<p>Three-dimensional orbits near the interior Lagrange point (L₁) of the Sun–Earth barycentre system are being considered for multiple missions. Trajectories at these Lagrange points are intrinsically unstable, necessitating spacecraft to utilize trajectory control to sustain proximity to their designated orbits. This research examines the station keeping of halo orbits around the Sun–Earth Lagrange point L₁ within the circular-restricted three-body problem (CRTBP) utilizing two control strategies: target point approach (TPA) and linear quadratic regulator (LQR) methods. Halo orbits with out-of-plane amplitudes of 120,000, 150,000 and 250,000 km were generated using a differential correction method. Random initial errors in the state vector of the satellite were introduced to simulate realistic perturbations, and a genetic algorithm (GA) was applied to optimize maneuver intervals in the TPA. The TPA was tested with different numbers of future target points (2, 3, 4 and 5). Results from different simulations indicate that the TPA is more fuel-efficient for small perturbations, while the LQR approach is more effective for larger initial dispersions. Additionally, a transformation from the Sun–Earth barycentric frame to the Earth-centred J2000 inertial frame is established. These findings provide valuable insights for designing efficient station-keeping strategies that balance maneuver costs with mission longevity. This study offers a comprehensive strategy for maintaining spacecraft near the desired halo orbit trajectories.</p>