This thesis aims to demonstrate the conditions under which a particular kind of ensemble control system is controllable. Previous studies on this topic have tended to make simplifying assumptions on the systems in view, and this paper attempts to remove some of those assumptions. Even in a non-linear ensemble system, it can be demonstrated that controllability is achievable under some circumstances. This controllability is limited, however, by the Hamiltonian preservation of area in the position-velocity plane. At the end of this thesis, some example systems will be simulated, demonstrating the concepts of the paper and showing that the controllability result is sound.
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