Indirect Optimization of Bang-Bang Control Problems and Applications to Formation Flying Missions

This thesis is focused on indirect optimization methods for the design of space missions, and, in particular, to a specific class of optimal control problems whose solution exhibits a discontinuous control law: the so called bang-bang optimal control. Any attempt to solving such problems by using an indirect method without any specific treatment of the bang-bang control inevitably results into a failure, except for trivial problems. The thesis compares two techniques, conceptually quite different, that aim to handle (or just to reduce) issues related to the discontinuous profile of the optimal control: the Multi-Bound Approach and the Continuation-Smoothing Technique. These two approaches are first tried out/tested on a very simple case (the rocket-sled problem) and then applied to obtain the solution of two rather complex problems: the cooperative rendezvous and the deployment of a two-spacecraft formation that flies in a High Eccentricity Orbit (referring to the Simbol-X project). The general philosophy that stands behind either approach is outlined, as well as relative strength and weakness. Range of applicability, effort required to the user, computational time, and convergence radius are analyzed and discussed.