# Control Barriers in Bayesian Learning of System Dynamics

arXiv: https://arxiv.org/abs/2012.14964 · HTML: https://mlsanity.com/paper/2012.14964/

## Key facts

- Cited by 17 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 29 Dec 2020.

## Built on by (most cited first, 17 of 17)

- [Safe Reinforcement Learning Using Robust Control Barrier Functions](https://mlsanity.com/paper/2110.05415/) (2021)
- [In-Distribution Barrier Functions: Self-Supervised Policy Filters that Avoid Out-of-Distribution States](https://mlsanity.com/paper/2301.12012/) (2023)
- [Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty](https://mlsanity.com/paper/2106.07108/) (2021)
- [Conformal Methods for Quantifying Uncertainty in Spatiotemporal Data: A Survey](https://mlsanity.com/paper/2209.03580/) (2022)
- [Can Learning Deteriorate Control? Analyzing Computational Delays in Gaussian Process-Based Event-Triggered Online Learning](https://mlsanity.com/paper/2305.08169/) (2023)
- [Safety Filters for Black-Box Dynamical Systems by Learning Discriminating Hyperplanes](https://mlsanity.com/paper/2402.05279/) (2024)
- [DADEE: Well-calibrated uncertainty quantification in neural networks for barriers-based robot safety](https://mlsanity.com/paper/2407.00616/) (2024)
- [Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functions](https://mlsanity.com/paper/2208.10733/) (2022)
- [Distance-Aware Error for Spline Networks: A Bottom-Up Approach to Uncertainty](https://mlsanity.com/paper/2501.04757/) (2025)
- [Safety-Critical Learning of Robot Control with Temporal Logic Specifications](https://mlsanity.com/paper/2109.02791/) (2021)
- [Model-Assisted Probabilistic Safe Adaptive Control With Meta-Bayesian Learning](https://mlsanity.com/paper/2307.00828/) (2023)
- [Real-Time Adaptive Safety-Critical Control with Gaussian Processes in High-Order Uncertain Models](https://mlsanity.com/paper/2402.18946/) (2024)
- [Barrier Certificates for Unknown Systems with Latent States and Polynomial Dynamics using Bayesian Inference](https://mlsanity.com/paper/2504.01807/) (2025)
- [Geometry of Radial Basis Neural Networks for Safety Biased Approximation of Unsafe Regions](https://mlsanity.com/paper/2210.05596/) (2022)
- [Episodic Gaussian Process-Based Learning Control with Vanishing Tracking Errors](https://mlsanity.com/paper/2307.04415/) (2023)
- [Bayesian meta learning for trustworthy uncertainty quantification](https://mlsanity.com/paper/2407.19287/) (2024)
- [Worst-Case Distance-Aware Error Bounds for Neural Networks](https://mlsanity.com/paper/2510.22021/) (2025)

## Abstract (arXiv)

This paper focuses on learning a model of system dynamics online while satisfying safety constraints. Our objective is to avoid offline system identification or hand-specified models and allow a system to safely and autonomously estimate and adapt its own model during operation. Given streaming observations of the system state, we use Bayesian learning to obtain a distribution over the system dynamics. Specifically, we propose a new matrix variate Gaussian process (MVGP) regression approach with an efficient covariance factorization to learn the drift and input gain terms of a nonlinear control-affine system. The MVGP distribution is then used to optimize the system behavior and ensure safety with high probability, by specifying control Lyapunov function (CLF) and control barrier function (CBF) chance constraints. We show that a safe control policy can be synthesized for systems with arbitrary relative degree and probabilistic CLF-CBF constraints by solving a second order cone program (SOCP). Finally, we extend our design to a self-triggering formulation, adaptively determining the time at which a new control input needs to be applied in order to guarantee safety.