Stackelberg Game–Based Robust Tracking Control for Spacecraft under Saturation Input Constraint

This paper investigates the challenge of trajectory deviation in spacecraft relative position control systems under input saturation constraints and adverse disturbances. First, a Stackelberg game framework is constructed to balance the robustness and tracking performance of the spacecraft control system by considering control inputs and adverse perturbations as players. To address the issue of input saturation constraints, this study introduces the hyperbolic tangent function to transform the constrained optimization problem into an unconstrained optimal control problem. An Actor–Critic framework based on reinforcement learning (RL) is used to approximate the coupled Hamilton–Jacobi (HJ) equation. In addition, the value function decomposition mechanism is introduced to realize the fast convergence of the optimal strategy by the decomposition of the value function. By using the Lyapunov stability theorem, it is proved that the robust tracking control (RTC) scheme can ensure the boundedness of all signals. Simulation results validate the effectiveness of the proposed Stackelberg game–based RTC scheme under input saturation constraints.