Graph-theoretic optimization for edge consensus

29 Jun 2020  ·  de Badyn Mathias Hudoba, Foight Dillon R., Calderone Daniel, Mesbahi Mehran, Smith Roy S. ·

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. read more

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Optimization and Control