Controllability and Accessibility on Graphs for Bilinear Systems Over Lie Groups

• 成果类型: Article
• 署名作者: Wang, Xing; Li, Bo; Li, Jr-Shin; Petersen, Ian R.; Shi, Guodong
• 署名单位: Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS; Chinese Academy of Sciences; University of Chinese Academy of Sciences, CAS; Washington University (WUSTL); Australian National University; University of Sydney
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3176431
• 发表日期: 2023
• 页码: 2277-2292
• 关键词: Controllability; Nonlinear systems; Algebra; Network systems; dynamical systems; CONFERENCES; australia; Bilinear systems; CONTROLLABILITY; graph theory; Lie groups

摘要

This article presents graph theoretic conditions for the controllability and accessibility of bilinear systems over the special orthogonal group, the special linear group and the general linear group, respectively, in the presence of drift terms. The controlled terms are assumed to take place between pairwise states. Such bilinear systems naturally induce two interaction graphs: one graph from the drift, and another from the controlled dynamics. As a result, the system controllability or accessibility becomes a property of the two graphs in view of the classical Lie algebra rank condition. We establish a systemic way of transforming the Lie bracket operations in the underlying Lie algebra, into specific operations of removing or creating links over the drift and controlled interaction graphs. As a result, we establish a series of graphical conditions for the controllability and accessibility of such bilinear systems, which rely only on the connectivity of the union of the drift and controlled interaction graphs. We present examples to illustrate the validity of the established results, and show that the proposed conditions are in fact considerably tight.