Distributedly solving network linear equations with event‐based algorithms. Issue 17 (1st November 2019)

• Record Type: Journal Article
• Authors: Liu, Qingchen; Liu, Yang; Yuan, Deming; Qin, Jiahu
• Is Part Of: IET control theory & applications. Volume 13:Issue 17(2019)
• Page Start: 2738
• Page End: 2746
• Publication Date: 2019-11-01
• Subjects: distributed control -- convergence -- approximation theory -- linear algebra -- set theory -- optimisation -- graph theory -- computational complexity -- continuous time systems; network flow -- distributedly solving network linear equations -- event‐based algorithms -- authors study -- event‐based network -- linear algebraic equation $\mathbf {z}=\mathbf -- undirected network -- dynamic state -- neighbours -- event‐based time instants -- asynchronous manner -- unique solution -- nodes states -- unique/common solution -- applied network -- convergence rates -- linear equation -- network structure -- time interval -- consecutive events; Control theory -- Periodicals; Automatic control -- Periodicals; 629.8312
• DOI: 10.1049/iet-cta.2018.6134
• Languages: English
• ISSNs: 1751-8644

Abstract

Abstract : In this study, distributed, event‐based network flows are studied for solving the linear algebraic equation z = H y over an undirected network. Each node holds a dynamic state, which is broadcast to its neighbours at a sequence of event‐based time instants in an asynchronous manner, at both its own and its neighbours' event times. Each node then updates its control rule for its dynamic states. It is shown that if the linear algebraic equation has a unique solution or an infinite set of solutions, all nodes states converge to a unique/common solution if the applied network is connected and the trigger function is well constructed. Convergence rates are established explicitly as a result of the linear equation, the network structure and the triggering conditions. An explicit lower bound on the time interval between consecutive events is obtained, and therefore the proposed network flow does not exhibit Zeno behaviour. Simulations are provided to illustrate the effectiveness of the proposed network flow. Additionally, they also investigate the scenario where nodes are only allowed to update their states at their own events, and demonstrate the similarity and difference compared to the proposed solution.