On Numerical Examination of Uniform Ensemble Controllability for Linear Ensemble Systems

In this letter, 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 L2 -space. We also demonstrate that under certain conditions, L2 -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.