Modal Barriers to Controllability in Networks With Linearly Coupled Homogeneous Subsystems

• 成果类型: Article
• 署名作者: Xue, Mengran; Roy, Sandip
• 署名单位: Washington State University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3063948
• 发表日期: 2021
• 页码: 6187-6193
• 关键词: Controllability; Eigenvalues and eigenfunctions; Multi-agent systems; Analytical models; Protocols; stability analysis; Couplings; Control of networks; CONTROLLABILITY; multiagent systems

摘要

The controllability of networks comprising linearly coupled identical subsystems is examined from a modal perspective. The eigenvalues of the network model are classified into the following two groups based on the subsystem structure:network-invariant modes, which have very high multiplicity regardless of the network's topology; and special-repeat modes, which have bounded multiplicity. In this article, we demonstrate that models with network-invariant modes are uncontrollable unless a sufficient fraction of the subsystems are actuated in any weakly connected partition, subject to a diagonalizability condition on the network matrix. Meanwhile, the controllability reduces to a purely graph-theoretic condition when the network model has only special-repeat modes. This characterization also differentiates the controllability of built networks with fixed interconnections from multiagent systems with designable protocols.