Strong Structural Controllability of Networks under Time-Invariant and Time-Varying Topological Perturbations

• 成果类型: Article
• 署名作者: Mousavi, Shima Sadat; Haeri, Mohammad; Mesbahi, Mehran
• 署名单位: Sharif University of Technology; Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Washington; University of Washington Seattle
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2992439
• 发表日期: 2021
• 页码: 1375-1382
• 关键词: Controllability; Linear systems; Perturbation methods; Robustness; uncertainty; Electrical engineering; Social networking (online); Linear time-varying (LTV) networks; network of networks; robustness of controllability; strong structural controllability; zero-forcing sets

摘要

This article investigates the robustness of strong structural controllability for linear time-invariant and linear time-varying directed networks with respect to structural perturbations, including edge deletions and additions. In this direction, we introduce a new construct referred to as a perfect graph associated with a network with a given set of control nodes. The tight upper bounds on the number of edges that can be added to, or removed from a network, while ensuring strong structural controllability, are then derived. Moreover, we obtain a characterization of critical edge sets, the maximal sets of edges whose any subset can be respectively added to or removed from a network while preserving strong structural controllability. In addition, procedures for combining networks to obtain strongly structurally controllable network of networks are proposed. Finally, controllability conditions are proposed for networks whose edge weights, as well as their structures, can vary over time.