Trajectory Generation Using a Modified Simple Shooting Method

摘要

Recently, several authors have studied the problem of trajectory redesign for hypersonic aircraft. The usual procedure for solving such problems is to set it up as a constrained optimal control problem. Lu and Schierman used direct methods to numerically solve the optimal control problems. Alternatively, one could use Pontryagin's Minimum Principle to obtain first-order necessary conditions for the optimal control problem and obtain a two-point boundary-value problem (TPBVP). Originally created to solve two-point boundary value problems (TPBVPs), the Modified Simple Shooting Method (MSSM) has been shown to be superior, both in speed and accuracy, to known methods for solving TPBVPs. Since optimal control problems can be formulated with differential equations and boundary conditions, it seems feasible to propose that the MSSM could be used to solve problems in optimal control. Here, the original MSSM algorithm was altered and used in conjunction with Pontryagin's Minimum Principle in an attempt to solve an optimal control problem in trajectory generation. In this paper, the authors consider the problem of trajectory redesign of the unpowered reentry phase for a hypersonic air vehicle. They consider outer loop equations governing the motion of the center of mass and consider the angle of attack to be the input variable. The lift and drag forces for the aircraft considered were obtained from a polynomial neural network approximation of experimental data. Effector deflections were chosen so that the aircraft Underwent trimmed flight. (6 figures, 7 refs.).