含有J2项摄动的卫星追逃轨道优化

研究含有摄动作用下卫星拦截逃逸的双边最优控制问题，其中假定拦截卫星和目标都使用幅值受限连续有限推力进行机动。在卫星所受二体引力基础上加入J2项非球形摄动，推导了两星的动力学方程。为了求得该微分对策问题的鞍点最优解，根据极大极小值的充分必要条件由系统的哈密顿函数得到双边最优时的控制输出，将最优控制问题转化为两点边值问题。针对该问题存在的初值难以获取、收敛困难等问题，采用启发式优化算法搜到鞍点解的初值，并将其带入非线性优化算法获得精确数值解，最后通过仿真给出了两星追逃过程中的最优轨迹和双边最优控制输出。 

Pursuit Evasion Game with J2 Perturbation

A two-side optimization problem where the intercepting satellite pursued the target satellite was studied in this paper. In the pursuit-evasion game, it was assumed that both sides use the continuous thruster and suffer from the earth central gravity with J2 perturbation. The dynamics equations were established to describe their three dimensional motion. Then the optimal control outputs of both side satellites were obtained by building the systems Hamilton and applying the functional extremal condition. The pursuit evasion games was transformed to the two point boundary value problem. At last the new problem was solved with the mixed numerical method where an initial solution was acquired by the genetic algorithm and sent to nonlinear programming as its starting value. Simulation was used to obtain the optimal interception and escaping trajectories of the two satellites and validate the proposed method.