# Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach

arXiv: https://arxiv.org/abs/2208.02319 · HTML: https://mlsanity.com/paper/2208.02319/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 32 references that are in the map.
- First posted on arXiv 3 Aug 2022.

## Builds on (most cited first, 20 of 20)

- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Efficient representation and approximation of model predictive control laws via deep learning](https://mlsanity.com/paper/1806.10644/) (2018)
- [Learning an Approximate Model Predictive Controller with Guarantees](https://mlsanity.com/paper/1806.04167/) (2018)
- [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)
- [Large Scale Model Predictive Control with Neural Networks and Primal Active Sets](https://mlsanity.com/paper/1910.10835/) (2019)
- [Infinite-Horizon Differentiable Model Predictive Control](https://mlsanity.com/paper/2001.02244/) (2020)
- [Near-Optimal Rapid MPC using Neural Networks: A Primal-Dual Policy Learning Framework](https://mlsanity.com/paper/1912.04744/) (2019)
- [A Neural Network Architecture to Learn Explicit MPC Controllers from Data](https://mlsanity.com/paper/1911.10789/) (2019)
- [Deep Learning Explicit Differentiable Predictive Control Laws for Buildings](https://mlsanity.com/paper/2107.11843/) (2021)
- [Learning Constrained Adaptive Differentiable Predictive Control Policies With Guarantees](https://mlsanity.com/paper/2004.11184/) (2020)
- [Control Barrier Functions for Mechanical Systems: Theory and Application to Robotic Grasping](https://mlsanity.com/paper/1903.09816/) (2019)
- [High-order Barrier Functions: Robustness, Safety and Performance-Critical Control](https://mlsanity.com/paper/2104.00101/) (2021)
- [Integral Control Barrier Functions for Dynamically Defined Control Laws](https://mlsanity.com/paper/2006.16936/) (2020)
- [Control Barrier Functions in Sampled-Data Systems](https://mlsanity.com/paper/2103.03677/) (2021)
- [A Robust, Multiple Control Barrier Function Framework for Input Constrained Systems](https://mlsanity.com/paper/2205.13726/) (2022)
- [Self-triggered Control for Safety Critical Systems using Control Barrier Functions](https://mlsanity.com/paper/1903.03692/) (2019)
- [Safe Controller Synthesis with Tunable Input-to-State Safe Control Barrier Functions](https://mlsanity.com/paper/2103.08041/) (2021)
- [Koopman-based Differentiable Predictive Control for the Dynamics-Aware Economic Dispatch Problem](https://mlsanity.com/paper/2203.08984/) (2022)

## Built on by (most cited first, 6 of 6)

- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Differentiable Safe Controller Design through Control Barrier Functions](https://mlsanity.com/paper/2209.10034/) (2022)
- [YANNs: Y-wise Affine Neural Networks for Exact and Efficient Representations of Piecewise Linear Functions](https://mlsanity.com/paper/2505.07054/) (2025)
- [Neural Control System for Continuous Glucose Monitoring and Maintenance](https://mlsanity.com/paper/2402.13852/) (2024)
- [End-to-End Learning of Safe Optimal Feedback Control in High Dimensions with Control Barrier Function Layers](https://mlsanity.com/paper/2607.20674/) (2026)
- [Topological Feasibility Guarantees for Differentiable Predictive Control](https://mlsanity.com/paper/2608.10332/) (2026)

## Abstract (arXiv)

We develop a novel form of differentiable predictive control (DPC) with safety and robustness guarantees based on control barrier functions. DPC is an unsupervised learning-based method for obtaining approximate solutions to explicit model predictive control (MPC) problems. In DPC, the predictive control policy parametrized by a neural network is optimized offline via direct policy gradients obtained by automatic differentiation of the MPC problem. The proposed approach exploits a new form of sampled-data barrier function to enforce offline and online safety requirements in DPC settings while only interrupting the neural network-based controller near the boundary of the safe set. The effectiveness of the proposed approach is demonstrated in simulation.