In this work, we consider the dynamics of the Circular Restricted Three-Body Problem for the Earth-Moon system. Taking into account the L1 equilibrium point in this dynamics, it is constructed a family of periodic orbits in the vicinity of this libration point, called halo orbits. The construction is built using an analytical approach as a first guess with a numerical method in addition, in order to correct the linear approximation procedure. Withal the stability of this libration point trajectories analyzed and proven to be unstable, a spacecraft moving near this point must use some correction maneuver to remain close to the nominal orbit. We proposed a station-keeping strategy applicable to those trajectories using optimal linear and nonlinear feedback control laws. The proposed nonlinear control law was synthesized through the solution of an Riccati equation.