mlsanityData to 14 Oct 2026

Learning Robust Output Control Barrier Functions from Safe Expert Demonstrations

arXiv 2111.09971 ↗First posted 18 Nov 2021eess.SY cs.LG cs.SYcited by 20

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Abstract (arXiv)

This paper addresses learning safe output feedback control laws from partial observations of expert demonstrations. We assume that a model of the system dynamics and a state estimator are available along with corresponding error bounds, e.g., estimated from data in practice. We first propose robust output control barrier functions (ROCBFs) as a means to guarantee safety, as defined through controlled forward invariance of a safe set. We then formulate an optimization problem to learn ROCBFs from expert demonstrations that exhibit safe system behavior, e.g., data collected from a human operator or an expert controller. When the parametrization of the ROCBF is linear, then we show that, under mild assumptions, the optimization problem is convex. Along with the optimization problem, we provide verifiable conditions in terms of the density of the data, smoothness of the system model and state estimator, and the size of the error bounds that guarantee validity of the obtained ROCBF. Towards obtaining a practical control algorithm, we propose an algorithmic implementation of our theoretical framework that accounts for assumptions made in our framework in practice. We validate our algorithm in the autonomous driving simulator CARLA and demonstrate how to learn safe control laws from simulated RGB camera images.

Key facts. Cited by 20 papers in the map (data through 14 Oct 2026). Builds on 45 of its 79 references that are in the map. First posted on arXiv 18 Nov 2021.

Builds on

45 of 79 references.

References · 45

  1. 2017CARLA: An Open Urban Driving Simulatorcited by 2,449
  2. 2018Lipschitz regularity of deep neural networks: analysis and efficient estimationcited by 415
  3. 2019Control Barrier Functions: Theory and Applicationscited by 372
  4. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 293
  5. 2019End-to-End Safe Reinforcement Learning through Barrier Functions for Safety-Critical Continuous Control Taskscited by 289
  6. 2016Control Barrier Function Based Quadratic Programs for Safety Critical Systemscited by 287
  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. 2021Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificatescited by 74
  11. 2019Learning for Safety-Critical Control with Control Barrier Functionscited by 69
  12. 2021Robust Control Barrier-Value Functions for Safety-Critical Controlcited by 51
33 more
  1. 2020Learning Certified Control using Contraction Metriccited by 49
  2. 2020Probably Approximately Correct Constrained Learningcited by 47
  3. 2020Learning Stability Certificates from Datacited by 45
  4. 2017Safe Learning of Quadrotor Dynamics Using Barrier Certificatescited by 35
  5. 2020Synthesis of Control Barrier Functions Using a Supervised Machine Learning Approachcited by 35
  6. 2020Neural Certificates for Safe Control Policiescited by 35
  7. 2020Imitation Learning with Stability and Safety Guaranteescited by 34
  8. 2020Guaranteeing Safety of Learned Perception Modules via Measurement-Robust Control Barrier Functionscited by 33
  9. 2019Control Barrier Functions for Systems with High Relative Degreecited by 31
  10. 2016Robustness of Control Barrier Functions for Safety Critical Controlcited by 30
  11. 2019Adaptive Safety with Control Barrier Functionscited by 25
  12. 2020Learning Hybrid Control Barrier Functions from Datacited by 24
  13. 2020Learning Lyapunov Functions for Hybrid Systemscited by 24
  14. 2020Learning Barrier Functions with Memory for Robust Safe Navigationcited by 21
  15. 2019Robust Guarantees for Perception-Based Controlcited by 20
  16. 2020Learning Safe Neural Network Controllers with Barrier Certificatescited by 18
  17. 2020Learning Barrier Functions for Constrained Motion Planning with Dynamical Systemscited by 17
  18. 2020ShieldNN: A Provably Safe NN Filter for Unsafe NN Controllerscited by 17
  19. 2018Permissive Barrier Certificates for Safe Stabilization Using Sum-of-squarescited by 15
  20. 2018Input-to-State Safety With Control Barrier Functionscited by 15
  21. 2021Learning Robust Hybrid Control Barrier Functions for Uncertain Systemscited by 14
  22. 2021Verification and Synthesis of Control Barrier Functionscited by 13
  23. 2020Training Neural Network Controllers Using Control Barrier Functions in the Presence of Disturbancescited by 9
  24. 2021Measurement-Robust Control Barrier Functions: Certainty in Safety with Uncertainty in Statecited by 8
  25. 2016Correctness Guarantees for the Composition of Lane Keeping and Adaptive Cruise Controlcited by 7
  26. 2021Episodic Learning for Safe Bipedal Locomotion with Control Barrier Functions and Projection-to-State Safetycited by 7
  27. 2021Safe Value Functionscited by 7
  28. 2021Data-Driven Robust Barrier Functions for Safe, Long-Term Operationcited by 4
  29. 2021Control Barrier Functions With Unmodeled Dynamics Using Integral Quadratic Constraintscited by 4
  30. 2019Constraint Learning for Control Tasks with Limited Duration Barrier Functionscited by 3
  31. 2021Control Barrier Function Meets Interval Analysis: Safety-Critical Control with Measurement and Actuation Uncertaintiescited by 3
  32. 2021Robust output feedback model predictive control using online estimation boundscited by 2
  33. 2021Safety-Constrained Learning and Control using Scarce Data and Reciprocal Barrierscited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 1; 2022: 3; 2023: 2; 2024: 3; 2025: 7; 2026: 4.

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  1. 2025Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysiscited by 45
  2. 2025Uncertainty-aware Latent Safety Filters for Avoiding Out-of-Distribution Failurescited by 33
  3. 2023In-Distribution Barrier Functions: Self-Supervised Policy Filters that Avoid Out-of-Distribution Statescited by 16
  4. 2023Safe Perception-Based Control under Stochastic Sensor Uncertainty using Conformal Predictioncited by 16
  5. 2022Chordal Sparsity for Lipschitz Constant Estimation of Deep Neural Networkscited by 15
  6. 2024Safety Filters for Black-Box Dynamical Systems by Learning Discriminating Hyperplanescited by 12
  7. 2025SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functionscited by 12
  8. 2024Learning Control Barrier Functions and their application in Reinforcement Learning: A Surveycited by 8
  9. 2025Learning Conservative Neural Control Barrier Functions from Offline Datacited by 5
  10. 2026Synthesis and Deployment of Maximal Robust Control Barrier Functions through Adversarial Reinforcement Learningcited by 5
  11. 2026Pixels to Proofs: Probabilistically-Safe Latent World Model Control via Parallel Conformal Robust MPCcited by 4
  12. 2025Conformal Safety Shielding for Imperfect-Perception Agentscited by 3
8 more
  1. 2021Adversarially Robust Stability Certificates can be Sample-Efficientcited by 2
  2. 2022Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functionscited by 2
  3. 2022Safe Reinforcement Learning with Probabilistic Control Barrier Functions for Ramp Mergingcited by 1
  4. 2025Learning Neural Control Barrier Functions from Expert Demonstrations using Inverse Constraint Learningcited by 1
  5. 2024Stability properties of gradient flow dynamics for the symmetric low-rank matrix factorization problemcited by 0
  6. 2025Optimal Parameter Adaptation for Safety-Critical Control via Safe Barrier Bayesian Optimizationcited by 0
  7. 2026Failing Gracefully: Mitigating Impact of Inevitable Robot Failurescited by 0
  8. 2026Generator-Independent Runtime Assurance under Partial Observationcited by 0