TY - GEN

T1 - Distributed two-time-scale methods over clustered networks

AU - Pham, Thiem V.

AU - Doan, Thinh T.

AU - Nguyen, Dinh Hoa

N1 - Publisher Copyright:
© 2021 American Automatic Control Council.

PY - 2021/5/25

Y1 - 2021/5/25

N2 - In this paper, we consider consensus problems over a network of nodes, where the network is divided into a number of clusters. We are interested in the case where the communication topology within each cluster is dense as compared to the sparse communication across the clusters. Moreover, each cluster has one leader which can communicate with other leaders in different clusters. The goal of the nodes is to agree at some common value under the presence of communication delays across the clusters. Our main contribution is to propose a novel distributed two-time-scale consensus algorithm, which pertains to the separation in network topology of clustered networks. In particular, one scale is to model the dynamics of the agents in each cluster, which is much faster (due to the dense communication) than the scale describing the slowly aggregated evolution between the clusters (due to the sparse communication). We prove the convergence of the proposed method in the presence of uniform, but possibly arbitrarily large, communication delays between the leaders. In addition, we provide an explicit formula for the convergence rate of such algorithm, which characterizes the impact of delays and the network topology. Our results shows that after a transient time characterized by the topology of each cluster, the convergence of the two-time-scale consensus method only depends on the connectivity of the leaders. Finally, we validate our theoretical results by a number of numerical simulations on different clustered networks.

AB - In this paper, we consider consensus problems over a network of nodes, where the network is divided into a number of clusters. We are interested in the case where the communication topology within each cluster is dense as compared to the sparse communication across the clusters. Moreover, each cluster has one leader which can communicate with other leaders in different clusters. The goal of the nodes is to agree at some common value under the presence of communication delays across the clusters. Our main contribution is to propose a novel distributed two-time-scale consensus algorithm, which pertains to the separation in network topology of clustered networks. In particular, one scale is to model the dynamics of the agents in each cluster, which is much faster (due to the dense communication) than the scale describing the slowly aggregated evolution between the clusters (due to the sparse communication). We prove the convergence of the proposed method in the presence of uniform, but possibly arbitrarily large, communication delays between the leaders. In addition, we provide an explicit formula for the convergence rate of such algorithm, which characterizes the impact of delays and the network topology. Our results shows that after a transient time characterized by the topology of each cluster, the convergence of the two-time-scale consensus method only depends on the connectivity of the leaders. Finally, we validate our theoretical results by a number of numerical simulations on different clustered networks.

UR - http://www.scopus.com/inward/record.url?scp=85111910166&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85111910166&partnerID=8YFLogxK

U2 - 10.23919/ACC50511.2021.9483255

DO - 10.23919/ACC50511.2021.9483255

M3 - Conference contribution

AN - SCOPUS:85111910166

T3 - Proceedings of the American Control Conference

SP - 4625

EP - 4630

BT - 2021 American Control Conference, ACC 2021

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2021 American Control Conference, ACC 2021

Y2 - 25 May 2021 through 28 May 2021

ER -