A note on problems with periodic target sets

For certain types of optimization problems, the target set may consist of an infinite number of points uniformly spaced along one or more of the state variable axes. This is true, for example, in the case of time optimal single-axis attitude control. Since the target set is noncompact, the maximum principle cannot be applied directly. However, a new set of state variables can be defined ahich eliminates this problem. The single-axis attitude control problem will be solved to demonstrate the method.