Sparse Linear Ensemble Systems and Structural Controllability

• 成果类型: Article
• 署名作者: Chen, Xudong
• 署名单位: University of Colorado System; University of Colorado Boulder
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3097289
• 发表日期: 2022
• 页码: 3337-3348
• 关键词: Controllability; complex systems; Aerospace electronics; statistics; sociology; scalability; Multi-agent systems; graph theory; linear ensemble systems; sparse systems; structural controllability

摘要

The article introduces and solves a structural controllability problem for continuum ensembles of linear time-invariant systems. All the individual linear systems of an ensemble are sparse, governed by the same sparsity pattern. Controllability of an ensemble system is, by convention, the capability of using a common control input to simultaneously steer every individual systems in it. A sparsity pattern is structurally controllable if it admits a controllable linear ensemble system. A main contribution of the article is to provide a graphical condition that is necessary and sufficient for a sparsity pattern to be structurally controllable. Like other structural problems, the property of being structural controllable is monotone. We provide a complete characterization of minimal sparsity patterns as well.