  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.

Optimization and Control