基于相对可达域的航天器博弈均衡求解方法  

Nash equilibrium solution method of spacecraft game based on the relative motion reachable set

作　　者：李靖林 姜中英 师鹏[1,2] 李文龙 LI Jinglin;JIANG Zhongying;SHI Peng;LI Wenlong(School of Astronautics,Beihang University,Beijing 100191,China;Key Laboratory of Spacecraft Design Optimization and Dynamic Simulation Technologies,Ministry of Education,Beijing 100191,China;Beijing Institute of Aerospace Information,Beijing 100854,China;Shanghai Institute of Satellite Engineering,Shanghai 201109,China)

机构地区：[1]北京航空航天大学宇航学院,北京100191 [2]航天器设计优化与动态模拟技术教育部重点实验室,北京100191 [3]北京航天情报与信息研究所,北京100854 [4]上海卫星工程研究所,上海201109

出　　处：《飞行力学》2024年第5期34-41,共8页Flight Dynamics

基　　金：上海航天科技创新基金资助(SAST2023-017)。

摘　　要：针对脉冲推力下的航天器追逃博弈问题,提出了一种基于微分博弈理论和相对可达域的纳什均衡求解方法。首先,构建了单脉冲追逃博弈场景,利用微分博弈理论推导了博弈的纳什均衡必要条件;其次,利用CW方程解析推导了航天器的相对可达域表达式并分析了可达域性质;然后,通过分析追逃双方航天器的相对可达域的可能空间关系,确定了博弈纳什均衡的存在情况;最后,利用相对可达域确定了航天器在猜测的纳什均衡下的终端状态,通过打靶法求解了纳什均衡策略,并仿真验证了所得策略在纳什均衡下的性质。结果表明,在纳什均衡状态下博弈双方将采用最大脉冲幅值朝着同一方向机动。A method for solving the Nash equilibrium in a pursuit-evasion game with impulse maneu-vering for spacecraft is proposed based on differential games and relative reachable domains.Firstly,a scenario of a single-impulse pursuit-evasion game was constructed.And the necessary conditions of Nash equilibrium were derived using differential game theory.Secondly,the expression of the rela-tive reachable domain for spacecraft was analytically derived using the CW equation,and its proper-ties were analyzed.Then,the existence of Nash equilibrium in the game was determined by exami-ning relationships of the relative reachable domains for both pursuer and evader.Finally,the guess-ing terminal states under the Nash equilibrium were determined by using the relative reachable do-main,and the Nash equilibrium strategies were solved by shooting method.The simulation results validate the Nash equilibrium properties of the obtained strategies,and indicate that both sides will use the maximum impulse amplitude at Nash equilibrium and maneuver in the same direction.

关 键 词：空间对抗 追逃博弈 微分对策 纳什均衡 可达域 

分 类 号：V448.2[航空宇航科学与技术—飞行器设计]