A Pontryagin-based NMPC approach for a LEO to GEO transfer space mission

Nowadays, the propellant consumption minimization is a fundamental task for space missions in order to save more money budget and to plan a longer duration for them. In the last years space technology has moved forward, overcoming classical astrodynamics methods as the Lambert's problem solution and the Hohmann transfer which are ideal and open-loop maneuvers that require a strong human effort. As it has been seen in control system literature, a MPC-based control strategy is a very interesting solution because allows us to deal with linear and nonlinear systems, to impose input and/or state constraints, to have a guidance and control strategy managed by a single algorithm and most important to have an optimum trade-off between performances and fuel consumption. The work of thesis consists into design a control algorithm through a Nonlinear Model Predictive Control approach in order to transfer a spacecraft from a Low Earth Orbit (LEO) to a Geostationary Orbit (GEO). Instead of using the classical numerical optimization approach, an analytical method based on Pontryagin Minimum (or Maximum) Principle has been involved, allowing to get an explicit optimal control law. Both the dynamical and internal prediction models, used for designing and simulating purposes, are based on the Modified Equinoctial Orbital Elements, a set of six equations that allows us to overcome some singularities that would be present using the standard Keplerian elements.