Learning Safety Filters for Unknown Discrete-Time Linear Systems

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