THE SEPARATE COMPUTATION OF ARCS FOR OPTIMAL FLIGHT PATHS WITH STATE VARIABLE INEQUALITY CONSTRAINTS.
HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS
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Separate computation of arcs is possible for a large class of optimization problems with state variable inequality constraints. Surprisingly, this class to the best of the authors knowledge includes all physical problems which have been solved analytically or numerically to date. Typically these problems have only one constrained arc. Even in more complex problems, separation of arcs can be used to search for additional constrained arcs. As an important example, a maximum range trajectory for a glider entering the Earths atmosphere at a supercircular velocity is determined, subject to a maximum altitude constraint after initial pull-up. It is shown that the optimal path can be divided into three arcs, which may be determined separately with no approximations. The three arcs are 1 the initial arc, beginning at specified initial condition and ending at the entry point onto the altitude constraint 2 the arc lying on the altitude constraint and 3 the terminal arc, beginning at the exit point of the altitude constraint and ending at some specified terminal altitude. The conjugate gradient method, a first order optimization scheme is shown to converge very rapidly to the individual unconstrained optimal arcs. Using this optimization scheme and taking advantage of the separation of arcs an investigation revealed that two locally optimum paths exist. The range of one exceeds the range of the other by about 250 nautical miles about 6 for the re-entry vehicle used here maximum lift-to-drag ratio is .9. Author
- Numerical Mathematics
- Spacecraft Trajectories and Reentry