基于梯度分割区间优化算法的双脉冲交会优化

研究非固定时间的航天器双脉冲交会轨迹优化问题,设计了基于梯度分割区间优化算法(GIOA)。该算法结合所研究问题的特点,使用每次只选择有限个区间进行操作的区间选择策略、基于梯度优化结果的区间分割策略、基于单调性的区间紧缩策略以及约束条件测试和基于梯度的目标优化估计值更新策略等。梯度优化算法仅用于区间分割和目标优化估计值更新,不但没有影响GIOA对区间优化算法全局性和收敛性的继承,同时加快了包含优化解的小宽度区间的出现,提高了目标优化估计值的更新速度,并由此提高了运算效率。区间选择策略的使用,控制了决策变量区间数量的增长,降低了算法运行的存储需求。算例仿真中,成功求解非固定时间双脉冲交会问题,并展示出算法的优势。 

Optimization of double-impulse rendezvous using gradient-splitting interval optimization algorithm

The optimal problem of time-open double-impulse rendezvous was studied and the gradient-splitting interval optimization algorithm (GIOA) was introduced. Considering the characteristics of the problem, GIOA utilized the interval selection strategy which selected a finite number of subintervals to compute, the interval splitting strategy based on the result of the gradient optimization algorithm, the interval contraction strategy based on monotonicity, the test of constraints and the updating strategy of target estimated value based on gradient, etc. As the gradient-algorithm was only used for the interval splitting strategy and the updating strategy of target estimated value, it had no negative effect on GIOA's inheriting of the global characteristic and convergence of the interval optimization algorithm. Simultaneously it accelerated the appearance of an interval containing the optimal value with small width and the updating rate of target estimated value. Thereby the operation efficiency was improved. By the interval selection strategy, the increase of subinterval numbers has been controlled, and the storage costs have been reduced. In the simulation, GIOA solves the optimal problem of time-open double-impulse rendezvous successfully, and shows the advantages of the algorithm.