Long-Term Electric-Propulsion Geostationary Station-Keeping via Integer Programming

摘要

The problem of the computation of correction maneuvers for the fuel-optimal long-term station-keeping within a predefined longitude and latitude window of a geostationary satellite equipped with electric propulsion is investigated. The use of electric thrusters imposes some additional operational constraints on actuation that can be reformulated as logical constraints on the control function. The resulting fuel-optimal station-keeping problem is therefore transformed into a mixed linear integer programming problem. The long-term horizon of station-keeping is divided in shorter control cycles synchronized with the cycles of orbit determination, and the long-term station-keeping problem amounts to solve a sequence of similar mixed linear integer programming problems with different initial conditions. Two different terminal constraints on geographical positions and/or linear velocities are added to the formulation of the mixed linear integer programming problems to ease the feasibility of the whole sequence of successive resolutions. Nonlinear perturbed simulations of the computed control strategies show their efficiency on a long-term station-keeping problem lasting one year.