# Learning Robust Hybrid Control Barrier Functions for Uncertain Systems

arXiv: https://arxiv.org/abs/2101.06492 · HTML: https://mlsanity.com/paper/2101.06492/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 30 references that are in the map.
- First posted on arXiv 16 Jan 2021.

## Builds on (most cited first, 18 of 18)

- [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)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [Probably Approximately Correct Constrained Learning](https://mlsanity.com/paper/2006.05487/) (2020)
- [Learning Stability Certificates from Data](https://mlsanity.com/paper/2008.05952/) (2020)
- [Synthesis of Control Barrier Functions Using a Supervised Machine Learning Approach](https://mlsanity.com/paper/2003.04950/) (2020)
- [Neural Certificates for Safe Control Policies](https://mlsanity.com/paper/2006.08465/) (2020)
- [Robustness of Control Barrier Functions for Safety Critical Control](https://mlsanity.com/paper/1612.01554/) (2016)
- [Learning Hybrid Control Barrier Functions from Data](https://mlsanity.com/paper/2011.04112/) (2020)
- [Learning Lyapunov Functions for Hybrid Systems](https://mlsanity.com/paper/2012.12015/) (2020)
- [Barrier-Certified Adaptive Reinforcement Learning with Applications to Brushbot Navigation](https://mlsanity.com/paper/1801.09627/) (2018)
- [Learning Barrier Functions for Constrained Motion Planning with Dynamical Systems](https://mlsanity.com/paper/2003.11500/) (2020)
- [ShieldNN: A Provably Safe NN Filter for Unsafe NN Controllers](https://mlsanity.com/paper/2006.09564/) (2020)
- [Permissive Barrier Certificates for Safe Stabilization Using Sum-of-squares](https://mlsanity.com/paper/1802.08917/) (2018)
- [Input-to-State Safety With Control Barrier Functions](https://mlsanity.com/paper/1803.03035/) (2018)
- [Training Neural Network Controllers Using Control Barrier Functions in the Presence of Disturbances](https://mlsanity.com/paper/2001.08088/) (2020)
- [Correctness Guarantees for the Composition of Lane Keeping and Adaptive Cruise Control](https://mlsanity.com/paper/1609.06807/) (2016)
- [A hybrid barrier certificate approach to satisfy linear temporal logic specifications](https://mlsanity.com/paper/2011.11464/) (2020)

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

- [The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems](https://mlsanity.com/paper/2309.05837/) (2023)
- [Safe Pontryagin Differentiable Programming](https://mlsanity.com/paper/2105.14937/) (2021)
- [Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations](https://mlsanity.com/paper/2111.09971/) (2021)
- [Gameplay Filters: Robust Zero-Shot Safety through Adversarial Imagination](https://mlsanity.com/paper/2405.00846/) (2024)
- [Joint Differentiable Optimization and Verification for Certified Reinforcement Learning](https://mlsanity.com/paper/2201.12243/) (2022)
- [Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Models](https://mlsanity.com/paper/2205.05787/) (2022)
- [Model Free Barrier Functions via Implicit Evading Maneuvers](https://mlsanity.com/paper/2107.12871/) (2021)
- [Gaussian Control Barrier Functions : A Non-Parametric Paradigm to Safety](https://mlsanity.com/paper/2203.15474/) (2022)
- [Formal Controller Synthesis for Markov Jump Linear Systems with Uncertain Dynamics](https://mlsanity.com/paper/2212.00679/) (2022)
- [Toward Generalist Neural Motion Planners for Robotic Manipulators: Challenges and Opportunities](https://mlsanity.com/paper/2603.24318/) (2026)
- [Policy Search using Dynamic Mirror Descent MPC for Model Free Off Policy RL](https://mlsanity.com/paper/2110.12239/) (2021)
- [Scaling Learning based Policy Optimization for Temporal Logic Tasks by Controller Network Dropout](https://mlsanity.com/paper/2403.15826/) (2024)
- [Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problem](https://mlsanity.com/paper/2411.15972/) (2024)
- [SafeMind: A Risk-Aware Differentiable Control Framework for Adaptive and Safe Quadruped Locomotion](https://mlsanity.com/paper/2604.09474/) (2026)

## Abstract (arXiv)

The need for robust control laws is especially important in safety-critical applications. We propose robust hybrid control barrier functions as a means to synthesize control laws that ensure robust safety. Based on this notion, we formulate an optimization problem for learning robust hybrid control barrier functions from data. We identify sufficient conditions on the data such that feasibility of the optimization problem ensures correctness of the learned robust hybrid control barrier functions. Our techniques allow us to safely expand the region of attraction of a compass gait walker that is subject to model uncertainty.