2 research outputs found
Limited Rate Distributed Weight-Balancing and Average Consensus Over Digraphs
Distributed quantized weight-balancing and average consensus over fixed
digraphs are considered. A digraph with non-negative weights associated to its
edges is weight-balanced if, for each node, the sum of the weights of its
out-going edges is equal to that of its incoming edges. This paper proposes and
analyzes the first distributed algorithm that solves the weight-balancing
problem using only finite rate and simplex communications among nodes
(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, finite rate
simplex communications between adjacent nodes -- some bits for the
weight-balancing problem, other for the average consensus. Convergence of the
proposed quantized consensus algorithm to the average of the real (i.e.,
unquantized) agent's initial values is proved, both almost surely and in th
mean for all positive integer . Finally, numerical results validate our
theoretical findings.Comment: Part of this work will be presented at the 57th IEEE Conference on
Decision and Contro
Finite rate distributed weight-balancing and average consensus over digraphs
This paper proposes the first distributed algorithm that solves the
weight-balancing problem using only finite rate and simplex communications
among nodes, compliant with the directed nature of the graph edges. It is
proved that the algorithm converges to a weight-balanced solution at sublinear
rate. The analysis builds upon a new metric inspired by positional system
representations, which characterizes the dynamics of information exchange over
the network, and on a novel step-size rule. Building on this result, a novel
distributed algorithm is proposed that solves the average consensus problem
over digraphs, using, at each timeslot, finite rate simplex communications
between adjacent nodes -- some bits for the weight-balancing problem and others
for the average consensus. Convergence of the proposed quantized consensus
algorithm to the average of the node's unquantized initial values is
established, both almost surely and in the moment generating function of the
error; and a sublinear convergence rate is proved for sufficiently large
step-sizes. Numerical results validate our theoretical findings.Comment: A preliminary version arXiv:1809.06440 of this paper has appeared at
IEEE CDC 201