Approximate optimal control for spacecraft fly-around missions under input saturation and prescribed-performance constraints

This paper investigates synchronized attitude-orbit control for spacecraft fly-around missions in the presence of parametric uncertainties, external disturbances, prescribed-performance tracking constraints, and input saturation. An integrated attitude-orbit model is established on SE(3) using screw theory. A time-varying prescribed performance function with a pre-assigned transition time is introduced to moderate the initial envelope contraction under saturation. Based on the transformed error, a logarithmic terminal sliding manifold is constructed to achieve finite-time sliding dynamics while avoiding the controller singularity of conventional terminal sliding-mode designs. For the reduced-order sliding-mode system, an ADP-based near-optimal controller with a non-quadratic input cost is developed to explicitly handle saturation, together with an adaptive critic update law that alleviates practical dependence on persistent excitation. Lyapunov analysis establishes uniformly ultimately bounded stability of the augmented closed-loop system. Simulations demonstrate effective tracking and reduced control effort under saturation constraints.