Vector-Valued Gossip over $w$-Holonomic Networks
Abstract
We study the weighted average consensus problem for a gossip network of agents with vector-valued states. For a given matrix-weighted graph, the gossip process is described by a sequence of pairs of adjacent agents communicating and updating their states based on the edge matrix weight. Our key contribution is providing conditions for the convergence of this non-homogeneous Markov process as well as the characterization of its limit set. To this end, we introduce the notion of "-holonomy" of a set of stochastic matrices, which enables the characterization of sequences of gossiping pairs resulting in reaching a desired consensus in a decentralized manner. Stated otherwise, our result characterizes the limiting behavior of infinite products of (non-commuting, possibly with absorbing states) stochastic matrices.
Keywords
Cite
@article{arxiv.2311.04455,
title = {Vector-Valued Gossip over $w$-Holonomic Networks},
author = {Erkan Bayram and Mohamed-Ali Belabbas and Tamer Başar},
journal= {arXiv preprint arXiv:2311.04455},
year = {2023}
}