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Energy-transfer edge centrality and its role in enhancing network controllability
P. V. Chanekar, E. Nozari, J. Cortés
IEEE Transactions on Network Science and Engineering 8 (1) (2021), 331-346

Abstract

The ability to modify the structure of network systems offers great opportunities to enhance their operation, improve their efficiency, and increase their resilience against failures and attacks. Complementary to the well-studied optimal sensor/actuator placement problem, this paper focus on the edge modification problem, i.e., improving network controllability by adding and/or re-weighting interconnections while keeping the actuation structure fixed. We consider a network system described by linear dynamics and propose a novel edge centrality measure that captures the extent to which an edge facilitates energy exchange across the network through its defining nodes. We analyze the effectiveness of the proposed measure in identifying those edges with significant impact on network controllability by characterizing its relationship with the gradients (with respect to edge weights) of the trace and the logdet of the Gramian. We also show that the optimal solution of the edge modification problem with trace of the Gramian as objective function lies on the boundary of the feasible search space. Finally, we build on the proposed edge centrality measure to design two network modification algorithms that restrict the search space to a smaller subset of all possible edges and numerically demonstrate their efficacy in terms of computational complexity and controllability enhancement.

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Mechanical and Aerospace Engineering, University of California, San Diego
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