AEROASSISTED COPLANAR ORBITAL TRANSFER OF FLIGHT VEHICLES USING THE SEQUENTIAL GRADIENT-RESTORATION ALGORITHM (OPTIMIZATION, BOLZA PROBLEM, GRAZING TRAJECTORY, MINIMAX)

[摘要] This thesis considers both classical and minimax problems of optimal control arising in the study of coplanar aeroassisted orbital transfer. The basic idea is to employ the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers via lift modulation in the sensible atmosphere. Within the framework of classical optimal control, the following problems are studied: (i) minimize the energy required for orbital transfer, Problem (P1); (ii) minimize the time integral of the heating rate, Problem (P2); (iii) minimize the time of flight during the atmospheric portion of the trajectory, Problem (P3); (iv) maximize the time of flight during the atmospheric portion of the trajectory, Problem (P4); (v) minimize the time integral of the square of the path inclination, Problem (P5); (vi) minimize the time integral of the square of the difference between the altitude and a reference altitude to be determined, Problem (P6); and (vii) minimize the sum of the squares of the initial and final path inclinations, Problem (P7). Within the framework of minimax optimal control, the following problems are studied: (i) minimize the peak heating rate, Problem (Q1); (ii) minimize the peak dynamic pressure, Problem (Q2); and (iii) minimize the peak altitude drop, Problem (Q3). If one disregards the bounds on the lift coefficient, one finds that the optimal solution from the energy viewpoint is the grazing trajectory, which is characterized by favorable values of the peak heating rate and peak dynamic pressure. While the grazing trajectory is not flyable, it represents a limiting solution that one should strive to approach in actual flight. For this reason, Problems (P5), (P6), (P7), (Q3) are introduced; their solutions, obtained by accounting for the bounds on the lift coefficient, are referred to as nearly-grazing trajectories. Numerical solutions are obtained by means of the sequential gradient-restoration algorithm for optimal control problems. Several numerical examples are presented, and their engineering implications are discussed. In particular, the merits of nearly-grazing trajectories are discussed.

[发布机构] Rice University