Monte-Carlo simulations play a key role in the current Attitude and Orbit Control Systems (AOCS) Verification and Validation (V&V) process, but it is generally time-consuming and it may fail in detecting worst-case configurations, especially in the presence of rare events. In such a case, $\mu$-analysis offers a nice alternative, although it cannot measure the probability of occurrence of the identified worst-cases, which can invalidate a control system on the basis of unlikely events. Probabilistic $\mu$-analysis was introduced in this context 20 years ago to bridge the gap between the two techniques, but until recently no practical tools were available. This paper summarizes recent advances on this topic with a particular emphasis on practical applications to space systems. More precisely, the proposed technique is applied to evaluate AOCS controllers in the context of a challenging high accuracy satellite pointing control problem. The way the proposed tools can be integrated into the traditional AOCS V&V process and used to tighten the V&V analysis gap is also highlighted.

Monte-Carlo 模拟在当前的姿态和轨道控制系统 (AOCS) 验证和验证 (V&V) 过程中发挥着关键作用，但它通常很耗时，并且可能无法检测最坏情况的配置，尤其是在存在以下情况时罕见事件。在这种情况下，$\mu$-analysis 提供了一个很好的替代方案，尽管它不能测量已识别的最坏情况的发生概率，这可能会根据不太可能发生的事件使控制系统无效。概率的$\mu$分析是在 20 年前在这种情况下引入的，以弥合两种技术之间的差距，但直到最近还没有可用的实用工具。本文总结了该主题的最新进展，特别强调了空间系统的实际应用。更准确地说，所提出的技术用于在具有挑战性的高精度卫星指向控制问题的背景下评估 AOCS 控制器。还强调了建议工具可以集成到传统 AOCS V&V 过程并用于缩小 V&V 分析差距的方式。