Trajectory Optimization and Feedback Control

Following an introduction and an enunciation to the basics of the calculus of variations and Pontryagin’s minimum principle, the fundamental of optimal control is presented. After illustrating the methodology with a couple of examples, the application to optimal trajectory tracking is discussed. This is followed by a number of application examples. These include an example of a spacecraft orbiting a central planet and the motion defined in a set of space fixed or planeto-centric coordinates, an example of a spacecraft orbiting a central planet and the motion defined in a relative motion frame of reference coordinates, an example of a spacecraft orbiting a central planet and the motion defined in a set of planeto-centric spherical coordinates and an example of a spacecraft orbiting a central planet with the motion defined in a rotating frame as in the analysis of the circular restricted three-body problem. The principles of linear optimal feedback control and its application to the synthesis of optimal trajectories as well as trajectory tracking are briefly revisited. Finally, the methods of Edelbaum and Petropolous, including the Q law, as well as other methods are discussed.