Stationkeeping of an L 2 Libration Point Satellite with D θ − Technique

A new method for 2 L libration-point orbit stationkeeping is proposed in this paper using continuous thrust. The circular restricted three-body problem with Sun and Earth as the two primaries is considered. The unstable orbit about the 2 L libration-point requires stationkeeping maneuvers to maintain the nominal path. In this study, an approach, called the “ D θ − technique,” based on optimal control theory gives a closed-form suboptimal feedback solution to solve this nonlinear control problem. In this approach the Hamiltonian-Jacobi-Bellman (HJB) equation is solved approximately by adding some perturbations to the cost function. The controller is designed such that the actual trajectory tracks a predetermined reference orbit with good accuracy. Numerical results employing this method demonstrate the potential of this method.