基于遗传算法的连续推力最短时间转移轨道设计  

An Effective Minimum-Time Orbital Transfer Design under Continuous Thrust

作　　者：高怀[1,2,3] 朱战霞[1,2] 刘剑[1,2] 

机构地区：[1]西北工业大学航天学院 [2]航天飞行动力学技术国家级重点实验室 [3]中国人民解放军96363部队

出　　处：《西北工业大学学报》2012年第2期187-191,共5页Journal of Northwestern Polytechnical University

基　　金：国家自然科学基金(10802064)资助

摘　　要：针对连续推力作用下的最优轨道转移问题,在推力不变的条件下,考虑时间最优,设计了最优转移轨道和推力的作用方式。首先,建立描述连续推力轨道转移的状态方程,用变分法进行求解;然后,分别基于极小值原理和bang-bang控制原理推导出用协态变量表示的时间最优制导律,其中基于极小值原理的最优控制避开了bang-bang控制可能出现的奇异区间。由于协态变量无法求解解析解,文章采用遗传算法对协态变量进行优化求解。最后以同平面两个圆轨道为例进行了数值仿真,结果表明两种方法得到的最短时间基本相同,但采用极小值原理的最优转移轨道更加节省燃料。To achieve the optimal orbit transfer under continuous thrust,under the condition that the thrust size does not change,we design the optimal orbital transfer by taking minimum time and fuel consumption into account.Sections 1 and 2 of the full paper explain our minimum-time orbital transfer design,which is more effective than previous ones and whose core consists of：（1） we derive the state equations for describing the orbital transfer under continuous thrust;（2） we deduce two minimum-time guidance laws which are expressed as co-state variables,using the minimum-value principle and the bang-bang control principle respectively;the optimal control with the minimum-value principle can eliminate the singular interval which may occur with the bang-bang control principle;（3） as it is difficult to obtain the analytical solutions of the co-state variables,we use the genetic algorithm to optimize and solve them.Section 3 gives two numerical simulation examples of the transfer of circular orbits in the same plane by using the minimum-value principle and the bang-bang control principle respectively;the simulation results,presented in Figs.2 through 7,and their analysis show preliminarily that the orbital transfers with both principles take nearly the same minimum time;however,the orbital transfer with the minimum principle is more fuel-conserving.

关 键 词：连续推力 极小值原理 周向推力 非开普勒轨道 遗传算法 BANG-BANG控制 

分 类 号：V412.41[航空宇航科学与技术—航空宇航推进理论与工程]