Improving Network Robustness through Edge Augmentation While Preserving Strong Structural Controllability

Abstract

In this paper, we consider a network of agents with Laplacian dynamics, and study the problem of improving network robustness by adding maximum number of edges within the network while preserving a lower bound on its strong structural controllability (SSC). Edge augmentation increases network's robustness to noise and structural changes, however, it could also deteriorate network controllability. By exploiting relationship between network controllability and distances between nodes in graphs, we formulate an edge augmentation problem with a constraint to preserve distances between certain node pairs, which in turn guarantees that a lower bound on SSC is maintained even after adding edges. In this direction, first we choose a node pair and maximally add edges while maintaining the distance between selected nodes. We show that an optimal solution belongs to a certain class of graphs called clique chains. Then, we present and analyze two algorithms to add edges while preserving distances between a certain collection of nodes. Finally, we evaluate our results on various networks.