Controllability Backbone in Networks

TL;DR

This paper introduces algorithms to identify minimal edge subsets, called controllability backbones, in networks that preserve strong structural controllability, aiding efficient network control analysis.

Contribution

It proposes novel algorithms for computing controllability backbones in networks based on SSC, using lower bounds from zero forcing and graph distances.

Findings

Algorithms effectively compute controllability backbones.

Backbones preserve network controllability properties.

Numerical evaluations demonstrate the methods' efficiency.

Abstract

This paper studies the controllability backbone problem in dynamical networks defined over graphs. The main idea of the controllability backbone is to identify a small subset of edges in a given network such that any subnetwork containing those edges/links has at least the same network controllability as the original network while assuming the same set of input/leader vertices. We consider the strong structural controllability (SSC) in our work, which is useful but computationally challenging. Thus, we utilize two lower bounds on the network's SSC based on the zero forcing notion and graph distances. We provide algorithms to compute controllability backbones while preserving these lower bounds. We thoroughly analyze the proposed algorithms and compute the number of edges in the controllability backbones. Finally, we compare and numerically evaluate our methods on random graphs.