Model mismatches prevail in real-world applications. Hence it is important to design robust safe control algorithms for systems with uncertain dynamic models. The major challenge is that uncertainty results in difficulty in finding a feasible safe control in real-time. Existing methods usually simplify the problem such as restricting uncertainty type, ignoring control limits, or forgoing feasibility guarantees. In this work, we overcome these issues by proposing a robust safe control framework for bounded state-dependent uncertainties. We first guarantee the feasibility of safe control for uncertain dynamics by learning a control-limits-aware, uncertainty-robust safety index. Then we show that robust safe control can be formulated as convex problems (Convex Semi-Infinite Programming or Second-Order Cone Programming) and propose corresponding optimal solvers that can run in real-time. In addition, we analyze when and how safety can be preserved under unmodeled uncertainties. Experiment results show that our method successfully finds robust safe control in real-time for different uncertainties and is much less conservative than a strong baseline algorithm.
翻译:模型不匹配在现实世界应用中普遍存在。 因此,重要的是为具有不确定动态模型的系统设计稳健的安全控制算法。 主要的挑战在于不确定性导致难以在实时找到可行的安全控制。 现有方法通常会简化问题, 如限制不确定性类型、 忽略控制限制或放弃可行性保障。 在这项工作中, 我们通过为受约束的受国家依赖的不确定性建议一个稳健的安全控制框架来克服这些问题。 我们首先通过学习控制- 限制、 不确定性- robust 安全指数来保证对不确定动态进行安全控制的可行性。 然后我们表明, 稳健的安全控制可以被发展成共解问题( Convex 半不完全程序或第二Order Cone 程序), 并提出可以实时运行的相应最佳解决方案。 此外, 我们分析安全何时以及如何在未建模的不确定性下得以保全。 实验结果表明, 我们的方法成功地在实时找到对不同不确定性的稳健安全控制, 并且比强的基线算法保守得多 。