TY - GEN

T1 - Distributed Quantized Weight-Balancing and Average Consensus over Digraphs

AU - Lee, Chang Shen

AU - Michelusi, Nicolo

AU - Scutari, Gesualdo

N1 - Publisher Copyright:
© 2018 IEEE.

PY - 2018/7/2

Y1 - 2018/7/2

N2 - This paper studies distributed quantized weight-balancing and average consensus over fixed digraphs. A digraph with non-negative weights associated to its edges is weight-balanced if, for each node, the sum of the weights of its outgoing edges is equal to that of its incoming edges. We propose and analyze the first distributed algorithm that solves the weight-balancing problem using only quantized (one-bit) information among nodes and simplex communications (compliant to the directed nature of the graph edges). Asymptotic convergence of the scheme is proved and a convergence rate analysis is provided. Building on this result, a novel distributed algorithm is proposed that solves the average consensus problem over digraphs, using, at each iteration, only two-bit simplex communications between adjacent nodes - one bit for the weight-balancing problem, the other for the average consensus. Convergence to the average of the real (i.e., unquantized) node's initial values is proved, both almost surely and in mean square sense. Finally, numerical results validate our theoretical findings.

AB - This paper studies distributed quantized weight-balancing and average consensus over fixed digraphs. A digraph with non-negative weights associated to its edges is weight-balanced if, for each node, the sum of the weights of its outgoing edges is equal to that of its incoming edges. We propose and analyze the first distributed algorithm that solves the weight-balancing problem using only quantized (one-bit) information among nodes and simplex communications (compliant to the directed nature of the graph edges). Asymptotic convergence of the scheme is proved and a convergence rate analysis is provided. Building on this result, a novel distributed algorithm is proposed that solves the average consensus problem over digraphs, using, at each iteration, only two-bit simplex communications between adjacent nodes - one bit for the weight-balancing problem, the other for the average consensus. Convergence to the average of the real (i.e., unquantized) node's initial values is proved, both almost surely and in mean square sense. Finally, numerical results validate our theoretical findings.

UR - http://www.scopus.com/inward/record.url?scp=85062175377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85062175377&partnerID=8YFLogxK

U2 - 10.1109/CDC.2018.8618973

DO - 10.1109/CDC.2018.8618973

M3 - Conference contribution

AN - SCOPUS:85062175377

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 5857

EP - 5862

BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 57th IEEE Conference on Decision and Control, CDC 2018

Y2 - 17 December 2018 through 19 December 2018

ER -