mlsanityData to 14 Oct 2026

Safe Control Under Input Limits with Neural Control Barrier Functions

arXiv 2211.11056 ↗First posted 20 Nov 2022cs.RO cs.AI cs.SYcited by 29

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Abstract (arXiv)

We propose new methods to synthesize control barrier function (CBF)-based safe controllers that avoid input saturation, which can cause safety violations. In particular, our method is created for high-dimensional, general nonlinear systems, for which such tools are scarce. We leverage techniques from machine learning, like neural networks and deep learning, to simplify this challenging problem in nonlinear control design. The method consists of a learner-critic architecture, in which the critic gives counterexamples of input saturation and the learner optimizes a neural CBF to eliminate those counterexamples. We provide empirical results on a 10D state, 4D input quadcopter-pendulum system. Our learned CBF avoids input saturation and maintains safety over nearly 100% of trials.

Key facts. Cited by 29 papers in the map (data through 14 Oct 2026). Builds on 27 of its 50 references that are in the map. First posted on arXiv 20 Nov 2022.

Builds on

27 of 50 references.

References · 27

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  7. 2020Neural Lyapunov Controlcited by 142
  8. 2021Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functionscited by 94
  9. 2020Learning Control Barrier Functions from Expert Demonstrationscited by 92
  10. 2018The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systemscited by 88
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  12. 2021Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificatescited by 74
15 more
  1. 2020Learning Stability Certificates from Datacited by 45
  2. 2019Control Barrier Functions for Systems with High Relative Degreecited by 31
  3. 2021Safe Control with Neural Network Dynamic Modelscited by 22
  4. 2018Learning Control Lyapunov Functions from Counterexamples and Demonstrationscited by 19
  5. 2021Safe Control Synthesis via Input Constrained Control Barrier Functionscited by 13
  6. 2021Verification and Synthesis of Control Barrier Functionscited by 13
  7. 2021Backup Control Barrier Functions: Formulation and Comparative Studycited by 12
  8. 2021BarrierNet: A Safety-Guaranteed Layer for Neural Networkscited by 12
  9. 2021Probabilistic Safety-Assured Adaptive Merging Control for Autonomous Vehiclescited by 11
  10. 2020Comparative Analysis of Control Barrier Functions and Artificial Potential Fields for Obstacle Avoidancecited by 9
  11. 2021Reactive and Safe Road User Simulations using Neural Barrier Certificatescited by 7
  12. 2020Learning Control Barrier Functions with High Relative Degree for Safety-Critical Controlcited by 6
  13. 2022A Robust, Multiple Control Barrier Function Framework for Input Constrained Systemscited by 6
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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 14; 2025: 6; 2026: 6.

29 papers.

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  1. 2024Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulationcited by 25
  2. 2024Safe Reinforcement Learning on the Constraint Manifold: Theory and Applicationscited by 15
  3. 2023Exact Verification of ReLU Neural Control Barrier Functionscited by 14
  4. 2024Safety Filters for Black-Box Dynamical Systems by Learning Discriminating Hyperplanescited by 12
  5. 2024Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagationcited by 12
  6. 2024Verification-Aided Learning of Neural Network Barrier Functions with Termination Guaranteescited by 7
  7. 2024ModelVerification.jl: a Comprehensive Toolbox for Formally Verifying Deep Neural Networkscited by 7
  8. 2023Value Functions are Control Barrier Functions: Verification of Safe Policies using Control Theorycited by 6
  9. 2025Two-Stage Learning of Stabilizing Neural Controllers via Zubov Sampling and Iterative Domain Expansioncited by 6
  10. 2024Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuationcited by 4
  11. 2023Learning Predictive Safety Filter via Decomposition of Robust Invariant Setcited by 3
  12. 2024Handling Long-Term Safety and Uncertainty in Safe Reinforcement Learningcited by 3
17 more
  1. 2024Certified Training with Branch-and-Bound for Lyapunov-stable Neural Controlcited by 3
  2. 2025Designing Control Barrier Function via Probabilistic Enumeration for Safe Reinforcement Learning Navigationcited by 3
  3. 2025Reachability Barrier Networks: Learning Hamilton-Jacobi Solutions for Smooth and Flexible Control Barrier Functionscited by 3
  4. 2025ORN-CBF: Learning Observation-conditioned Residual Neural Control Barrier Functions via Hypernetworkscited by 2
  5. 2026Parallel Differentiable Reachability for Learning and Planning with Certified Neural Dynamics and Controllerscited by 2
  6. 2024The Feasibility Theory of Constrained Reinforcement Learning: A Tutorial Studycited by 1
  7. 2024Domain Adaptive Safety Filters via Deep Operator Learningcited by 1
  8. 2024Safe PDE Boundary Control with Neural Operatorscited by 1
  9. 2025Neural Control Barrier Functions from Physics Informed Neural Networkscited by 1
  10. 2026CN-CBF: Composite Neural Control Barrier Function for Robot Navigation in Dynamic Environmentscited by 1
  11. 2026Provably Safe, Yet Scalable Reinforcement Learningcited by 1
  12. 2024Fault Tolerant Neural Control Barrier Functions for Robotic Systems under Sensor Faults and Attackscited by 0
  13. 2024Pareto Control Barrier Function for Inner Safe Set Maximization Under Input Constraintscited by 0
  14. 2025Learning Dynamics under Environmental Constraints via Measurement-Induced Bundle Structurescited by 0
  15. 2026Efficient Verification of Neural Control Barrier Functions with Smooth Nonlinear Activationscited by 0
  16. 2026VertexCBF: Improving Neural Control Barrier Functions via Vertex-Restricted Control Searchcited by 0
  17. 2026Safe Reinforcement Learning with Receding-Horizon Safety Critic and Differentiable Action Shieldscited by 0