Adaptive Optimal Formation Tracking Control for Constrained Multiple Spacecraft Based on Model-Free Differential Graphical Games

This paper investigates the problem of adaptive optimal formation tracking control for multiple spacecraft with control input constraints and entirely unknown dynamics. In practical spacecraft missions such as debris removal or collaborative observation, ensuring optimal coordination under uncertain system models presents significant challenges. To address this, a distributed adaptive control framework is developed based on differential graphical games and low-gain feedback design. By embedding a tunable low-gain parameter into a parameterized algebraic Riccati equation (ARE), we derive a class of distributed optimal control policies that prevent input saturation. Furthermore, a model-free adaptive dynamic programming approach based on value iteration is utilized to solve the parameterized ARE without prior knowledge of the spacecraft dynamics. Adaptive coupling gains are also introduced to ensure closed-loop stability. Rigorous analysis of asymptotic stability is provided, and simulation results demonstrate the effectiveness of the proposed method in spacecraft formation tracking scenarios.