Closed-Loop Strategy Synthesis for Real-Time Spacecraft Pursuit–Evasion Games in Elliptical Orbits

Existing studies on the spacecraft pursuit–evasion problem are usually computationally intensive, typically relying on heuristic search methods or nonlinear programming techniques to derive open-loop strategies. These approaches hinder on-orbit implementation, particularly on platforms with limited computational resources. This article addresses two types of games, intercept and rendezvous games, in elliptical orbits with a time-varying thrust profile. A real-time closed-loop approach is proposed to solve the spacecraft pursuit–evasion problem using a convex-based method. First, the two-sided differential game problem is transformed into an equivalent discounted minimum time transfer problem. The optimal terminal time is then determined through the bisection method by iteratively solving a sequence of convex subproblems. Finally, the proposed open-loop strategy is synthesized into a receding horizon feedback pursuit strategy, ensuring the win. Numerical results demonstrate that the proposed method can solve pursuit–evasion games in real time, achieving a solution time of approximately 100 ms. This significantly reduces computational time compared to existing approaches and eliminates the need for manual parameter tuning. Moreover, the feedback strategy has proven robust in Monte Carlo simulations against an evader executing unknown actions, and empirical evidence of its guaranteed performance is provided.