Graph-theoretic optimization for edge consensus
Mathias Hudoba de Badyn, Dillon R. Foight, Daniel Calderone, Mehran, Mesbahi, Roy S. Smith
TL;DR
This paper presents a graph-theoretic approach to optimize the $\\mathcal{H}_2$ norm in consensus networks using edge Laplacian representations, proposing greedy algorithms for minimal norm spanning trees and edge additions.
Contribution
It introduces a greedy algorithm for finding minimum-$\mathcal{H}_2$ norm spanning trees and strategies for edge addition to optimize network performance.
Findings
Greedy algorithm effectively finds minimum-$\mathcal{H}_2$ norm spanning trees.
Adding edges between slow nodes minimally increases the $\\mathcal{H}_2$ norm.
Edge selection strategies improve consensus network optimization.
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.
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