@inproceedings{7c8c549520fb4641afcf7e837affe172,
title = "Controllability over Graphs for Bilinear Systems over Lie Groups",
abstract = "This paper presents graph theoretic conditions for the controllability and accessibility of bilinear systems over the special orthogonal group and the general linear group, respectively, in the presence of drift terms. 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.",
keywords = "Bilinear systems, Controllability, Graph theory, Lie groups",
author = "Xing Wang and Bo Li and Li, \{Jr Shin\} and Petersen, \{Ian R.\} and Guodong Shi",
note = "Publisher Copyright: {\textcopyright} 2020 IEEE.; 59th IEEE Conference on Decision and Control, CDC 2020 ; Conference date: 14-12-2020 Through 18-12-2020",
year = "2020",
month = dec,
day = "14",
doi = "10.1109/CDC42340.2020.9304294",
language = "English",
series = "Proceedings of the IEEE Conference on Decision and Control",
publisher = "Institute of Electrical and Electronics Engineers Inc.",
pages = "5580--5585",
booktitle = "2020 59th IEEE Conference on Decision and Control, CDC 2020",
address = "United States",
}