# A predictive safety filter for learning-based control of constrained nonlinear dynamical systems

arXiv: https://arxiv.org/abs/1812.05506 · HTML: https://mlsanity.com/paper/1812.05506/

## Key facts

- Cited by 118 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Dec 2018.

## Built on by (most cited first, 30 of 118)

- [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)
- [Constrained Policy Optimization via Bayesian World Models](https://mlsanity.com/paper/2201.09802/) (2022)
- [SafeDreamer: Safe Reinforcement Learning with World Models](https://mlsanity.com/paper/2307.07176/) (2023)
- [Provably Safe Reinforcement Learning: Conceptual Analysis, Survey, and Benchmarking](https://mlsanity.com/paper/2205.06750/) (2022)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Provably Safe Reinforcement Learning via Action Projection using Reachability Analysis and Polynomial Zonotopes](https://mlsanity.com/paper/2210.10691/) (2022)
- [Synthesis of Model Predictive Control and Reinforcement Learning: Survey and Classification](https://mlsanity.com/paper/2502.02133/) (2025)
- [ActSafe: Active Exploration with Safety Constraints for Reinforcement Learning](https://mlsanity.com/paper/2410.09486/) (2024)
- [Safe Reinforcement Learning with Chance-constrained Model Predictive Control](https://mlsanity.com/paper/2112.13941/) (2021)
- [GoSafeOpt: Scalable Safe Exploration for Global Optimization of Dynamical Systems](https://mlsanity.com/paper/2201.09562/) (2022)
- [Safety Filtering While Training: Improving the Performance and Sample Efficiency of Reinforcement Learning Agents](https://mlsanity.com/paper/2410.11671/) (2024)
- [CBF-RL: Safety Filtering Reinforcement Learning in Training with Control Barrier Functions](https://mlsanity.com/paper/2510.14959/) (2025)
- [Gameplay Filters: Robust Zero-Shot Safety through Adversarial Imagination](https://mlsanity.com/paper/2405.00846/) (2024)
- [Active Uncertainty Reduction for Safe and Efficient Interaction Planning: A Shielding-Aware Dual Control Approach](https://mlsanity.com/paper/2302.00171/) (2023)
- [Risk-averse autonomous systems: A brief history and recent developments from the perspective of optimal control](https://mlsanity.com/paper/2109.08947/) (2021)
- [SHARP: Shielding-Aware Robust Planning for Safe and Efficient Human-Robot Interaction](https://mlsanity.com/paper/2110.00843/) (2021)
- [Safety Filters for Black-Box Dynamical Systems by Learning Discriminating Hyperplanes](https://mlsanity.com/paper/2402.05279/) (2024)
- [SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functions](https://mlsanity.com/paper/2509.24243/) (2025)
- [Safe Chance Constrained Reinforcement Learning for Batch Process Control](https://mlsanity.com/paper/2104.11706/) (2021)
- [Log Barriers for Safe Black-box Optimization with Application to Safe Reinforcement Learning](https://mlsanity.com/paper/2207.10415/) (2022)
- [Failure-Aware RL: Reliable Offline-to-Online Reinforcement Learning with Self-Recovery for Real-World Manipulation](https://mlsanity.com/paper/2601.07821/) (2026)
- [End-to-End Imitation Learning with Safety Guarantees using Control Barrier Functions](https://mlsanity.com/paper/2212.11365/) (2022)
- [Approximate non-linear model predictive control with safety-augmented neural networks](https://mlsanity.com/paper/2304.09575/) (2023)
- [Embodied Foundation Models at the Edge: A Survey of Deployment Constraints and Mitigation Strategies](https://mlsanity.com/paper/2603.16952/) (2026)
- [Contingency-constrained economic dispatch with safe reinforcement learning](https://mlsanity.com/paper/2205.06212/) (2022)
- [Shielded Reinforcement Learning for Hybrid Systems](https://mlsanity.com/paper/2308.14424/) (2023)
- [Safe Guaranteed Exploration for Non-linear Systems](https://mlsanity.com/paper/2402.06562/) (2024)
- [Learning to Boost the Performance of Stable Nonlinear Systems](https://mlsanity.com/paper/2405.00871/) (2024)
- [A view on learning robust goal-conditioned value functions: Interplay between RL and MPC](https://mlsanity.com/paper/2502.06996/) (2025)

## Abstract (arXiv)

The transfer of reinforcement learning (RL) techniques into real-world applications is challenged by safety requirements in the presence of physical limitations. Most RL methods, in particular the most popular algorithms, do not support explicit consideration of state and input constraints. In this paper, we address this problem for nonlinear systems with continuous state and input spaces by introducing a predictive safety filter, which is able to turn a constrained dynamical system into an unconstrained safe system and to which any RL algorithm can be applied `out-of-the-box'. The predictive safety filter receives the proposed control input and decides, based on the current system state, if it can be safely applied to the real system, or if it has to be modified otherwise. Safety is thereby established by a continuously updated safety policy, which is based on a model predictive control formulation using a data-driven system model and considering state and input dependent uncertainties.