  Many systems exhibit a mixture of continuous and discrete dynamics. We
consider a family of mixed-integer non-convex non-linear optimisation problems
obtained in discretisations of optimal control of such systems. For this
family, a branch-and-bound algorithm solves the discretised problem to global
optimality.
  As an example, we consider water systems, where variations in flow and
variations in water levels are continuous, while decisions related to
fixed-speed pumps and whether gates that may be opened and closed are discrete.
We show that the related optimal-control problems come from the family we
introduce -- and implement deterministic solvers with global convergence
guarantees.
