  In this paper we consider the problem of the optimal control of an ensemble
of affine-control systems. After proving the well-posedness of the minimization
problem under examination, we establish a $\Gamma$-convergence result that
allows us to substitute the original (and usually infinite) ensemble with a
sequence of finite increasing-in-size sub-ensembles. The solutions of the
optimal control problems involving these sub-ensembles provide approximations
in the $L^2$-strong topology of the minimizers of the original problem. Using
again a $\Gamma$-convergence argument, we manage to derive a Maximum Principle
for ensemble optimal control problems with end-point cost. Moreover, in the
case of finite sub-ensembles, we can address the minimization of the related
cost through numerical schemes. In particular, we propose an algorithm that
consists of a subspace projection of the gradient field induced on the space of
admissible controls by the approximating cost functional. In addition, we
consider an iterative method based on the Pontryagin Maximum Principle.
Finally, we test the algorithms on an ensemble of linear systems in
$\mathbb{R}^2$.
