Computation of the Distance-Based Bound on Strong Structural Controllability in Networks

• 成果类型: Article
• 署名作者: Shabbir, Mudassir; Abbas, Waseem; Yazcoglu, A. Yasin; Koutsoukos, Xenofon
• 署名单位: Vanderbilt University; University of Texas System; University of Texas Dallas; University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3160682
• 发表日期: 2023
• 页码: 1768-1775
• 关键词: Controllability; Heuristic algorithms; Approximation algorithms; Laplace equations; computer science; Greedy algorithms; dynamic programming; graph algorithms; Network topology; strong structural controllability

摘要

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.