基于混合优化算法的空间拦截轨道优化设计

基于改进高斯法(IGM)和遗传算法(GA)的混合优化算法,为解决空间拦截轨道燃料消耗和转移时间的综合最优问题,提出一种空间拦截轨道设计方法.首先,引入牛顿-拉夫逊迭代法对原始高斯法进行改进,解决原始高斯法在解算空间拦截轨道时收敛速度慢、转移角范围小等问题;接着,给出并证明改进高斯法迭代方程有唯一解的充分必要条件.当给定初始轨道参数时,用此条件判断可否用椭圆轨道进行转移;然后给出转移时间,最大脉冲速度等约束条件,对编码方式进行改进,给出混合优化算法的计算步骤;最后以空间拦截轨道优化问题为例,进行仿真分析.仿真结果表明,与传统优化算法相比,混合优化算法收敛的遗传代数少,耗时短,能够较好地运用于空间拦截轨道的设计.

Space interception orbit optimization design based on hybrid optimal algorithm

Based on a hybrid algorithm combining genetic algorithm (GA) with improved Gauss method (IGM), a design method of space interception orbit was proposed for solving time-fuel-optimal trajectory planning problem of interceptor. First, classical Gauss method was improved by applying Newton-Raphson iteration, solving the problem of the classical Gauss method of slow convergence speed and small transfer angle. Then, a theorem on the necessary and sufficient condition for the existence of unique solution was proved. When the initial orbital parameters were given, this condition could be used to judge whether elliptical orbit could be introduced as the interception orbit. After that, constraints of transfer time and maximum pulse rate were given, as well as the calculation steps of hybrid optimal algorithm, and way of coding was improved. Finally taking optimization problem of space interception orbit as an example, simulation was carried out. Simulation result shows that the hybrid algorithm has fewer generations and shorter consuming time compared with conventional optimal algorithm, indicating the algorithm is applicable in determining interception orbit in space.