Solution of two-point boundary value problems in optimal maneuvers of flexible vehicles.

摘要

Obtaining solutions to nonlinear two-point boundary value problems is often a formidable task that is effectively restricted to a relatively small number of numerical methods. An asymptotic perturbation method that can be applied to a large class of nonlinear two-point boundary value problems is presented and compared with some of the classical numerical methods available. Simple examples are included to illustrate the application of the perturbation method.; Two distinct types of optimal maneuvers of flexible vehicles are examined in this dissertation. An optimal control problem for three-dimensional attitude acquisition of a rigid and a flexible spacecraft is formulated, and the perturbation method is used to determine the solution for each problem. For the rigid body attitude maneuvers, large-angle solutions are generated. However, the flexible spacecraft optimal maneuvers are solved only for small angular motions and small flexural amplitudes. In the second type of problem, single-axis, time-optimal maneuvers of a flexible body are considered. A sub-optimal problem is developed, and numerical simulations for controlling multiple modes are presented. The solutions are then parameterized such that the optimal control can be calculated from algebraic interpolation of solution sets.