Model mismatches prevail in real-world applications. Ensuring safety for systems with uncertain dynamic models is critical. However, existing robust safe controllers may not be realizable when control limits exist. And existing methods use loose over-approximation of uncertainties, leading to conservative safe controls. To address these challenges, we propose a control-limits aware robust safe control framework for bounded state-dependent uncertainties. We propose safety index synthesis to find a robust safe controller guaranteed to be realizable under control limits. And we solve for robust safe control via Convex Semi-Infinite Programming, which is the tightest formulation for convex bounded uncertainties and leads to the least conservative control. In addition, we analyze when and how safety can be preserved under unmodeled uncertainties. Experiment results show that our robust safe controller is always realizable under control limits and is much less conservative than strong baselines.

翻译：模型失配在现实应用中普遍存在。确保具有不确定动态模型的系统安全性至关重要。然而，现有鲁棒安全控制器在存在控制极限时可能无法实现，且现有方法采用松弛的过近似不确定性处理，导致保守的安全控制。为应对这些挑战，我们提出了一种面向有界状态依赖不确定性的控制极限感知鲁棒安全控制框架。通过安全指标综合，我们能够找到在控制极限下保证可实现的鲁棒安全控制器；同时，我们利用凸半无限规划求解鲁棒安全控制——这是针对凸有界不确定性的最紧凑形式，可实现最小保守控制。此外，我们分析了在未建模不确定性下安全性的保持条件与机制。实验结果表明，所提出的鲁棒安全控制器在控制极限下始终可实现，且保守性远低于强基线方法。