A Computationally-Friendly Data-Driven Safety Filter for Control-Affine Discrete-Time Systems Subject to Unknown Process Noise

A supervisory safety filter is developed to minimally modify nominal control inputs to a nonlinear controlaffine discrete-time system to ensure satisfaction of potentially time-varying state and input constraints, i.e., safety constraints, with high probability. The system model is known while the environment model, i.e., distribution of additive Gaussian process noise, is unknown. State measurements are used to learn the statistics of the process noise. The safety filter employs a robust optimization problem involving tightening of the safety constraints based on the learned statistics and the corresponding confidence.