학술논문
Computation of the Distance-Based Bound on Strong Structural Controllability in Networks
Document Type
Periodical
Author
Source
IEEE Transactions on Automatic Control IEEE Trans. Automat. Contr. Automatic Control, IEEE Transactions on. 68(3):1768-1775 Mar, 2023
Subject
Language
ISSN
0018-9286
1558-2523
2334-3303
1558-2523
2334-3303
Abstract
In this article, 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.