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arXiv · 2006.16201

Graph-theoretic optimization for edge consensus

Mathias Hudoba de Badyn·Dillon R. Foight·Daniel Calderone·Mehran Mesbahi·Roy S. Smith
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Abstract

We consider network structures that optimize the $\mathcal{H}_2$ 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-$\mathcal{H}_2$ norm spanning tree, as well as how to choose edges to optimize the $\mathcal{H}_2$ 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 $\mathcal{H}_2$ norm.

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Mathias Hudoba de Badyn, Dillon R. Foight, Daniel Calderone, Mehran Mesbahi, Roy S. Smith. 2020-06-29. Graph-theoretic optimization for edge consensus. https://arxiv.org/abs/2006.16201

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