  We consider mixed-integer optimal control problems with combinatorial
constraints that couple over time such as minimum dwell times. We analyze a
lifting and decomposition approach into a mixed-integer optimal control problem
without combinatorial constraints and a mixed-integer problem for the
combinatorial constraints in the control space. Both problems can be solved
very efficiently with existing methods such as outer convexification with
sum-up-rounding strategies and mixed-integer linear programming techniques. The
coupling is handled using a penalty-approach. We provide an exactness result
for the penalty which yields a solution approach that convergences to partial
minima. We compare the quality of these dedicated points with those of other
heuristics amongst an academic example and also for the optimization of
electric transmission lines with switching of the network topology for flow
reallocation in order to satisfy demands.
