月球最优软着陆两点边值问题的数值解法

借助庞特里亚金最大值原理(Pontryagin′s Maximal Principle,PMP),将月球燃耗最优软着陆问题转化为终端时间自由型两点边值问题(Two Point Boundary Value Problem,TPBVP)。采用一种基于初值猜测技术的线性摄动法求解TPBVP,得到最优软着陆轨迹。仿真结果表明,初值猜测技术得出的伴随变量初值均落在线性摄动法的收敛区间内,收敛速度快,优化精度高。最后研究了不同制动推力大小对软着陆性能的影响,结论为:增大制动发动机推力,既可缩短软着陆的时间,又能减少软着陆的燃料消耗。

Numerical Solution of TPBVP for Optimal Lunar Soft Landing

With the help of Pontryagin′s maximal principle(PMP),the fuel optimal lunar soft landing problem was converted into a two point boundary value problem(TPBVP) of variable final time.Initial adjoint guess technique was introduced to provide approximate initial adjoint variables by solving linear algebra equations in the neighborhood of the initial time.Linear perturbation method,which can deal with TPBVP with variable final time,was used to solve the TPBVP.Simulation results indicate that the guessed initial adjoint variables are just in the convergence regions of linear perturbation method,and the convergence rate is rapid.The optimal soft landing trajectories varied with thrust magnitude were investigated.The results show that high-thrust can not only reduce landing time,but also brake fuel consumption.