TY - GEN
T1 - On Numerical Examination of Uniform Ensemble Controllability for Linear Ensemble Systems
AU - Miao, Wei
AU - Cheng, Gong
AU - Li, Jr Shin
N1 - Funding Information:
This work was supported in part by the National Science Foundation under the awards CMMI-1933976 and ECCS-1810202.
Publisher Copyright:
© 2021 American Automatic Control Council.
PY - 2021/5/25
Y1 - 2021/5/25
N2 - In this paper, we propose a numerical approach to examine uniform ensemble controllability of linear ensemble systems. We show that the linear ensemble defined on the Banach space of compactly supported continuous functions is uniformly ensemble controllable if the differentiation set associated with the ensemble is dense, and only if the reachable set is dense, in the L^{2}-space. We also demonstrate that under certain conditions, L^{2}-denseness of the differentiation set is necessary for uniform ensemble controllability of a linear ensemble system. Then, we provide a tractable numerical method to test the denseness of an arbitrary set in Hilbert space with a quantifiable error bound, which informs uniform ensemble controllability. We conduct several numerical experiments to illustrate the efficacy and robustness of the proposed numerical approach.
AB - In this paper, we propose a numerical approach to examine uniform ensemble controllability of linear ensemble systems. We show that the linear ensemble defined on the Banach space of compactly supported continuous functions is uniformly ensemble controllable if the differentiation set associated with the ensemble is dense, and only if the reachable set is dense, in the L^{2}-space. We also demonstrate that under certain conditions, L^{2}-denseness of the differentiation set is necessary for uniform ensemble controllability of a linear ensemble system. Then, we provide a tractable numerical method to test the denseness of an arbitrary set in Hilbert space with a quantifiable error bound, which informs uniform ensemble controllability. We conduct several numerical experiments to illustrate the efficacy and robustness of the proposed numerical approach.
UR - http://www.scopus.com/inward/record.url?scp=85111932198&partnerID=8YFLogxK
U2 - 10.23919/ACC50511.2021.9482706
DO - 10.23919/ACC50511.2021.9482706
M3 - Conference contribution
AN - SCOPUS:85111932198
T3 - Proceedings of the American Control Conference
SP - 2467
EP - 2472
BT - 2021 American Control Conference, ACC 2021
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2021 American Control Conference, ACC 2021
Y2 - 25 May 2021 through 28 May 2021
ER -