Distributed Resource Allocation over Time-varying Balanced Digraphs with Discrete-time Communication

Consider a group of nodes aiming to solve a resource allocation problem cooperatively and distributedly. Specifically, each node has access to its own local cost function and local network resource, and the goal is to minimize the sum of the local cost functions subject to a global network resource constraint. The communication among the nodes occurs at discrete-time steps and the communication topology is described by a strongly connected and weight-balanced digraph that may be time-varying. We propose a continuous-time algorithm that solves this problem. Particularly, a novel passivity-based perspective of the proposed algorithmic dynamic at each individual node is provided, which enables us to analyze the convergence of the overall distributed algorithm over time-varying digraphs. To exempt from the difficult-to-satisfy assumption of continuous-time communication among nodes, we also develop an asynchronous distributed event-triggered scheme building on the passivity-based notion. Additionally, a synchronous periodic communication strategy is also derived through analyzing the passivity degradation over sampling of the distributed dynamic at each node.