含J2摄动的有限时间航天器追逃博弈问题研究

航天器追逃博弈是航天器在轨捕获任务的一个重要问题，具有极高的军民两用双重价值．针对有限时间且考虑J2摄动的航天器追逃博弈问题，本文提出了一种精确的求解方法．该方法的核心思想是将有限时间的航天器追逃博弈问题建模为有限时间二人零和对策，则博弈中两航天器的最优控制策略可以转化为有限时间二人零和对策的鞍点解．在鞍点解的求解过程中，本文首先基于考虑J2摄动的非线性动力学方程，将两航天器动力学方程和始末边值条件与鞍点解必要条件结合得到两点边值问题，然后提出一种结合遗传算法和配点法的混合算法求解该两点边值问题以得到精确的鞍点解．本文利用数值仿真对所提方法的有效性进行了验证．结果表明：(i) 在航天器追逃博弈过程中，J2摄动对两航天器的最优控制策略具有较大影响；(ii) 所提方法能够精确求解出两航天器在有限时间的追逃博弈过程中的最优控制策略．

On Fixed-Duration Spacecraft Pursuit-Evasion Game with J2 Perturbation

The spacecraft pursuit-evasion game (SPE game) is an important issue for spacecraft's on-orbit capture missions, and it has extremely high dual value for both military and civilian. This paper proposes an accurate method for the SPE game problem with fixed duration and considering the influence of the J2 perturbation. The core idea of this method is to model the fixed-duration SPE game problem as a fixed-duration two-player zero-sum game. Then the optimal control strategy of the two spacecrafts can be transformed into the saddle point solution of the zero-sum game. Based on the nonlinear dynamic equation considering the J2 perturbation, this paper combines the dynamic equations of the two spacecrafts and the initial and final boundary conditions for the saddle point solution to obtain a two-point boundary value problem, and then a hybrid method combining the genetic algorithm and the collocation algorithm is proposed to solve the TPBVP and to obtain the saddle point solution. Numerical simulations are carried out to verify the effectiveness of the proposed method. The simulations results show that: (i) the J2 perturbation has a great influence on the optimal control strategy of the two spacecraft in the SPE game; (ii) the optimal control strategy in the fixedduration SPE game can be obtained by the hybrid method.