基于CW方程的航天器追逃问题半直接求解方法  

Semi-Direct Collocation Method to Spacecraft Pursuit-Evasion Problem Based on CW Equations

作　　者：孙松涛 祝强军 宋斌 SUN Songtao;ZHU Qiangjun;SONG Bin(Shanghai Institute of Aerospace System Engineering,Shanghai 201109,China)

机构地区：[1]上海宇航系统工程研究所

出　　处：《上海航天》2019年第3期68-74,共7页Aerospace Shanghai

摘　　要：针对时间固定的两航天器追逃问题,提出一种以半直接配点法研究追逃双方最优控制策略的求解方法。航天器追逃问题是基于微分对策的追逃问题,该问题是含有追逐者和逃逸者控制变量的两点边值问题。若采用必要条件求解,则对迭代初值要求高,收敛困难。在两航天器均为连续小推力的假设条件下,以终端距离为支付函数,给出半直接配点法的求解过程。在此数值方法中,根据半直接转换将微分对策问题转化为最优控制问题,采用Gauss-Lobbato配点法将此最优问题最终转化为非线性规划问题,继而通过序列二次规划算法求解。这种半直接配点法避免了对微分对策问题最优策略的必要条件(两点边值问题)求解。采用该方法求解对迭代初值不敏感,且数值稳定性好。数值仿真实例验证了这种求解方法的可行性。该方法提高了求解两点边值问题的收敛性,为求解含有双方控制变量的微分对策问题提供了一种思路。In view of the spacecraft pursuit-evasion problem in the fixed time,the semi-direct collocation (SDC) method is adopted to investigate the strategies for the pursuing and evading spacecraft. The spacecraft pursuit-evasion problem is a differential game of pursuit and evasion,and is a two-point boundary-value problem with respect to pursuer’s control variables and evader’s control variables. The solution of the problem is difficult to be given via the necessary conditions of the differential game. Based on the assumption of the continuous low thrust,the terminal distance is the payoff function,and the solution of the problem is obtained by SDC. In SDC,the differential game is transformed to an optimal control problem,the optimal control problem is equal to the nonlinear mathematical programming via Gauss-Lobbato collocation method,and it is solved by the sequential quadratic programming method. SDC is insensitive to the iterative initial value,and its numerical stability is good. The optimal control strategies for both sides and trajectories are shown by the simulation. The proposed method is more convergent than that on account of the necessary conditions,and is provided as a new path to solve the pursuit-evasion problem.

关 键 词：航天器追逃问题 微分对策 最优控制 两点边值问题 半直接配点法 非线性规划 

分 类 号：V11[航空宇航科学与技术—人机与环境工程]