Long Flight-Time Range-Optimal Atmospheric Flight Vehicle Trajectories

摘要

Indirect solutions based on Pontryagin's minimum principle are obtained for the problem of maximizing the downrange of a high-performance atmospheric flight vehicle operating in the vertical plane. Control variables are the load factor which appears non-linearly in the equations of motion, and the throttle setting which appears only linearly. Both controls are subject to fixed bounds. Additionally, a dynamic pressure limit is imposed, which represents a first-order state-inequality constraint. In an earlier paper, an identical problem was solved, however, the optimal switching structure could not be determined for "long" flight times above 62 seconds. The present paper correctly identifies these switching structures. All trajectories obtained involve singular control along arcs with active dynamic pressure limit.