In this paper, an Hamiltonian Structure-Preserving control is proposed to stabilise in the sense of Lyapunov an unstable distant prograde orbit in the Sun-(Earth-Moon) system of the restricted three-body problem by means of solar radiation pressure. This orbit shows a saddle x center equilibrium which becomes a stable x unstable foci in the farther side of the orbit with respect to the Earth-Moon distance. The controller acceleration is generated by the solar radiation pressure where the magnitude of the acceleration can be controlled by a "morphing" deployable structure (reflective area-changing surface), and its orientation toward the Sun-line direction. It will be shown that the proposed controller admits different sets of gains that guarantee the stability; moreover, it is possible to find analytically the minimum set of gains to have Lyapunov stability, which is a necessary but not sufficient condition. An algorithm was used to identify the stability regions as a function of the gain sets. Finally, the feedback control law is described in terms of area-changing and its orientation angle time history to identify the structural drivers in terms of projected area and its reflectivity properties required.
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