# Probabilistic model predictive safety certification for learning-based control

arXiv: https://arxiv.org/abs/1906.10417 · HTML: https://mlsanity.com/paper/1906.10417/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2019.

## Built on by (most cited first, 22 of 22)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [How to Certify Machine Learning Based Safety-critical Systems? A Systematic Literature Review](https://mlsanity.com/paper/2107.12045/) (2021)
- [HardNet: Hard-Constrained Neural Networks with Universal Approximation Guarantees](https://mlsanity.com/paper/2410.10807/) (2024)
- [Robust Uncertainty Bounds in Reproducing Kernel Hilbert Spaces: A Convex Optimization Approach](https://mlsanity.com/paper/2104.09582/) (2021)
- [Risk-averse autonomous systems: A brief history and recent developments from the perspective of optimal control](https://mlsanity.com/paper/2109.08947/) (2021)
- [Safe and Efficient Reinforcement Learning Using Disturbance-Observer-Based Control Barrier Functions](https://mlsanity.com/paper/2211.17250/) (2022)
- [HYPERmotion: Learning Hybrid Behavior Planning for Autonomous Loco-manipulation](https://mlsanity.com/paper/2406.14655/) (2024)
- [Safe Reinforcement Learning via Confidence-Based Filters](https://mlsanity.com/paper/2207.01337/) (2022)
- [Adaptive Stochastic Nonlinear Model Predictive Control with Look-ahead Deep Reinforcement Learning for Autonomous Vehicle Motion Control](https://mlsanity.com/paper/2311.04303/) (2023)
- [Stability-Constrained Markov Decision Processes Using MPC](https://mlsanity.com/paper/2102.01383/) (2021)
- [A Dynamic Safety Shield for Safe and Efficient Reinforcement Learning of Navigation Tasks](https://mlsanity.com/paper/2412.04153/) (2024)
- [Trajectory Optimization of Chance-Constrained Nonlinear Stochastic Systems for Motion Planning Under Uncertainty](https://mlsanity.com/paper/2106.02801/) (2021)
- [Reinforcement Learning with Model Predictive Control for Highway Ramp Metering](https://mlsanity.com/paper/2311.08820/) (2023)
- [Reinforcement Learning with Ensemble Model Predictive Safety Certification](https://mlsanity.com/paper/2402.04182/) (2024)
- [Safe Reinforcement Learning for Power System Control: A Review](https://mlsanity.com/paper/2407.00681/) (2024)
- [Safe Reinforcement Learning for Strategic Bidding of Virtual Power Plants in Day-Ahead Markets](https://mlsanity.com/paper/2307.05812/) (2023)
- [Generalized Policy Improvement Algorithms with Theoretically Supported Sample Reuse](https://mlsanity.com/paper/2206.13714/) (2022)
- [Model-Assisted Probabilistic Safe Adaptive Control With Meta-Bayesian Learning](https://mlsanity.com/paper/2307.00828/) (2023)
- [Q-learning-based Model-free Safety Filter](https://mlsanity.com/paper/2411.19809/) (2024)
- [Uncertainty-Aware Predictive Safety Filters for Probabilistic Neural Network Dynamics](https://mlsanity.com/paper/2604.26836/) (2026)
- [CoCoNav: Conformal Control for Safe Robot Navigation in Crowds](https://mlsanity.com/paper/2608.07751/) (2026)

## Abstract (arXiv)

Reinforcement learning (RL) methods have demonstrated their efficiency in simulation environments. However, many applications for which RL offers great potential, such as autonomous driving, are also safety critical and require a certified closed-loop behavior in order to meet safety specifications in the presence of physical constraints. This paper introduces a concept, called probabilistic model predictive safety certification (PMPSC), which can be combined with any RL algorithm and provides provable safety certificates in terms of state and input chance constraints for potentially large-scale systems. The certificate is realized through a stochastic tube that safely connects the current system state with a terminal set of states, that is known to be safe. A novel formulation in terms of a convex receding horizon problem allows a recursively feasible real-time computation of such probabilistic tubes, despite the presence of possibly unbounded disturbances. A design procedure for PMPSC relying on bayesian inference and recent advances in probabilistic set invariance is presented. Using a numerical car simulation, the method and its design procedure are illustrated by enhancing a simple RL algorithm with safety certificates.