# Learning Safety Filters for Unknown Discrete-Time Linear Systems

arXiv: https://arxiv.org/abs/2111.00631 · HTML: https://mlsanity.com/paper/2111.00631/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 1 Nov 2021.

## Builds on (most cited first, 12 of 12)

- [End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Tasks](https://mlsanity.com/paper/1903.08792/) (2019)
- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [Learning for Safety-Critical Control with Control Barrier Functions](https://mlsanity.com/paper/1912.10099/) (2019)
- [Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functions](https://mlsanity.com/paper/2004.07584/) (2020)
- [Linear model predictive safety certification for learning-based control](https://mlsanity.com/paper/1803.08552/) (2018)
- [Safely Learning to Control the Constrained Linear Quadratic Regulator](https://mlsanity.com/paper/1809.10121/) (2018)
- [Safe Multi-Agent Interaction through Robust Control Barrier Functions with Learned Uncertainties](https://mlsanity.com/paper/2004.05273/) (2020)
- [Control Barrier Functions for Unknown Nonlinear Systems using Gaussian Processes](https://mlsanity.com/paper/2010.05818/) (2020)
- [Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guarantees](https://mlsanity.com/paper/2111.00411/) (2021)
- [Bayesian Safe Learning and Control with Sum-of-Squares Analysis and Polynomial Kernels](https://mlsanity.com/paper/2004.00662/) (2020)
- [Adaptive Model Predictive Safety Certification for Learning-based Control -- Extended Version](https://mlsanity.com/paper/2109.13033/) (2021)
- [Safe Learning-Based Control of Stochastic Jump Linear Systems: a Distributionally Robust Approach](https://mlsanity.com/paper/1903.10040/) (2019)

## Abstract (arXiv)

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.