# Differentiable Safe Controller Design through Control Barrier Functions

arXiv: https://arxiv.org/abs/2209.10034 · HTML: https://mlsanity.com/paper/2209.10034/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 32 references that are in the map.
- First posted on arXiv 20 Sep 2022.

## Builds on (most cited first, 26 of 26)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions](https://mlsanity.com/paper/2109.06697/) (2021)
- [Deep Learning in Robotics: A Review of Recent Research](https://mlsanity.com/paper/1707.07217/) (2017)
- [Enforcing robust control guarantees within neural network policies](https://mlsanity.com/paper/2011.08105/) (2020)
- [Control Barrier Functions for Systems with High Relative Degree](https://mlsanity.com/paper/1903.04706/) (2019)
- [Safe Optimal Control Using Stochastic Barrier Functions and Deep Forward-Backward SDEs](https://mlsanity.com/paper/2009.01196/) (2020)
- [Computationally Efficient Safe Reinforcement Learning for Power Systems](https://mlsanity.com/paper/2110.10333/) (2021)
- [BarrierNet: A Safety-Guaranteed Layer for Neural Networks](https://mlsanity.com/paper/2111.11277/) (2021)
- [Distributed neural network control with dependability guarantees: a compositional port-Hamiltonian approach](https://mlsanity.com/paper/2112.09046/) (2021)
- [Learning Constrained Adaptive Differentiable Predictive Control Policies With Guarantees](https://mlsanity.com/paper/2004.11184/) (2020)
- [Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environments](https://mlsanity.com/paper/2201.01347/) (2022)
- [Safety-Critical Control using Optimal-decay Control Barrier Function with Guaranteed Point-wise Feasibility](https://mlsanity.com/paper/2103.12375/) (2021)
- [Recursive Feasibility Guided Optimal Parameter Adaptation of Differential Convex Optimization Policies for Safety-Critical Systems](https://mlsanity.com/paper/2109.10949/) (2021)
- [Safe and Efficient Model Predictive Control Using Neural Networks: An Interior Point Approach](https://mlsanity.com/paper/2203.12196/) (2022)
- [Neural Lyapunov Differentiable Predictive Control](https://mlsanity.com/paper/2205.10728/) (2022)
- [Approximate Optimal Control for Safety-Critical Systems with Control Barrier Functions](https://mlsanity.com/paper/2008.04122/) (2020)
- [Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach](https://mlsanity.com/paper/2208.02319/) (2022)
- [Feasibility Guaranteed Traffic Merging Control Using Control Barrier Functions](https://mlsanity.com/paper/2203.04348/) (2022)
- [Explicit Solutions for Safety Problems Using Control Barrier Functions](https://mlsanity.com/paper/2204.09380/) (2022)

## Built on by (most cited first, 8 of 8)

- [Empowering Autonomous Driving with Large Language Models: A Safety Perspective](https://mlsanity.com/paper/2312.00812/) (2023)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Safety Filtering While Training: Improving the Performance and Sample Efficiency of Reinforcement Learning Agents](https://mlsanity.com/paper/2410.11671/) (2024)
- [Safe Perception-Based Control under Stochastic Sensor Uncertainty using Conformal Prediction](https://mlsanity.com/paper/2304.00194/) (2023)
- [Learning Adaptive Safety for Multi-Agent Systems](https://mlsanity.com/paper/2309.10657/) (2023)
- [Deep Fictitious Play-Based Potential Differential Games for Learning Human-Like Interaction at Unsignalized Intersections](https://mlsanity.com/paper/2506.12283/) (2025)
- [Tail-Safe Hedging: Explainable Risk-Sensitive Reinforcement Learning with a White-Box CBF--QP Safety Layer in Arbitrage-Free Markets](https://mlsanity.com/paper/2510.04555/) (2025)
- [Topological Feasibility Guarantees for Differentiable Predictive Control](https://mlsanity.com/paper/2608.10332/) (2026)

## Abstract (arXiv)

Learning-based controllers, such as neural network (NN) controllers, can show high empirical performance but lack formal safety guarantees. To address this issue, control barrier functions (CBFs) have been applied as a safety filter to monitor and modify the outputs of learning-based controllers in order to guarantee the safety of the closed-loop system. However, such modification can be myopic with unpredictable long-term effects. In this work, we propose a safe-by-construction NN controller which employs differentiable CBF-based safety layers, and investigate the performance of safe-by-construction NN controllers in learning-based control. Specifically, two formulations of controllers are compared: one is projection-based and the other relies on our proposed set-theoretic parameterization. Both methods demonstrate improved closed-loop performance over using CBF as a separate safety filter in numerical experiments.