Robust control of the Hill's problem with drag

There are significant advantages associated with the analysis of satellite trajectory control problems in the Hill's analysis framework. As with the circular restricted three-body problem (CRTBP) equations, the Hill's equations support three-dimensional “halo” orbits that require station-keeping control. These orbits are typically in regions of space close to a libration point. In most cases these orbits are unstable, with drag effects introducing uncertain exogenous forces. A two-degree-of-freedom (Formula presented.) control strategy is used to maintain a pre-selected orbit and introduce a quantifiable robust stability margin. The control study presented is based on a time-periodic (Formula presented.) state feedback law, and a time-periodic feed-forward control that is based on a linearized drag model. The efficacy of these ideas is demonstrated by simulation.