# Probabilistic Safety Constraints for Learned High Relative Degree System Dynamics

arXiv: https://arxiv.org/abs/1912.10116 · HTML: https://mlsanity.com/paper/1912.10116/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Dec 2019.

## Built on by (most cited first, 9 of 9)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Sample-efficient Safe Learning for Online Nonlinear Control with Control Barrier Functions](https://mlsanity.com/paper/2207.14419/) (2022)
- [Safe Exploration Method for Reinforcement Learning under Existence of Disturbance](https://mlsanity.com/paper/2209.15452/) (2022)
- [Safe Reinforcement Learning with Probabilistic Control Barrier Functions for Ramp Merging](https://mlsanity.com/paper/2212.00618/) (2022)
- [Robust Model Based Reinforcement Learning Using L1 Adaptive Control](https://mlsanity.com/paper/2403.14860/) (2024)
- [Robustifying Reinforcement Learning Policies with L1 Adaptive Control](https://mlsanity.com/paper/2106.02249/) (2021)
- [Guaranteed Trajectory Tracking under Learned Dynamics with Contraction Metrics and Disturbance Estimation](https://mlsanity.com/paper/2112.08222/) (2021)
- [ProBF: Learning Probabilistic Safety Certificates with Barrier Functions](https://mlsanity.com/paper/2112.12210/) (2021)
- [Safely Learning Controlled Stochastic Dynamics](https://mlsanity.com/paper/2506.02754/) (2025)

## Abstract (arXiv)

This paper focuses on learning a model of system dynamics online while satisfying safety constraints.Our motivation is to avoid offline system identification or hand-specified dynamics models and allowa system to safely and autonomously estimate and adapt its own model during online operation.Given streaming observations of the system state, we use Bayesian learning to obtain a distributionover the system dynamics. In turn, the distribution is used to optimize the system behavior andensure safety with high probability, by specifying a chance constraint over a control barrier function.