mlsanityData to 7 Oct 2026

Robust Control Barrier-Value Functions for Safety-Critical Control

arXiv 2104.02808 ↗First posted 6 Apr 2021eess.SY cs.SYcited by 47

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Abstract (arXiv)

This paper works towards unifying two popular approaches in the safety control community: Hamilton-Jacobi (HJ) reachability and Control Barrier Functions (CBFs). HJ Reachability has methods for direct construction of value functions that provide safety guarantees and safe controllers, however the online implementation can be overly conservative and/or rely on chattering bang-bang control. The CBF community has methods for safe-guarding controllers in the form of point-wise optimization using quadratic programs (CBF-QP), where the CBF-based safety certificate is used as a constraint. However, finding a valid CBF for a general dynamical system is challenging. This paper unifies these two methods by introducing a new reachability formulation inspired by the structure of CBFs to construct a Control Barrier-Value Function (CBVF). We verify that CBVF is a viscosity solution to a novel Hamilton-Jacobi-Isaacs Variational Inequality and preserves the same safety guarantee as the original reachability formulation. Finally, inspired by the CBF-QP, we propose a QP-based online control synthesis for systems affine in control and disturbance, whose solution is always the CBVF's optimal control signal robust to bounded disturbance. We demonstrate the benefit of using the CBVFs for double-integrator and Dubins car systems by comparing it to previous methods.

Key facts. Cited by 47 papers in the map (data through 7 Oct 2026). First posted on arXiv 6 Apr 2021.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 6; 2023: 6; 2024: 11; 2025: 14; 2026: 6.

47 papers.

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  1. 2021Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learningcited by 337
  2. 2023The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systemscited by 77
  3. 2024Safe Offline Reinforcement Learning with Feasibility-Guided Diffusion Modelcited by 62
  4. 2022Reachability Constrained Reinforcement Learningcited by 52
  5. 2023Iterative Reachability Estimation for Safe Reinforcement Learningcited by 33
  6. 2021Joint Synthesis of Safety Certificate and Safe Control Policy using Constrained Reinforcement Learningcited by 25
  7. 2022ISAACS: Iterative Soft Adversarial Actor-Critic for Safetycited by 24
  8. 2021Learning Robust Output Control Barrier Functions from Safe Expert Demonstrationscited by 19
  9. 2022SABLAS: Learning Safe Control for Black-box Dynamical Systemscited by 17
  10. 2022Safe Model-Based Reinforcement Learning with an Uncertainty-Aware Reachability Certificatecited by 16
  11. 2023In-Distribution Barrier Functions: Self-Supervised Policy Filters that Avoid Out-of-Distribution Statescited by 15
  12. 2024Gameplay Filters: Robust Zero-Shot Safety through Adversarial Imaginationcited by 12
35 more
  1. 2024Hamilton-Jacobi Reachability in Reinforcement Learning: A Surveycited by 11
  2. 2023Deception Game: Closing the Safety-Learning Loop in Interactive Robot Autonomycited by 9
  3. 2024One Filter to Deploy Them All: Robust Safety for Quadrupedal Navigation in Unknown Environmentscited by 8
  4. 2021Safe Value Functionscited by 7
  5. 2025How to Train Your Latent Control Barrier Function: Smooth Safety Filtering Under Hard-to-Model Constraintscited by 7
  6. 2025V-OCBF: Learning Safety Filters from Offline Data via Value-Guided Offline Control Barrier Functionscited by 5
  7. 2024Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuationcited by 4
  8. 2025Hierarchical Multi-Agent Reinforcement Learning with Control Barrier Functions for Safety-Critical Autonomous Systemscited by 4
  9. 2024DADEE: Well-calibrated uncertainty quantification in neural networks for barriers-based robot safetycited by 3
  10. 2025Reachability Barrier Networks: Learning Hamilton-Jacobi Solutions for Smooth and Flexible Control Barrier Functionscited by 3
  11. 2025Verifiable Safety Q-Filters via Hamilton-Jacobi Reachability and Multiplicative Q-Networkscited by 3
  12. 2022Gaussian Control Barrier Functions : A Non-Parametric Paradigm to Safetycited by 2
  13. 2022Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functionscited by 2
  14. 2025ORN-CBF: Learning Observation-conditioned Residual Neural Control Barrier Functions via Hypernetworkscited by 2
  15. 2024Myopically Verifiable Probabilistic Certificates for Safe Control and Learningcited by 1
  16. 2024Domain Adaptive Safety Filters via Deep Operator Learningcited by 1
  17. 2024Pre-Trained Vision Models as Perception Backbones for Safety Filters in Autonomous Drivingcited by 1
  18. 2024Safe PDE Boundary Control with Neural Operatorscited by 1
  19. 2025Certified Approximate Reachability (CARe): Formal Error Bounds on Deep Learning of Reachable Setscited by 1
  20. 2026DualShield: Safe Model Predictive Diffusion via Reachability Analysis for Interactive Autonomous Drivingcited by 1
  21. 2026CN-CBF: Composite Neural Control Barrier Function for Robot Navigation in Dynamic Environmentscited by 1
  22. 2023Learned Risk Metric Maps for Kinodynamic Systemscited by 0
  23. 2023Solving Robust MDPs through No-Regret Dynamicscited by 0
  24. 2024Pareto Control Barrier Function for Inner Safe Set Maximization Under Input Constraintscited by 0
  25. 2025Safe Beyond the Horizon: Efficient Sampling-based MPC with Neural Control Barrier Functionscited by 0
  26. 2025Neural Network-assisted Interval Reachability for Systems with Control Barrier Function-Based Safe Controllerscited by 0
  27. 2025Learning Dynamics under Environmental Constraints via Measurement-Induced Bundle Structurescited by 0
  28. 2025Safety-Aware Imitation Learning via MPC-Guided Disturbance Injectioncited by 0
  29. 2025Safe and Nonconservative Contingency Planning for Autonomous Vehicles via Online Learning-Based Reachable Set Barrierscited by 0
  30. 2025Tail-Safe Hedging: Explainable Risk-Sensitive Reinforcement Learning with a White-Box CBF--QP Safety Layer in Arbitrage-Free Marketscited by 0
  31. 2025Learning Neural Control Barrier Functions from Expert Demonstrations using Inverse Constraint Learningcited by 0
  32. 2026ShardNet: Training Neural Controllers with Hard, Non-Convex Constraintscited by 0
  33. 2026Robust Peak-cost Constrained Reinforcement Learningcited by 0
  34. 2026Humanoid Safe Stop via Learned Stoppability Valuecited by 0
  35. 2026LEAP-CBF: A Safety Filter for Uncertain Systems with Least-Effort Adversarial Potentialscited by 0