Optimal Pursuit Strategies in Missile Interception: Mean Field Game Approach

This paper investigates Mean Field Game methods to solve missile interception strategies in three-dimensional space, with a focus on analyzing the pursuit–evasion problem in many-to-many scenarios. By extending traditional missile interception models, an efficient solution is proposed to avoid dimensional explosion and communication burdens, particularly for large-scale, multi-missile systems. The paper presents a system of stochastic differential equations with control constraints, describing the motion dynamics between the missile (pursuer) and the target (evader), and defines the associated cost function, considering proximity group distributions with other missiles and targets. Next, Hamilton–Jacobi–Bellman equations for the pursuers and evaders are derived, and the uniqueness of the distributional solution is proved. Furthermore, using the ϵ-Nash equilibrium framework, it is demonstrated that, under the MFG model, participants can deviate from the optimal strategy within a certain tolerance, while still minimizing the cost. Finally, the paper summarizes the derivation process of the optimal strategy and proves that, under reasonable assumptions, the system can achieve a uniquely stable equilibrium, ensuring the stability of the strategies and distributions of both the pursuers and evaders. The research provides a scalable solution to high-risk, multi-agent control problems, with significant practical applications, particularly in fields such as missile defense systems.