Noether's Theorem for Control Problems on Time Scales
  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. 
Agnieszka B. Malinowska and Moulay Rchid Sidi Ammi
math.OC