Characteristic Elastic Systems of Time-Limited Optimal Maneuvers

Optimizing an elastic system and its active control is discussed. Maneuvers from an initial state to a final state in a finite time interval are considered. An active generalized control force that accomplishes the desired maneuver of a prespecified system is optimal if it minimizes a given quadratic cost function. By also varying a set of design parameters, the elastic system can be determined so as to further minimize the cost function. Here, the elastic system that minimizes the actual control cost is compared with the system that minimizes the ratio of actual cost to the cost of optimally maneuvering a rigid system of the same inertial properties. It is shown that an elastic system corresponding to an extremum of the ratio is actually a characteristic of the time-limited maneuver. Because both the spatial domain and the time interval are fixed, a characteristic elastic system is tuned to the specified temporal boundary conditions. The implication for rest-to-rest, spinup, and spin reversal maneuvers of spacecraft is that the optimal control for a characteristic elastic spacecraft is identical to the optimal control for the same spacecraft as if it were rigid.