Computation of the Distance-based Bound on Strong Structural Controllability in Networks
Abstract
In this paper, we study the problem of computing a tight lower bound on the dimension of the strong structurally controllable subspace (SSCS) in networks with Laplacian dynamics. The bound is based on a sequence of vectors containing the distances between leaders (nodes with external inputs) and followers (remaining nodes) in the underlying network graph. Such vectors are referred to as the distance-to-leaders vectors. {We give exact and approximate algorithms to compute the longest sequences of distance-to-leaders vectors, which directly provide distance-based bounds on the dimension of SSCS. The distance-based bound is known to outperform the other known bounds (for instance, based on zero-forcing sets), especially when the network is partially strong structurally controllable. Using these results, we discuss an application of the distance-based bound in solving the leader selection problem for strong structural controllability. Further, we characterize strong structural controllability in path and cycle graphs with a given set of leader nodes using sequences of distance-to-leaders vectors. Finally, we numerically evaluate our results on various graphs.
Keywords
Cite
@article{arxiv.1909.03565,
title = {Computation of the Distance-based Bound on Strong Structural Controllability in Networks},
author = {Mudassir Shabbir and Waseem Abbas and A. Yasin Yazicioglu and Xenofon Koutsoukos},
journal= {arXiv preprint arXiv:1909.03565},
year = {2021}
}