# Fault Tolerant Neural Control Barrier Functions for Robotic Systems under Sensor Faults and Attacks

arXiv: https://arxiv.org/abs/2402.18677 · HTML: https://mlsanity.com/paper/2402.18677/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 42 references that are in the map.
- First posted on arXiv 28 Feb 2024.

## Builds on (most cited first, 23 of 23)

- [CARLA: An Open Urban Driving Simulator](https://mlsanity.com/paper/1711.03938/) (2017)
- [Control Barrier Functions: Theory and Applications](https://mlsanity.com/paper/1903.11199/) (2019)
- [Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods](https://mlsanity.com/paper/2202.11762/) (2022)
- [A Survey of End-to-End Driving: Architectures and Training Methods](https://mlsanity.com/paper/2003.06404/) (2020)
- [Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functions](https://mlsanity.com/paper/2109.06697/) (2021)
- [Learning Control Barrier Functions from Expert Demonstrations](https://mlsanity.com/paper/2004.03315/) (2020)
- [Deep Learning for Time-Series Analysis](https://mlsanity.com/paper/1701.01887/) (2017)
- [Synthesis of Control Barrier Functions Using a Supervised Machine Learning Approach](https://mlsanity.com/paper/2003.04950/) (2020)
- [Robustness of Control Barrier Functions for Safety Critical Control](https://mlsanity.com/paper/1612.01554/) (2016)
- [Safe Control Under Input Limits with Neural Control Barrier Functions](https://mlsanity.com/paper/2211.11056/) (2022)
- [Learning Hybrid Control Barrier Functions from Data](https://mlsanity.com/paper/2011.04112/) (2020)
- [Learning Safe, Generalizable Perception-based Hybrid Control with Certificates](https://mlsanity.com/paper/2201.00932/) (2022)
- [Safety Certification for Stochastic Systems via Neural Barrier Functions](https://mlsanity.com/paper/2206.01463/) (2022)
- [Formal Synthesis of Stochastic Systems via Control Barrier Certificates](https://mlsanity.com/paper/1905.04585/) (2019)
- [Safety Guarantees for Neural Network Dynamic Systems via Stochastic Barrier Functions](https://mlsanity.com/paper/2206.07811/) (2022)
- [Convex synthesis and verification of control-Lyapunov and barrier functions with input constraints](https://mlsanity.com/paper/2210.00629/) (2022)
- [Verification and Synthesis of Control Barrier Functions](https://mlsanity.com/paper/2104.14001/) (2021)
- [BarrierNet: A Safety-Guaranteed Layer for Neural Networks](https://mlsanity.com/paper/2111.11277/) (2021)
- [High-order Barrier Functions: Robustness, Safety and Performance-Critical Control](https://mlsanity.com/paper/2104.00101/) (2021)
- [Dynamic Control Barrier Function-based Model Predictive Control to Safety-Critical Obstacle-Avoidance of Mobile Robot](https://mlsanity.com/paper/2209.08539/) (2022)
- [A Semi-Algebraic Framework for Verification and Synthesis of Control Barrier Functions](https://mlsanity.com/paper/2209.00081/) (2022)
- [Verification and Synthesis of Robust Control Barrier Functions: Multilevel Polynomial Optimization and Semidefinite Relaxation](https://mlsanity.com/paper/2303.10081/) (2023)
- [Safe Control for Nonlinear Systems Under Faults and Attacks Via Control Barrier Functions](https://mlsanity.com/paper/2207.05146/) (2022)

## Abstract (arXiv)

Safety is a fundamental requirement of many robotic systems. Control barrier function (CBF)-based approaches have been proposed to guarantee the safety of robotic systems. However, the effectiveness of these approaches highly relies on the choice of CBFs. Inspired by the universal approximation power of neural networks, there is a growing trend toward representing CBFs using neural networks, leading to the notion of neural CBFs (NCBFs). Current NCBFs, however, are trained and deployed in benign environments, making them ineffective for scenarios where robotic systems experience sensor faults and attacks. In this paper, we study safety-critical control synthesis for robotic systems under sensor faults and attacks. Our main contribution is the development and synthesis of a new class of CBFs that we term fault tolerant neural control barrier function (FT-NCBF). We derive the necessary and sufficient conditions for FT-NCBFs to guarantee safety, and develop a data-driven method to learn FT-NCBFs by minimizing a loss function constructed using the derived conditions. Using the learned FT-NCBF, we synthesize a control input and formally prove the safety guarantee provided by our approach. We demonstrate our proposed approach using two case studies: obstacle avoidance problem for an autonomous mobile robot and spacecraft rendezvous problem, with code available via https://github.com/HongchaoZhang-HZ/FTNCBF.