Abstract
This article investigates optimal cooperative control algorithms for spacecraft formation flying system that can guarantee collision avoidance between spacecrafts. By selecting potential functions to avoid collisions and constructing index cost functions to describe optimal control, the optimal control algorithms based on the state-dependent Riccati equations, which only require local information vectors, are presented that can guarantee the formation spacecraft to track the reference trajectory without collisions and achieve optimal performance states. Finally, the corresponding proof analysis by Lyapunov stability theory shows that the closed-loop system for spacecraft formation flying is asymptotically stable. The simulation results demonstrate the effectiveness of the proposed optimal cooperative control algorithms with desired control objectives, including trajectory tracking, formation optimality, and collision avoidance.