A learning-based safety filter is developed for discrete-time linear time-invariant systems with unknown models subject to Gaussian noises with unknown covariance. Safety is characterized using polytopic constraints on the states and control inputs. The empirically learned model and process noise covariance with their confidence bounds are used to construct a robust optimization problem for minimally modifying nominal control actions to ensure safety with high probability. The optimization problem relies on tightening the original safety constraints. The magnitude of the tightening is larger at the beginning since there is little information to construct reliable models, but shrinks with time as more data becomes available.

翻译：针对模型未知且受未知协方差高斯噪声影响的离散时间线性时不变系统，本文提出了一种基于学习的安全滤波器。安全性通过状态与控制输入的多面体约束进行刻画。利用经验学习模型及其置信区间下的过程噪声协方差，构建鲁棒优化问题，以最小程度修改标称控制动作，确保高概率的安全性。该优化问题依赖于对原始安全约束的收紧。由于初始阶段缺乏构建可靠模型所需信息，约束收紧幅度较大，但随时间推移与数据积累而逐渐收缩。