This paper presents a novel approach to the robust solution of optimal impulsive control problems under aleatory and epistemic uncertainty. The novel approach uses belief Markov decision processes to reformulate the control problem in terms of uncertainty distributions, called beliefs, rather than the realizations of the system states. This formulation leads to the definition of a belief optimal control problem where the cost function and constraints are functions of the uncertainty distributions. The control formulation encompasses orbit determination arcs as well. The belief optimization is solved with a shooting-like transcription and a nonlinear programming solver to optimize the resulting discretized problem. Both aleatory and epistemic uncertainties are propagated with a nonintrusive polynomial expansion to capture the nonlinearities of the dynamics. Finally, this new approach is applied to the robust optimization of a flyby trajectory of the Europa Clipper mission in a scenario characterized by knowledge, execution, and observation uncertainty.

本文提出了一种新颖的方法来解决随机和认知不确定性下的最优脉冲控制问题。这种新颖的方法使用信念马尔可夫决策过程来根据不确定性分布（称为信念）而不是系统状态的实现来重新表述控制问题。这个公式导致了信念最优控制问题的定义，其中成本函数和约束是不确定性分布的函数。控制公式也包括轨道确定弧。信念优化通过类似射击的转录和非线性规划求解器来解决，以优化产生的离散化问题。偶然的和认知的不确定性都通过非侵入式多项式展开来传播，以捕捉动力学的非线性。最后，在以知识、执行和观察不确定性为特征的场景中，将这种新方法应用于欧罗巴快船任务的飞越轨迹的稳健优化。