As autonomous systems become more complex and integral in our society, the need to accurately model and safely control these systems has increased significantly. In the past decade, there has been tremendous success in using deep learning techniques to model and control systems that are difficult to model using first principles. However, providing safety assurances for such systems remains difficult, partially due to the uncertainty in the learned model. In this work, we aim to provide safety assurances for systems whose dynamics are not readily derived from first principles and, hence, are more advantageous to be learned using deep learning techniques. Given the system of interest and safety constraints, we learn an ensemble model of the system dynamics from data. Leveraging ensemble uncertainty as a measure of uncertainty in the learned dynamics model, we compute a maximal robust control invariant set, starting from which the system is guaranteed to satisfy the safety constraints under the condition that realized model uncertainties are contained in the predefined set of admissible model uncertainty. We demonstrate the effectiveness of our method using a simulated case study with an inverted pendulum and a hardware experiment with a TurtleBot. The experiments show that our method robustifies the control actions of the system against model uncertainty and generates safe behaviors without being overly restrictive. The codes and accompanying videos can be found on the project website.

翻译：随着自主系统在社会中变得日益复杂和不可或缺，精确建模并安全控制这些系统的需求显著增加。过去十年间，深度学习技术在难以通过第一性原理建模的系统的建模与控制中取得了巨大成功。然而，为这类系统提供安全保障仍面临挑战，部分原因在于学习模型存在不确定性。本研究旨在为动态特性难以通过第一性原理推导，因而更适合采用深度学习技术学习的系统提供安全保障。针对目标系统及其安全约束，我们从数据中学习系统动态的集成模型。以集成不确定性作为学习动态模型不确定性的度量，我们计算出一个最大鲁棒控制不变集：只要实际模型不确定性保持在预设的可接受模型不确定性集合内，从该集合出发的系统能确保满足安全约束。我们通过倒立摆的仿真案例研究和TurtleBot的硬件实验验证了方法的有效性。实验表明，该方法能增强系统控制动作对模型不确定性的鲁棒性，在不产生过度保守性的同时生成安全行为。相关代码与视频可在项目网站获取。