Cyber-physical systems (CPS) designed in simulators behave differently in the real-world. Once they are deployed in the real-world, we would hence like to predict system failures during runtime. We propose robust predictive runtime verification (RPRV) algorithms under signal temporal logic (STL) tasks for general stochastic CPS. The RPRV problem faces several challenges: (1) there may not be sufficient data of the behavior of the deployed CPS, (2) predictive models are based on a distribution over system trajectories encountered during the design phase, i.e., there may be a distribution shift during deployment. To address these challenges, we assume to know an upper bound on the statistical distance (in terms of an f-divergence) between the distributions at deployment and design time, and we utilize techniques based on robust conformal prediction. Motivated by our results in [1], we construct an accurate and an interpretable RPRV algorithm. We use a trajectory prediction model to estimate the system behavior at runtime and robust conformal prediction to obtain probabilistic guarantees by accounting for distribution shifts. We precisely quantify the relationship between calibration data, desired confidence, and permissible distribution shift. To the best of our knowledge, these are the first statistically valid algorithms under distribution shift in this setting. We empirically validate our algorithms on a Franka manipulator within the NVIDIA Isaac sim environment.

翻译：在模拟器中设计的网络物理系统（CPS）在实际环境中表现不同。因此，当它们部署到现实世界后，我们需要在运行时预测系统故障。针对一般随机CPS的信号时态逻辑（STL）任务，我们提出了鲁棒预测性运行时验证（RPRV）算法。RPRV问题面临多项挑战：（1）可能缺乏已部署CPS行为的足够数据；（2）预测模型基于设计阶段遇到的系统轨迹分布，即部署期间可能出现分布漂移。为应对这些挑战，我们假设已知部署与设计阶段分布之间统计距离（以f-散度衡量）的上界，并采用基于鲁棒共形预测的技术。受我们在文献[1]中结果的启发，我们构建了一种精确且可解释的RPRV算法。我们使用轨迹预测模型估计系统运行时行为，并通过鲁棒共形预测考虑分布漂移以获得概率保证。我们精确量化了校准数据、期望置信度与可允许分布漂移之间的关系。据我们所知，这是该场景下首批具备统计有效性的分布漂移处理算法。我们在NVIDIA Isaac仿真环境中使用Franka机械臂进行了实验验证。