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 dimen...
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MDPI AG
2025-04-01
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| Series: | Aerospace |
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| author | Yu Bai Di Zhou Zhen He |
| author_facet | Yu Bai Di Zhou Zhen He |
| author_sort | Yu Bai |
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| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula>-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. |
| format | Article |
| id | doaj-art-c56a6bad13f84e60a085e215083160ff |
| institution | OA Journals |
| issn | 2226-4310 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Aerospace |
| spelling | doaj-art-c56a6bad13f84e60a085e215083160ff2025-08-20T02:24:39ZengMDPI AGAerospace2226-43102025-04-0112430210.3390/aerospace12040302Optimal Pursuit Strategies in Missile Interception: Mean Field Game ApproachYu Bai0Di Zhou1Zhen He2School of Astronautics, Harbin Institute of Technology, Harbin 150001, ChinaSchool of Astronautics, Harbin Institute of Technology, Harbin 150001, ChinaSchool of Astronautics, Harbin Institute of Technology, Harbin 150001, ChinaThis 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϵ</mi></semantics></math></inline-formula>-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.https://www.mdpi.com/2226-4310/12/4/302mean field gamesmissile interceptionforward–backward stochastic differential equations (FBSDEs)<i>ϵ</i>-Nash equilibrium |
| spellingShingle | Yu Bai Di Zhou Zhen He Optimal Pursuit Strategies in Missile Interception: Mean Field Game Approach Aerospace mean field games missile interception forward–backward stochastic differential equations (FBSDEs) <i>ϵ</i>-Nash equilibrium |
| title | Optimal Pursuit Strategies in Missile Interception: Mean Field Game Approach |
| title_full | Optimal Pursuit Strategies in Missile Interception: Mean Field Game Approach |
| title_fullStr | Optimal Pursuit Strategies in Missile Interception: Mean Field Game Approach |
| title_full_unstemmed | Optimal Pursuit Strategies in Missile Interception: Mean Field Game Approach |
| title_short | Optimal Pursuit Strategies in Missile Interception: Mean Field Game Approach |
| title_sort | optimal pursuit strategies in missile interception mean field game approach |
| topic | mean field games missile interception forward–backward stochastic differential equations (FBSDEs) <i>ϵ</i>-Nash equilibrium |
| url | https://www.mdpi.com/2226-4310/12/4/302 |
| work_keys_str_mv | AT yubai optimalpursuitstrategiesinmissileinterceptionmeanfieldgameapproach AT dizhou optimalpursuitstrategiesinmissileinterceptionmeanfieldgameapproach AT zhenhe optimalpursuitstrategiesinmissileinterceptionmeanfieldgameapproach |