  A unique feature of hybrid dynamical systems (systems whose evolution is
subject to both continuous- and discrete-time laws) is Zeno trajectories.
Usually these trajectories are avoided as they can cause incorrect numerical
results as the problem becomes ill-conditioned. However, these are difficult to
justifiably avoid as determining when and where they occur is a non-trivial
task. It turns out that in optimal control problems, not only can they not be
avoided, but are sometimes required in synthesizing the solutions. This work
explores the pedagogical example of the bouncing ball to demonstrate the
importance of "Zeno control executions."
