An event-based distributed least square linear equation solver employing network flow

In this article, we study a distributed, second-order, event-triggered network flow for solving linear algebraic equations described by the form z=Hy in the sense of least squares. An undirected graph is utilized to describe the distributed computation network. In the network, each node broadcasts its dynamic states to its neighbors in an asynchronous fashion, and updates the flow at the isolated event times. We construct a specific trigger function to determine the event times, in which an exponential decay function is introduced as a comparison term. We show that if the linear algebraic equation has a unique least squares solution, all nodes states converge to this unique solution exponentially fast, when the applied network is connected and the decay rate of the comparison term satisfies certain bounds determined jointly by the topology and the linear equations information. We obtain a strictly positive lower bound on the time interval between consecutive events for time t∈[0,∞), and therefore the event-triggered system does not exhibit Zeno behavior. We provide numerical examples to verify the effectiveness of the proposed event-based network flow. In addition, we illustrate the importance of the strictly positive inter-event time interval, in comparison with the case that the inter-event time interval may converge to zero when time t goes to infinity.