【摘要】 针对大气层内可回收火箭的动力下降问题,提出一种多阶段的鲁棒优化(Robust optimization, RO)方法.由于大气层内存在未知风场,如何在火箭下降段考虑这种不确定性具有十分重要的意义.首先,建立一个关于高度的不确定风场模型,在该风场下给出火箭动力下降的鲁棒最优控制问题.为了求解该问题,使用一种对不等式约束采取一阶近似并将一阶项作为安全裕量加入约束的鲁棒优化方法,得到一个可以求解的单阶段鲁棒优化算法.其次,定量给出安全裕量的上界,基于该上界提出一种多阶段鲁棒优化算法,避免单阶段鲁棒优化算法中安全裕量可能过大导致无法求解的问题.最后,通过仿真对比各个算法在多个实际风场下的性能,结果表明所提出的多阶段鲁棒优化方法同时具有较高的落点精度和对于不同风场的鲁棒性.更多还原

【Abstract】 This paper proposes a multi-stage robust optimization(RO) method for the endoatmospheric powered descent problem of reusable rockets. Due to the unknown wind field in the atmosphere, it is of great significance to consider this uncertainty during the rocket descent phase. Firstly, a model of uncertain wind field with respect to altitude is established, and a robust optimal control problem for rocket powered descent is formulated under this wind field. To solve this problem, a tractable single-stage RO algorithm is developed by approximating the inequality constraints using a first-order expansion and incorporating the first-order term as a safety margin. Secondly, an upper bound on the safety margin is quantitatively derived. Based on this upper bound, a multi-stage RO algorithm is proposed, which avoids the infeasibility problem caused by the excessively large safety margin in the single-stage RO algorithm. Finally, simulation results are presented to compare the performance of each algorithm under various actual wind fields. The results demonstrate that the proposed multi-stage RO method achieves both high landing accuracy and robustness against different wind fields.更多还原