  We prove a generalization of Noether's theorem for optimal control problems
defined on time scales. Particularly, our results can be used for
discrete-time, quantum, and continuous-time optimal control problems. The
generalization involves a one-parameter family of maps which depend also on the
control and a Lagrangian which is invariant up to an addition of an exact delta
differential. We apply our results to some concrete optimal control problems on
an arbitrary time scale.
