针对受约束轨道追逃博弈问题的循环差分进化求解框架  

A cyclic differential evolution framework for constrained orbitalpursuit-evasion games

作　　者：张去非 季明江 闫斌 刘才山[1] 曹璐 ZHANG QuFei;JI MingJiang;YAN Bin;LIU CaiShan;CAO Lu(College of Engineering,Peking University,Beijing 100871,China;National Innovation Institute of Defense Technology,Academy of Military Science,Beijing 100071,China)

机构地区：[1]北京大学工学院,北京100871 [2]军事科学院国防科技创新研究院,北京100071

出　　处：《中国科学:物理学、力学、天文学》2025年第2期257-268,共12页Scientia Sinica Physica,Mechanica & Astronomica

摘　　要：轨道追逃博弈问题得到了广泛的研究,但大多数均建立在无过程约束的假设上.本文针对受轨道高度约束的轨道追逃博弈问题,推导了鞍点存在性条件.基于方程系数矩阵的性质,将其解耦降维为两组两点边值问题.利用罚函数法处理过程约束,并将两点边值问题转化为针对最优性条件的最优化问题.继而提出了一种循环差分进化(DE)求解框架用于求解该最优化问题,以兼顾全局搜索能力和收敛效率.仿真结果表明,该求解框架相较于传统差分进化算法,大幅提高了求解效率和精度.最后,通过对比无轨道约束工况仿真结果,揭示了轨道高度约束对于防止航天器与地球碰撞的现实意义.Orbital pursuit-evasion games have been widely studied, but most of the research is based on the assumption of no processconstraints. For orbital pursuit-evasion games subject to orbital height constraints, the conditions for the existence of saddlepoints are derived. Based on the properties of the coefficient matrix, the equations are decoupled and reduced in dimensionto two two-point boundary value problems (TPBVPs). The penalty function method is used to handle process constraints,and the two TPBVPs are then transformed into an optimization problem for the optimal conditions. This paper proposesa cyclic differential evolution framework for solving this optimization problem and conducts simulation. The simulationresults verify the efficiency and accuracy of the framework, and reveal the practical significance of orbital height constraintsfor preventing collisions between spacecraft and the Earth.

关 键 词：轨道追逃博弈 轨道高度约束 罚函数 两点边值问题 循环DE求解框架 

分 类 号：V412.41[航空宇航科学与技术—航空宇航推进理论与工程]