Distributedly solving network linear equations with event-based algorithms

摘要

In this study, distributed, event-based network flows are studied for solving the linear algebraic equation 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.