摘要
针对时间固定的两航天器追逃问题,基于微分对策理论研究了追逃双方的最优控制策略及求解方法。研究在两航天器均为连续小推力假设条件下,以终端距离为支付函数,追踪器希望支付最小,逃逸器希望支付最大,并考虑时变的轨道高度及时变的角速度建立对策模型,模型具有高维时变特征;由对策必要条件,对策研究最终转化为高维时变非线性两点边值问题的求解。提出采用多重打靶法和多目标遗传算法的混合算法,可以解决航天器追逃这类两点边值问题,并给出数值求解的具体方法。方法中,涉及边值问题中的协态变量初值估计时,采用多目标遗传算法给出初值估计,再由多重打靶法求两点边值问题的解。仿真实例表明:混合算法针对这类追逃问题,既能保证计算精度,又具有较好的鲁棒性,算例最终给出了追逃双方的最优控制策略和相应的追逃轨迹。
For the problem of pursuit-evasion with fixed duration for two spacecraft, an optimal control strategy and its numerical solution method are investigated based on the differential game theory. The two spacecraft are conflicted with each other under the assumed condition of low continuous thrust in a dynamics system with time-dependent angular velocity and trajectory altitude. The terminal distance is taken as a payoff. The pursuer tries to minimize the payoff, and the evader tries to maximize it. Consequently, a high-order time-dependent nonlinear two-point boundary-value problem is introduced by using the necessary condition of the differential game. In this paper, a hybrid algorithm is presented by combining the multiple-shooting method with the genetic algorithm for solving this type of pursuit-evasion problem. In this hybrid algorithm, an improved multi-objective genetic algorithm is adopted to obtain the initial estimation of the costate variables, and the result of the genetic algorithm is used as a feeder for the multiple shooting method to solve the solution of the complex two-point boundary-value problem. It is shown by the simulations that this hybrid algorithm has guarantee accuracy and robustness for the problem. Simultaneously, the optimal strategies and the corresponding pursuit-evasion trajectory are obtained.
出处
《宇航学报》
EI
CAS
CSCD
北大核心
2014年第5期537-544,共8页
Journal of Astronautics
关键词
航天器追逃
微分对策
控制策略
两点边值问题
混合算法
Pursuit-evasion of spacecraft
Differential game
Optimal strategy
Two-point boundary-value problem
Hybrid algorithm
