  In this paper, we tackle the long-standing challenges of ensemble control
analysis and design using a convex-geometric approach in a Hilbert space
setting. Specifically, we formulate the control of linear ensemble systems as a
convex feasibility problem in a Hilbert space, which can be solved by iterative
weighted projections. Such a non-trivial geometric interpretation not only
enables a systematic design principle for constructing feasible, optimal, and
constrained ensemble control signals, but also makes it possible for numerical
examination of ensemble reachability and controllability. Furthermore, we
incorporate this geometric approach into an iterative framework and illustrate
its capability to derive feasible controls for steering bilinear ensemble
systems. We conduct various numerical experiments on the control of linear and
bilinear ensembles to validate the theoretical developments and demonstrate the
applicability of the proposed convex-geometric approach.
