Nonlinear tracking of optimal maneuvers in spacecraft formations

We solve a minimum-energy, point-to-point optimal maneuver problem for satellite proximity flight in a perturbed orbit. We perform this control optimization on the nonlinear system using the Maximum Principle, and on a particular linear approximation using the minimum energy transfer theorem. In both cases we assume unperturbed dynamics. We then use a sliding mode controller to track the optimal trajectories in the presence of bounded, finite disturbances that correspond to perturbations on the order of J₂ or less. We find that the sliding mode tracking controller is able to track the optimal desired trajectory in the presence of orbital disturbances and with initial condition error using reasonable input commands.