Neighboring optimal control for open-time multiburn orbital transfers

While a parametric approach has been proposed recently to establish the neighboring optimal control (NOC) for multiburn orbital transfer problems with fixed final time, it is not applicable once the final time is free. Indeed, it is quite common for orbital transfer missions to leave their final time free. In this paper, we continue developing the parametric approach and extend it to establishing the NOC for such problems with free final time. The key idea is to construct a new parameterized family of extremals such that every neighboring extremal around a nominal one is totally determined by its final time and a vector. Then, the NOC for free-time scenarios is readily established through deriving the Taylor expansion of the parameterized neighboring extremals; as a by-product, some prerequisite conditions, fundamental for establishing the NOC, are formulated. Moreover, a scheme for performing the NOC is proposed accordingly. Finally, to illustrate the improvement of this paper, a free-time multiburn orbital transfer problem is computed and some Monte Carlo campaigns are tested in the presence of various perturbations, showing that the final condition errors are significantly reduced by employing the NOC developed in the paper.