摘要
为了减少有限推力作用下月球探测器软着陆所需的燃料消耗,提出了应用非线性规划方法来求解该最优控制问题。首先,从庞德里亚金极大值原理出发,将有限推力作用下月球软着陆问题转化为数学上的两点边值问题;在考虑边界条件及横截条件的前提下,将该两点边值问题转化为针对共轭变量初值和末时刻的优化问题;然后应用非线性规划方法求解所形成的参数优化问题。为了降低共轭变量初值选取的敏感性,引入共轭变量与控制变量之间的变换,用控制变量初值代替了共轭变量初值。实验仿真结果显示,本文方法能够成功实现月面软着陆,并且比传统的打靶法减少了2.1%的燃料消耗,表明本文提出的设计方法简单、有效。
In order to decrease the fuel consumption under a finite thrust, a method applying nonlinear programming is presented to solve the optimal control problem on the soft landing of a lunar probe. Based on Pontryagin maximum principle, the lunar soft landing problem is transformed into a two- point boundary value problem in mathematics. In consideration of the bound condition and transversality condition, the resulted two-point boundary value problem is converted into a parameter optimization problem aiming at the initial values of conjugate variables and the terminal time,then it is solved by the nonlinear programming. To reduce the sensitivity of conjugate initial values, the initial values of control variables are used to replace the initial values of conjugate variables based on the transformation between conjugation variables and control variables. The simulated result demonstrates that the proposed method leads to a successful implementation of the lunar soft landing and reduces .by 2.1% fuel consumption as compared with that of the traditional method,which shows that the proposed design scheme is simple and effective.
出处
《光学精密工程》
EI
CAS
CSCD
北大核心
2009年第9期2153-2158,共6页
Optics and Precision Engineering
基金
国家自然科学基金重点资助项目(No.60535010)
教育部博士点基金资助项目(No.20060213037)
长江学者创新团队发展计划资助项目
关键词
飞行器控制
导航技术
月球软着陆
非线性规划
aerocraft control
navigation technology
lunar soft landing
nonlinear programming
