Learning Safety Filters for Unknown Discrete-Time Linear Systems

TL;DR

This paper introduces a learning-based safety filter for unknown discrete-time linear systems that ensures safety through robust optimization and adaptive constraint tightening based on data confidence.

Contribution

It develops a novel safety filter framework that learns model and noise covariance with confidence bounds to guarantee safety in unknown linear systems.

Findings

The safety filter maintains system safety with high probability.

Constraint tightening adapts over time as more data is collected.

The approach effectively balances safety and control performance.

Abstract

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.