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：随着自主系统变得日益复杂并融入社会，精确建模并安全控制这些系统的需求显著增长。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中取得了巨大成功，但在为这类系统提供安全保障方面仍面临挑战，部分原因在于学习模型存在不确定性。本研究致力于为动力学无法直接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。针对目标系统及安全约束，我们从数据中学习系统动力学的集成模型。利用集成不确定性作为学习动力学模型不确定性的度量，我们计算最大鲁棒控制不变集——从该集合出发，系统在实现模型不确定性被包含于预定义的可接受模型不确定性集合的条件下，必然满足安全约束。我们通过倒立摆仿真案例研究与TurtleBot硬件实验验证了方法的有效性。实验表明，该方法能够增强系统控制动作对模型不确定性的鲁棒性，在不过度约束的前提下生成安全行为。相关代码及配套视频可在项目网站获取。