Criterion for Winning Closed-Loop Strategies in Orbital Games

Distance regulation and maintenance between a spacecraft and a non-cooperative target is a critical aspect of space missions, which can be modeled as a closed-loop orbital game under incomplete information. The existence of winning strategies in such games is influenced by multiple key decision variables, with complex coupling relationships among them. To address this issue, this paper proposes a quantitative discriminant condition based on the decision-making period of both players, the maximum impulsive control magnitude, the relative distance to the target, and the allowable tolerance. Under this condition, a closed-loop feedback strategy can be designed to maximize the game performance metric, in terms of the reachability and maintainability of the target region. Subject to constraints on decision-making period and maneuverability, the proposed optimal strategy for orbital game consists of two phases: (1) a tactical approach phase, which enables the spacecraft to approach the target region rapidly, and (2) a tactical station-keeping phase, which stabilizes the spacecraft within the region. Finally, numerical simulations validate the effectiveness of the proposed quantitative discriminant conditions.