad Sci, Acad Math & Syst Sci, Ins 更多
通讯作者地址：[Li, T]East China Normal Univ, Dept Math, Shanghai Key Lab Pure Math & Math Practice, Shanghai 200241, Peoples R China.
来源：SYSTEMS & CONTROL LETTERS
关键词：Consensus; Sensor network; Martingale difference sequence; Stochastic; approximation; Convergence rate
摘要：In this paper, we study the convergence rates of the discrete-time stochastic approximation consensus algorithms over sensor networks with communication noises under general digraphs. Basic results of stochastic analysis and algebraic graph theory are used to investigate the dynamics of the consensus error, and the mean square and sample path convergence rates of the consensus error are both given in terms of the graph and noise parameters. Especially, calculation methods to estimate the mean square limit bounds are presented under balanced digraphs, and sufficient conditions on the network topology and the step sizes are given to achieve the fast convergence rate. For the sample path limit bounds, estimation methods are also presented under undirected graphs. (C) 2017 Elsevier B.V. All rights reserved.