| Previous research into fuel-optimal periodic indicated little net performance gain over best steady-state flight for more complex, spherical-earth models. In this research, periodic flight trajectories are found which possess substantial fuel savings over optimal static cruise, for a range of complex point-mass models subjected to a vehicle acceleration constraint, including those for which active engine cooling is modeled. Sufficient conditions for optimality of a periodic process are extended to accommodate the presence of mixed state/control inequality constraint. Optimal regulation of such constrained periodic trajectories is also studied and extended to encompass optimal regulation of slowly-varying systems to optimal quasi-periodic trajectories. This controller is demonstrated to perform well for both a simple two-state periodic problem and the hypersonic cruise problem with slow mass decrease. Finally, new structural aspects of the second variation of a periodic process are brought to light. |
