@article{1138,
  author = {Mudassir Shabbir and Waseem Abbas and Yasin Yazıcıoğlu and Xenofon Koutsoukos},
  title = {Computation of the Distance-Based Bound on Strong Structural Controllability in Networks},
  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.},
  year = {2023},
  journal = {IEEE Transactions on Automatic Control},
  volume = {68},
  number = {3},
  pages = {1768-1775},
  month = {03/2023},
  issn = {1558-2523},
  url = {https://ieeexplore.ieee.org/document/9738436},
  doi = {10.1109/TAC.2022.3160682},
}