Stabilization of Spacecraft Flight in Halo Orbits: An$H_infty $Approach

Abstract

The problem of stabilizing the motion of a spacecraft in an unstable orbit around the interior Sun–Earth libration point ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_1$</tex> ) is addressed in this paper. Modern control techniques, which extend the traditional <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$ cal H_infty $</tex> framework to periodic discrete linear time-varying systems, are employed in the solution of the problem. Nonlinear simulation results are presented and it is shown that the control effort required can be provided by next-generation electric propulsion systems.