Predefined-time Lyapunov function-based sliding mode control for spacecraft rendezvous and docking

This study focuses on the predefined-time control problem for spacecraft rendezvous and docking (R&D), with particular attention to the effects of external disturbances, actuator faults, and actuator saturation. First, the relative motion model incorporates gravity gradient torque and perturbative forces induced by the J₂ term to enhance the practical applicability of the controller. Subsequently, a new Lyapunov function with predefined-time stability properties is proposed, and a predefined-time sliding mode controller is developed based on sliding mode control theory to ensure that the system states converge within a specified time. The proposed controller is general and can be extended to other nonlinear control problems. Additionally, a control torque redistribution scheme is designed to reduce actuator workload and energy consumption, enabling optimal control allocation even under the influence of disturbances, faults, and saturation. Finally, comparative simulations are conducted to validate the effectiveness and robustness of the proposed control strategy.