# Predictive control barrier functions: Enhanced safety mechanisms for learning-based control

arXiv: https://arxiv.org/abs/2105.10241 · HTML: https://mlsanity.com/paper/2105.10241/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2021.

## Built on by (most cited first, 14 of 14)

- [Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysis](https://mlsanity.com/paper/2502.00935/) (2025)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Dynamic Model Predictive Shielding for Provably Safe Reinforcement Learning](https://mlsanity.com/paper/2405.13863/) (2024)
- [On the Optimality, Stability, and Feasibility of Control Barrier Functions: An Adaptive Learning-Based Approach](https://mlsanity.com/paper/2305.03608/) (2023)
- [Generative AI for Autonomous Driving: A Review](https://mlsanity.com/paper/2505.15863/) (2025)
- [A Multiplicative Value Function for Safe and Efficient Reinforcement Learning](https://mlsanity.com/paper/2303.04118/) (2023)
- [Safety Filter Design for Neural Network Systems via Convex Optimization](https://mlsanity.com/paper/2308.08086/) (2023)
- [Uncertainty Aware-Predictive Control Barrier Functions: Safer Human Robot Interaction through Probabilistic Motion Forecasting](https://mlsanity.com/paper/2508.20812/) (2025)
- [Sample Efficient Certification of Discrete-Time Control Barrier Functions](https://mlsanity.com/paper/2509.03899/) (2025)
- [PCARNN-DCBF: Minimal-Intervention Geofence Enforcement for Ground Vehicles](https://mlsanity.com/paper/2511.15522/) (2025)
- [Failing Gracefully: Mitigating Impact of Inevitable Robot Failures](https://mlsanity.com/paper/2608.05313/) (2026)
- [Turning Safety into Competence: Minimally Exploitable Robot Policies via Safety-Filtered Reinforcement Learning](https://mlsanity.com/paper/2609.27312/) (2026)
- [LEAP-CBF: A Safety Filter for Uncertain Systems with Least-Effort Adversarial Potentials](https://mlsanity.com/paper/2609.28364/) (2026)
- [Safe Reinforcement Learning with Receding-Horizon Safety Critic and Differentiable Action Shields](https://mlsanity.com/paper/2610.20255/) (2026)

## Abstract (arXiv)

While learning-based control techniques often outperform classical controller designs, safety requirements limit the acceptance of such methods in many applications. Recent developments address this issue through so-called predictive safety filters, which assess if a proposed learning-based control input can lead to constraint violations and modifies it if necessary to ensure safety for all future time steps. The theoretical guarantees of such predictive safety filters rely on the model assumptions and minor deviations can lead to failure of the filter putting the system at risk. This paper introduces an auxiliary soft-constrained predictive control problem that is always feasible at each time step and asymptotically stabilizes the feasible set of the original safety filter, thereby providing a recovery mechanism in safety-critical situations. This is achieved by a simple constraint tightening in combination with a terminal control barrier function. By extending discrete-time control barrier function theory, we establish that the proposed auxiliary problem provides a `predictive' control barrier function. The resulting algorithm is demonstrated using numerical examples.