On Numerical Examination of Uniform Ensemble Controllability for Linear Ensemble Systems

Wei Miao, Gong Cheng, Jr Shin Li

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publication2021 American Control Conference, ACC 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781665441971
StatePublished - May 25 2021
Event2021 American Control Conference, ACC 2021 - Virtual, New Orleans, United States
Duration: May 25 2021May 28 2021

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619


Conference2021 American Control Conference, ACC 2021
Country/TerritoryUnited States
CityVirtual, New Orleans


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