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基于矩阵博弈的潜艇防御模型
Submarine Defense Model Based on Matrix Game

DOI: 10.12677/pm.2025.152047, PP. 70-78

Keywords: 潜艇防御,矩阵博弈,零和博弈,最优策略
Submarine Defense
, Matrix Game, Zero-Sum Game, Optimal Strategy

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Abstract:

潜艇作为现代海战中不可或缺的作战平台,承担着重要的战略和战术任务。其隐蔽性和高机动性使其成为海上作战中的强大力量。然而,随着鱼雷技术的不断进步,防御鱼雷攻击成为潜艇在水下作战中的一项重大挑战。本文研究了潜艇在水下作战中防御鱼雷攻击的最优策略问题,将潜艇与鱼雷的对抗转化为追逃博弈模型,假设敌方鱼雷攻击潜艇时,潜艇通过改变航向来规避攻击。通过应用博弈论中的零和博弈理论和矩阵博弈模型,本文分析了潜艇和鱼雷在有限策略集合下的最优对策。研究表明,基于潜艇和鱼雷的运动学特性及其有限策略,构建的收益矩阵能够为双方提供最优策略。最后通过具体算例与数值仿真验证了模型的合理性与可行性。
Submarines constitute an indispensable asset in modern naval warfare, executing pivotal strategic and tactical missions. Their inherent stealth and superior maneuverability empower them to operate covertly in contested maritime environments. However, continuous advancements in torpedo technology have rendered the development of effective countermeasures against torpedo attacks a critical challenge in underwater combat. This paper formulates the submarine torpedo counter-measure problem as an optimal control problem within the framework of pursuit-evasion game theory. Specifically, the engagement is modeled as a zero-sum differential game where the submarine employs evasive maneuvers, principally through heading adjustments to mitigate the threat posed by an incoming torpedo. By employing a matrix game model defined over a finite discrete strategy set, we derive the Nash equilibrium solutions. The constructed payoff matrix, based on the kinematic constraints and maneuverability limitations of the submarine and torpedo, facilitates the determination of optimal strategies for both adversaries. Numerical simulations and case studies further validate the analytical robustness and practical feasibility of the proposed model in realistic underwater combat scenarios.

References

[1]  杨静, 吴金平, 刘剑, 等. 一种半监督学习潜艇规避防御智能决策方法[J]. 兵工学报, 2024, 45(10): 3474-3487.
[2]  吴金平. 潜艇作战建模与仿真[M]. 北京: 国防工业出版社, 2017.
[3]  丁文强, 丁浩, 赵志允. 潜艇强机动变深规避鱼雷攻击仿真研究[J]. 现代防御技术, 2024, 52(1): 124-129.
[4]  Isaacs, R. (1965) Differential Games. Wiley.
[5]  李世令, 孙东平, 周宝林. 博弈论在弹道导弹核潜艇威慑能力定性评估中的应用[J]. 装备环境工程, 2012, 9(2): 61-63.
[6]  郭力强, 马亮, 张会, 杨静, 范学满, 程卓. 基于博弈对抗的鱼雷抗干扰攻击建模与优化方法研究[J]. 系统仿真学报, 2023, 35(8): 1814-1823.
[7]  张东俊, 王维平, 黎潇, 等. 基于判别矩阵的潜艇作战态势认知决策建模方法[J]. 系统仿真学报, 2020, 32(2): 182-190.
[8]  郭洪宇, 初阳, 刘志, 张磊, 李小波, 刘国杰. 基于深度强化学习潜艇攻防对抗训练指挥决策研究[J]. 指挥控制与仿真, 2022, 44(1): 103-111.
[9]  Neumann, J. and Morgenstern, O. (1944) Theory of Games and Economic Behavior. Princeton University Press.
[10]  John, C. and Peter, P. (2018) The Matrix Games Handbook: Professional Applications from Education to Analysis and Wargaming Paperback. The History of Wargaming Project.
[11]  赵慧瑾, 陈彧. 基于矩阵博弈的智能水声对抗建模与仿真[J/OL]. 系统仿真学报: 1-16.
https://link.cnki.net/doi/10.16182/j.issn1004731x.joss.24-0044, 2024-09-26.
[12]  王芳杰, 黄鹏, 张子俊. 基于矩阵博弈的近距空战自主机动决策方法[J]. 航空器, 2023, 30(6): 56-63.
[13]  柏铁朝, 许建, 陈炫树, 冯大奎, 王先洲. 基于CFD的潜艇操纵性数值仿真发展综述[J]. 舰船科学技术, 2020, 42(5): 1-7.
[14]  周敏佳, 袁志勇. 潜艇自航式诱饵组合对抗使用方法[J]. 探测与控制学报, 2015, 37(2): 12-14+18.
[15]  郝昕然, 于洋, 崔燕, 等. 潜艇防御两阶段追逃微分博弈模型[J]. 兵器装备工程学报, 2023, 44(S1): 103-110.
[16]  高红伟, 彼得罗相. 动态合作博弈[M]. 北京: 科学出版社, 2009.

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