TY - GEN
T1 - Computing controllability of systems on SO(n) over graphs
AU - Li, Jr Shin
AU - Zhang, Wei
AU - Wang, Liang
N1 - Funding Information:
This work was supported in part by the NSF under the award CMMI-1462796 and AFOSR under the award FA9550-17-1-0166.
Funding Information:
*This work was supported in part by the NSF under the award CMMI-1462796 and AFOSR under the award FA9550-17-1-0166.
Publisher Copyright:
© 2017 IEEE.
PY - 2017/6/28
Y1 - 2017/6/28
N2 - In this paper, we present a new algebraic framework that provides an effective approach to investigate controllability of systems defined on the special orthogonal group. The central idea is to map Lie bracket operations of the vector fields governing the system dynamics to permutation multiplications in a symmetric group, so that controllability and controllable submanifolds can be characterized by permutation cycles. This new notion enables a visualization of controllability analysis over an undirected graph and facilitates the design of efficient computational algorithms to examine controllability and identify the controllable submanifold by computing permutation cycles. Furthermore, the developed methodology reveals the relationship between controllability of a system and connectivity of the associated graph, which renders a transparent way to understand controllability over graphs. The method is directly applicable to characterize the degree of controllability and reachability of systems defined on compact Lie groups and on graphs, such as quantum networks, multi-Agent systems, and Markov chains.
AB - In this paper, we present a new algebraic framework that provides an effective approach to investigate controllability of systems defined on the special orthogonal group. The central idea is to map Lie bracket operations of the vector fields governing the system dynamics to permutation multiplications in a symmetric group, so that controllability and controllable submanifolds can be characterized by permutation cycles. This new notion enables a visualization of controllability analysis over an undirected graph and facilitates the design of efficient computational algorithms to examine controllability and identify the controllable submanifold by computing permutation cycles. Furthermore, the developed methodology reveals the relationship between controllability of a system and connectivity of the associated graph, which renders a transparent way to understand controllability over graphs. The method is directly applicable to characterize the degree of controllability and reachability of systems defined on compact Lie groups and on graphs, such as quantum networks, multi-Agent systems, and Markov chains.
UR - http://www.scopus.com/inward/record.url?scp=85046130910&partnerID=8YFLogxK
U2 - 10.1109/CDC.2017.8264476
DO - 10.1109/CDC.2017.8264476
M3 - Conference contribution
AN - SCOPUS:85046130910
T3 - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
SP - 5511
EP - 5516
BT - 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 56th IEEE Annual Conference on Decision and Control, CDC 2017
Y2 - 12 December 2017 through 15 December 2017
ER -