Solving the Minimum-Fuel Low-Thrust Geostationary Station Keeping Problem via the Switching Systems Theory

The optimal station keeping control problem of a geostationary satellite equipped with electric thrusters is recast as a switched system commutation times optimisation problem, considering that a system with a bang-bang control profile is composed by several subsystems, one for which all the controls are off and the other ones one for which one of the controls is on. In order to optimise the commutation times, the optimal firing sequence has to be known in advance. This sequence is provided by a two-step decomposition technique and the proposed method can be interpreted as a third step. Simulation results on a realistic example validate the benefit of this third optimisation step on the control sequence fuel consumption.