Using Differential Flatness for solving the Minimum-Fuel Low-Thrust Geostationary Station-Keeping Problem

Abstract

International audienceThe minimum fuel station keeping of a geostationary satellite equipped with electric thrusters undergoing the Earth non-spherical disturbing gravitational potential up to degree and order 2 is first recast by transforming the linear time varying relative dynamics in a time invariant one with a Floquet-Lyapunov transformation. In a second step, the flatness property of the system is used to convert the genuine optimal control problem to a linear programming problem. This problem is solved for an ideal geostationary satellite with one thruster mounted on each face