mlsanityData to 7 Oct 2026

Control Barrier Function Based Quadratic Programs for Safety Critical Systems

arXiv 1609.06408 ↗First posted 21 Sep 2016math.OC cs.SY eess.SYcited by 261

Not on the map. Why?

Abstract (arXiv)

Safety critical systems involve the tight coupling between potentially conflicting control objectives and safety constraints. As a means of creating a formal framework for controlling systems of this form, and with a view toward automotive applications, this paper develops a methodology that allows safety conditions -- expressed as control barrier functions -- to be unified with performance objectives -- expressed as control Lyapunov functions -- in the context of real-time optimization-based controllers. Safety conditions are specified in terms of forward invariance of a set, and are verified via two novel generalizations of barrier functions; in each case, the existence of a barrier function satisfying Lyapunov-like conditions implies forward invariance of the set, and the relationship between these two classes of barrier functions is characterized. In addition, each of these formulations yields a notion of control barrier function (CBF), providing inequality constraints in the control input that, when satisfied, again imply forward invariance of the set. Through these constructions, CBFs can naturally be unified with control Lyapunov functions (CLFs) in the context of a quadratic program (QP); this allows for the achievement of control objectives (represented by CLFs) subject to conditions on the admissible states of the system (represented by CBFs). The mediation of safety and performance through a QP is demonstrated on adaptive cruise control and lane keeping, two automotive control problems that present both safety and performance considerations coupled with actuator bounds.

Key facts. Cited by 261 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Sep 2016.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 22; 2022: 27; 2023: 30; 2024: 30; 2025: 61; 2026: 91.

261 papers.

Sort:

By area:

  1. 2023The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systemscited by 77
  2. 2021Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificatescited by 71
  3. 2023SafeDiffuser: Safe Planning with Diffusion Probabilistic Modelscited by 69
  4. 2022Enforcing Hard Constraints with Soft Barriers: Safe Reinforcement Learning in Unknown Stochastic Environmentscited by 54
  5. 2021Safe Reinforcement Learning Using Robust Control Barrier Functionscited by 44
  6. 2022LyaNet: A Lyapunov Framework for Training Neural ODEscited by 43
  7. 2024A Survey of Constraint Formulations in Safe Reinforcement Learningcited by 42
  8. 2021Reachability Analysis of Neural Feedback Loopscited by 41
  9. 2023Iterative Reachability Estimation for Safe Reinforcement Learningcited by 33
  10. 2021Multi-Agent Constrained Policy Optimisationcited by 32
  11. 2025VLSA: Vision-Language-Action Models with Plug-and-Play Safety Constraint Layercited by 32
  12. 2025Uncertainty-aware Latent Safety Filters for Avoiding Out-of-Distribution Failurescited by 30
38 more
  1. 2022Lyapunov Density Models: Constraining Distribution Shift in Learning-Based Controlcited by 28
  2. 2021Safe Pontryagin Differentiable Programmingcited by 25
  3. 2021Safe Occlusion-aware Autonomous Driving via Game-Theoretic Active Perceptioncited by 22
  4. 2021Safe Control with Neural Network Dynamic Modelscited by 21
  5. 2021Learning Robust Output Control Barrier Functions from Safe Expert Demonstrationscited by 19
  6. 2022SABLAS: Learning Safe Control for Black-box Dynamical Systemscited by 17
  7. 2023MEGA-DAgger: Imitation Learning with Multiple Imperfect Expertscited by 17
  8. 2023In-Distribution Barrier Functions: Self-Supervised Policy Filters that Avoid Out-of-Distribution Statescited by 15
  9. 2023Safe Perception-Based Control under Stochastic Sensor Uncertainty using Conformal Predictioncited by 15
  10. 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificatescited by 15
  11. 2026ODESteer: A Unified ODE-Based Steering Framework for LLM Alignmentcited by 15
  12. 2021Learning Robust Hybrid Control Barrier Functions for Uncertain Systemscited by 14
  13. 2021Neural Network Verification in Controlcited by 14
  14. 2023Active Uncertainty Reduction for Safe and Efficient Interaction Planning: A Shielding-Aware Dual Control Approachcited by 13
  15. 2023Trajectory Generation, Control, and Safety with Denoising Diffusion Probabilistic Modelscited by 13
  16. 2024SAFE-GIL: SAFEty Guided Imitation Learning for Robotic Systemscited by 13
  17. 2021SHARP: Shielding-Aware Robust Planning for Safe and Efficient Human-Robot Interactioncited by 12
  18. 2022Spatial-Temporal-Aware Safe Multi-Agent Reinforcement Learning of Connected Autonomous Vehicles in Challenging Scenarioscited by 12
  19. 2025A Physics-Informed Machine Learning Framework for Safe and Optimal Control of Autonomous Systemscited by 12
  20. 2021BarrierNet: A Safety-Guaranteed Layer for Neural Networkscited by 11
  21. 2024Dynamic Model Predictive Shielding for Provably Safe Reinforcement Learningcited by 11
  22. 2025SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functionscited by 11
  23. 2021Efficient Reachability Analysis of Closed-Loop Systems with Neural Network Controllerscited by 10
  24. 2021Safe Adaptive Learning-based Control for Constrained Linear Quadratic Regulators with Regret Guaranteescited by 10
  25. 2022On the Forward Invariance of Neural ODEscited by 10
  26. 2022End-to-End Imitation Learning with Safety Guarantees using Control Barrier Functionscited by 10
  27. 2023Safe Reinforcement Learning with Dual Robustnesscited by 10
  28. 2024LLM4AD: Large Language Models for Autonomous Driving -- Concept, Review, Benchmark, Experiments, and Future Trendscited by 10
  29. 2023Safe Deep Policy Adaptationcited by 9
  30. 2023State-Wise Safe Reinforcement Learning With Pixel Observationscited by 9
  31. 2024Embedding Safety into RL: A New Take on Trust Region Methodscited by 9
  32. 2021Safe Exploration in Model-based Reinforcement Learning using Control Barrier Functionscited by 8
  33. 2022Learning Differentiable Safety-Critical Control using Control Barrier Functions for Generalization to Novel Environmentscited by 8
  34. 2022Differentiable Safe Controller Design through Control Barrier Functionscited by 8
  35. 2023Constrained Meta-Reinforcement Learning for Adaptable Safety Guarantee with Differentiable Convex Programmingcited by 8
  36. 2024Safety Filters for Black-Box Dynamical Systems by Learning Discriminating Hyperplanescited by 8
  37. 2024Safe Guaranteed Exploration for Non-linear Systemscited by 8
  38. 2025CBF-RL: Safety Filtering Reinforcement Learning in Training with Control Barrier Functionscited by 8

50 most cited of 261 All 261 (JSON)