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This thesis considers the numerical solution of minimax problems of optimal control (also called Chebyshev problems) arising in the reentry of a space glider. First, a transformation technique is employed in order to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations. The transformation requires the proper augmentation of the state vector x(t), the control vector u(t), and the parameter vector (pi), as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the vector parameter being optimized. The transformation technique is then applied to the following Chebyshev problems of interest in the reentry of a space glider: (Q1) minimization of the peak dynamic pressure; and (Q2) minimization of the peak heating rate. A new way of studying the problem of reentry is presented which decomposes the problem into two subproblems: Problem (R) and Problem (S). Problem (R) consists of optimizing the subsystem which defines the longitudinal motion and includes the relations due to the transformation of the Chebyshev problem. This problem, also called the primary problem, is solved as a Mayer-Bolza problem and yields the solution for the performance index and the controls determining the trajectory. Problem (S), also called the secondary problem, reduces to the determination of the switching times for the bank angle, so as to meet the remaining boundary conditions. Numerical results are obtained by means of the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer. Reference is made to the hypervelocity regime, an exponential atmosphere, and a space glider whose trajectory is controlled by means of the angle of attack and the angle of bank.

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.