On the Structural Target Controllability of Undirected Networks

• 成果类型: Article
• 署名作者: Li, Jingqi; Chen, Ximing; Pequito, Sergio; Pappas, George J.; Preciado, Victor M.
• 署名单位: University of California System; University of California Berkeley; University of Pennsylvania; Delft University of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3041420
• 发表日期: 2021
• 页码: 4836-4843
• 关键词: Controllability; Symmetric matrices; graph theory; Linear systems; dynamical systems; tools; computational complexity; networked control systems; structured linear systems; target controllability

摘要

In this article, we study the target controllability problem of networked dynamical systems,in which we are tasked to steer a subset of network nodes toward a desired objective. More specifically, we derive necessary and sufficient conditions for the structural target controllability of linear time-invariant (LTI) systems with symmetric state matrices, such as those representing undirected dynamical networks with unknown link weights. To achieve our goal, we first characterize the generic rank of symmetrically structured matrices, as well as the modes of any numerical realization. Subsequently, we provide graph-theoretic necessary and sufficient conditions for the structural target controllability of undirected networks with multiple control nodes. In addition, we show that these results can be extended and lead to a necessary and sufficient condition of the structural output controllability. However, different from structural target controllability, we prove that verifying the proposed conditions on structural output controllability in undirected networks is NP-hard.