# Bayesian Learning-Based Adaptive Control for Safety Critical Systems

arXiv: https://arxiv.org/abs/1910.02325 · HTML: https://mlsanity.com/paper/1910.02325/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2019.

## Built on by (most cited first, 19 of 19)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Review](https://mlsanity.com/paper/2107.12045/) (2021)
- [NeBula: Quest for Robotic Autonomy in Challenging Environments; TEAM CoSTAR at the DARPA Subterranean Challenge](https://mlsanity.com/paper/2103.11470/) (2021)
- [Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty](https://mlsanity.com/paper/2106.07108/) (2021)
- [Safe and Efficient Model-free Adaptive Control via Bayesian Optimization](https://mlsanity.com/paper/2101.07825/) (2021)
- [Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertainty](https://mlsanity.com/paper/2104.08261/) (2021)
- [The Effect of Prior Lipschitz Continuity on the Adversarial Robustness of Bayesian Neural Networks](https://mlsanity.com/paper/2101.02689/) (2021)
- [Safe Exploration Method for Reinforcement Learning under Existence of Disturbance](https://mlsanity.com/paper/2209.15452/) (2022)
- [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)
- [Adaptive Robust Model Predictive Control via Uncertainty Cancellation](https://mlsanity.com/paper/2212.01371/) (2022)
- [Model-Assisted Probabilistic Safe Adaptive Control With Meta-Bayesian Learning](https://mlsanity.com/paper/2307.00828/) (2023)
- [Bayesian inference for data-efficient, explainable, and safe robotic motion planning: A review](https://mlsanity.com/paper/2307.08024/) (2023)
- [Real-Time Adaptive Safety-Critical Control with Gaussian Processes in High-Order Uncertain Models](https://mlsanity.com/paper/2402.18946/) (2024)
- [Combining Bayesian Inference and Reinforcement Learning for Agent Decision Making: A Review](https://mlsanity.com/paper/2505.07911/) (2025)
- [Error-Aware Policy Learning: Zero-Shot Generalization in Partially Observable Dynamic Environments](https://mlsanity.com/paper/2103.07732/) (2021)
- [Adaptive Bayesian Optimization for High-Precision Motion Systems](https://mlsanity.com/paper/2404.14602/) (2024)
- [Adaptive MPC-based quadrupedal robot control under periodic disturbances](https://mlsanity.com/paper/2505.12361/) (2025)
- [Worst-Case Distance-Aware Error Bounds for Neural Networks](https://mlsanity.com/paper/2510.22021/) (2025)

## Abstract (arXiv)

Deep learning has enjoyed much recent success, and applying state-of-the-art model learning methods to controls is an exciting prospect. However, there is a strong reluctance to use these methods on safety-critical systems, which have constraints on safety, stability, and real-time performance. We propose a framework which satisfies these constraints while allowing the use of deep neural networks for learning model uncertainties. Central to our method is the use of Bayesian model learning, which provides an avenue for maintaining appropriate degrees of caution in the face of the unknown. In the proposed approach, we develop an adaptive control framework leveraging the theory of stochastic CLFs (Control Lyapunov Functions) and stochastic CBFs (Control Barrier Functions) along with tractable Bayesian model learning via Gaussian Processes or Bayesian neural networks. Under reasonable assumptions, we guarantee stability and safety while adapting to unknown dynamics with probability 1. We demonstrate this architecture for high-speed terrestrial mobility targeting potential applications in safety-critical high-speed Mars rover missions.