Optimal Rocket-Powered Ascent Study

The Goddard Problem is that of maximizing the final altitude for a vertically ascending, rocket-powered vehicle under the influence of an inverse square gravitational field and atmospheric drag. The present study is concerned with the effects of two additional constraints: a dynamic pressure limit [qmax], and a specified final time [tf]. Nine different switching structures involving zero-thrust arcs, full-thrust arcs, singular-thrust arcs, and constrained arcs are obtained for prescribed values of qmax and final time tf between tf,min and tf*. Here tf,min is the minimum possible time within which all the fuel can be burned, and tf* is the optimal final time. For all points in the above defined domain of the qmax,tf-plane the associated optimal switching structure is clearly identified. Finally, a comparison between the optimal solutions and a simple intuitive feedback law is given.