Finite-Time Distributed Flow Balancing

• 成果类型: Article
• 署名作者: Hadjicostis, Christoforos N.; Dominguez-Garcia, Alejandro D.; Rikos, Apostolos, I
• 署名单位: University of Cyprus; University of Illinois System; University of Illinois Urbana-Champaign; Royal Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3137150
• 发表日期: 2022
• 页码: 6926-6933
• 关键词: Balancing; Distributed algorithms; distributed balancing; feasible circulation; finite-time; flow networks

摘要

We consider a flow network that is described by a digraph, each edge of which can admit a flow within a certain interval, with nonnegative end points that correspond to lower and upper flow limits. We propose and analyze a distributed iterative algorithm for solving, in finite time, the so-called feasible circulation problem, which consists of computing flows that are admissible (i.e., within the given intervals at each edge) and balanced (i.e., the total in-flow equals the total out-flow at each node). The algorithm assumes a communication topology that allows bidirectional message exchanges between pairs of nodes that are physically connected (i.e., nodes that share a directed edge in the physical topology) and is shown to converge to a feasible and balanced solution as long as the necessary and sufficient circulation conditions are satisfied with strict inequality. In case, the initial flows and flow limits are commensurable (i.e., they are integer multiples of a given constant), then the proposed algorithm reduces to a previously proposed finite-time balancing algorithm, for which we provide an explicit bound on the number of steps required for termination.