mlsanityData to 7 Oct 2026

Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction methods

arXiv 2202.11762 ↗First posted 23 Feb 2022cs.RO cs.SY eess.SYcited by 148

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Abstract (arXiv)

Learning-enabled control systems have demonstrated impressive empirical performance on challenging control problems in robotics, but this performance comes at the cost of reduced transparency and lack of guarantees on the safety or stability of the learned controllers. In recent years, new techniques have emerged to provide these guarantees by learning certificates alongside control policies -- these certificates provide concise, data-driven proofs that guarantee the safety and stability of the learned control system. These methods not only allow the user to verify the safety of a learned controller but also provide supervision during training, allowing safety and stability requirements to influence the training process itself. In this paper, we provide a comprehensive survey of this rapidly developing field of certificate learning. We hope that this paper will serve as an accessible introduction to the theory and practice of certificate learning, both to those who wish to apply these tools to practical robotics problems and to those who wish to dive more deeply into the theory of learning for control.

Key facts. Cited by 148 papers in the map (data through 7 Oct 2026). First posted on arXiv 23 Feb 2022.

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Citing papers per year: 2022: 5; 2023: 34; 2024: 46; 2025: 34; 2026: 29.

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  1. 2023Toward General-Purpose Robots via Foundation Models: A Survey and Meta-Analysiscited by 99
  2. 2023The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systemscited by 77
  3. 2023Direct Parameterization of Lipschitz-Bounded Deep Networkscited by 49
  4. 2023Iterative Reachability Estimation for Safe Reinforcement Learningcited by 33
  5. 2024Multi-Agent Reinforcement Learning for Autonomous Driving: A Surveycited by 30
  6. 2024A Survey of Robotic Language Grounding: Tradeoffs between Symbols and Embeddingscited by 23
  7. 2022Safety Certification for Stochastic Systems via Neural Barrier Functionscited by 22
  8. 2023Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verificationcited by 20
  9. 2022Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systemscited by 18
  10. 2023Closed-loop Analysis of Vision-based Autonomous Systems: A Case Studycited by 18
  11. 2022Learning Riemannian Stable Dynamical Systems via Diffeomorphismscited by 17
  12. 2023AutoCost: Evolving Intrinsic Cost for Zero-violation Reinforcement Learningcited by 16
38 more
  1. 2023Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEscited by 16
  2. 2023Fossil 2.0: Formal Certificate Synthesis for the Verification and Control of Dynamical Modelscited by 15
  3. 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificatescited by 15
  4. 2023Exact Verification of ReLU Neural Control Barrier Functionscited by 14
  5. 2024Neural Contractive Dynamical Systemscited by 14
  6. 2023Trajectory Generation, Control, and Safety with Denoising Diffusion Probabilistic Modelscited by 13
  7. 2023Compositional Policy Learning in Stochastic Control Systems with Formal Guaranteescited by 12
  8. 2024Safe Reinforcement Learning on the Constraint Manifold: Theory and Applicationscited by 12
  9. 2024Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagationcited by 12
  10. 2023Stable and Safe Reinforcement Learning via a Barrier-Lyapunov Actor-Critic Approachcited by 11
  11. 2024Hamilton-Jacobi Reachability in Reinforcement Learning: A Surveycited by 11
  12. 2022Temporal Logic Imitation: Learning Plan-Satisficing Motion Policies from Demonstrationscited by 10
  13. 2023Online Control Barrier Functions for Decentralized Multi-Agent Navigationcited by 10
  14. 2024LyZNet: A Lightweight Python Tool for Learning and Verifying Neural Lyapunov Functions and Regions of Attractioncited by 10
  15. 2025Real-Time Out-of-Distribution Failure Prevention via Multi-Modal Reasoningcited by 10
  16. 2023State-Wise Safe Reinforcement Learning With Pixel Observationscited by 9
  17. 2024Safety Filters for Black-Box Dynamical Systems by Learning Discriminating Hyperplanescited by 8
  18. 2024CBF-LLM: Safe Control for LLM Alignmentcited by 8
  19. 2024Provably Safe Neural Network Controllers via Differential Dynamic Logiccited by 7
  20. 2024Verification-Aided Learning of Neural Network Barrier Functions with Termination Guaranteescited by 7
  21. 2024Human-AI Safety: A Descendant of Generative AI and Control Systems Safetycited by 7
  22. 2025How to Train Your Latent Control Barrier Function: Smooth Safety Filtering Under Hard-to-Model Constraintscited by 7
  23. 2023Data-Driven Control with Inherent Lyapunov Stabilitycited by 6
  24. 2023A General Framework for Verification and Control of Dynamical Models via Certificate Synthesiscited by 6
  25. 2024Actor-Critic Physics-informed Neural Lyapunov Controlcited by 6
  26. 2024Unifying Qualitative and Quantitative Safety Verification of DNN-Controlled Systemscited by 6
  27. 2025Two-Stage Learning of Stabilizing Neural Controllers via Zubov Sampling and Iterative Domain Expansioncited by 6
  28. 2023Learning Control-Oriented Dynamical Structure from Datacited by 5
  29. 2023Value Functions are Control Barrier Functions: Verification of Safe Policies using Control Theorycited by 5
  30. 2024Contractive Dynamical Imitation Policies for Efficient Out-of-Sample Recoverycited by 5
  31. 2025Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systemscited by 5
  32. 2025V-OCBF: Learning Safety Filters from Offline Data via Value-Guided Offline Control Barrier Functionscited by 5
  33. 2023ROSGPT_Vision: Commanding Robots Using Only Language Models' Promptscited by 4
  34. 2023Neural Potential Field for Obstacle-Aware Local Motion Planningcited by 4
  35. 2024Learning Performance-Oriented Control Barrier Functions Under Complex Safety Constraints and Limited Actuationcited by 4
  36. 2024Deep Learning for Computing Convergence Rates of Markov Chainscited by 4
  37. 2024Ensuring Both Positivity and Stability Using Sector-Bounded Nonlinearity for Systems with Neural Network Controllerscited by 4
  38. 2024Safe and Reliable Training of Learning-Based Aerospace Controllerscited by 4

50 most cited of 148 All 148 (JSON)