The fuel-optimal control problem in aeroassisted non-coplanar orbital transfer is addressed. The equations of motion for the atmospheric manoeuvre are non-linear and the optimal (nominal) trajectory and control are obtained. In order to follow the nominal trajectory under actual conditions, a neighbouring optimum guidance scheme is designed using linear quadratic regulator theory for onboard real-time implementation. One of the state variables is used as the independent variable in preference to the time. The weighting matrices in the performance index are chosen by a combination of a heuristic method and an optimal modal approach. The necessary feedback control law is obtained in order to minimize the deviations from the nominal conditons. The results are presented to a typical aeroassisted non-coplanar orbital transfer problem.
Bibliographical noteFunding Information:
This research was supported by NASA Grant NAG-I-736, with Dr Daniel D. Moerder as Technical Monitor, from the Spacecraft Control Branch, NASA Langely Research Center, Hampton, Virginia.