TY - GEN
T1 - Controllability over Graphs for Bilinear Systems over Lie Groups
AU - Wang, Xing
AU - Li, Bo
AU - Li, Jr Shin
AU - Petersen, Ian R.
AU - Shi, Guodong
N1 - Publisher Copyright:
© 2020 IEEE.
PY - 2020/12/14
Y1 - 2020/12/14
N2 - 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.
AB - 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.
KW - Bilinear systems
KW - Controllability
KW - Graph theory
KW - Lie groups
UR - http://www.scopus.com/inward/record.url?scp=85095490214&partnerID=8YFLogxK
U2 - 10.1109/CDC42340.2020.9304294
DO - 10.1109/CDC42340.2020.9304294
M3 - Conference contribution
AN - SCOPUS:85095490214
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5580
EP - 5585
BT - 2020 59th IEEE Conference on Decision and Control, CDC 2020
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 59th IEEE Conference on Decision and Control, CDC 2020
Y2 - 14 December 2020 through 18 December 2020
ER -