MINIMAX OPTIMAL CONTROL IN THE REENTRY OF A SPACE GLIDER
Doctor of Philosophy
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.