Graph-theoretic optimization for edge consensus
Abstract
We consider network structures that optimize the norm of weighted, time scaled consensus networks, under a minimal representation of such consensus networks described by the edge Laplacian. We show that a greedy algorithm can be used to find the minimum- norm spanning tree, as well as how to choose edges to optimize the norm when edges are added back to a spanning tree. In the case of edge consensus with a measurement model considering all edges in the graph, we show that adding edges between slow nodes in the graph provides the smallest increase in the norm.
Cite
@article{arxiv.2006.16201,
title = {Graph-theoretic optimization for edge consensus},
author = {Mathias Hudoba de Badyn and Dillon R. Foight and Daniel Calderone and Mehran Mesbahi and Roy S. Smith},
journal= {arXiv preprint arXiv:2006.16201},
year = {2020}
}
Comments
8 pages, 3 figures. Accepted to the 24th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2020), which has been postponed to August 2021. This version is the extended paper, which includes the proofs that were submitted for review