mlsanityData to 7 Oct 2026

Hamilton-Jacobi Reachability: A Brief Overview and Recent Advances

arXiv 1709.07523 ↗First posted 21 Sep 2017eess.SY cs.SY math.DScited by 186

Not on the map. Why?

Abstract (arXiv)

Hamilton-Jacobi (HJ) reachability analysis is an important formal verification method for guaranteeing performance and safety properties of dynamical systems; it has been applied to many small-scale systems in the past decade. Its advantages include compatibility with general nonlinear system dynamics, formal treatment of bounded disturbances, and the availability of well-developed numerical tools. The main challenge is addressing its exponential computational complexity with respect to the number of state variables. In this tutorial, we present an overview of basic HJ reachability theory and provide instructions for using the most recent numerical tools, including an efficient GPU-parallelized implementation of a Level Set Toolbox for computing reachable sets. In addition, we review some of the current work in high-dimensional HJ reachability to show how the dimensionality challenge can be alleviated via various general theoretical and application-specific insights.

Key facts. Cited by 186 papers in the map (data through 7 Oct 2026). First posted on arXiv 21 Sep 2017.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 24; 2022: 16; 2023: 26; 2024: 36; 2025: 37; 2026: 47.

186 papers.

Sort:

By area:

  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. 2022Safe Reinforcement Learning by Imagining the Near Futurecited by 67
  4. 2024Safe Offline Reinforcement Learning with Feasibility-Guided Diffusion Modelcited by 62
  5. 2024Agile But Safe: Learning Collision-Free High-Speed Legged Locomotioncited by 53
  6. 2022Reachability Constrained Reinforcement Learningcited by 52
  7. 2023Conformal Decision Theory: Safe Autonomous Decisions from Imperfect Predictionscited by 46
  8. 2025Generalizing Safety Beyond Collision-Avoidance via Latent-Space Reachability Analysiscited by 44
  9. 2021Safety and Liveness Guarantees through Reach-Avoid Reinforcement Learningcited by 43
  10. 2021Reachability Analysis of Neural Feedback Loopscited by 41
  11. 2023Iterative Reachability Estimation for Safe Reinforcement Learningcited by 33
  12. 2022Lyapunov Density Models: Constraining Distribution Shift in Learning-Based Controlcited by 28
38 more
  1. 2022Safe Control Under Input Limits with Neural Control Barrier Functionscited by 27
  2. 2021Safe Pontryagin Differentiable Programmingcited by 25
  3. 2022Sim-to-Lab-to-Real: Safe Reinforcement Learning with Shielding and Generalization Guaranteescited by 24
  4. 2022ISAACS: Iterative Soft Adversarial Actor-Critic for Safetycited by 24
  5. 2021Safe Control with Neural Network Dynamic Modelscited by 21
  6. 2023Verification of Neural Reachable Tubes via Scenario Optimization and Conformal Predictioncited by 21
  7. 2022Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systemscited by 18
  8. 2021Value Iteration in Continuous Actions, States and Timecited by 17
  9. 2023Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal Abstractionscited by 16
  10. 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificatescited by 15
  11. 2021Neural Network Verification in Controlcited by 14
  12. 2024Solving Minimum-Cost Reach Avoid using Reinforcement Learningcited by 14
  13. 2021Safe Autonomous Racing via Approximate Reachability on Ego-visioncited by 13
  14. 2021Sampling-Based Robust Control of Autonomous Systems with Non-Gaussian Noisecited by 13
  15. 2021Conservative and Adaptive Penalty for Model-Based Safe Reinforcement Learningcited by 13
  16. 2023Active Uncertainty Reduction for Safe and Efficient Interaction Planning: A Shielding-Aware Dual Control Approachcited by 13
  17. 2024SAFE-GIL: SAFEty Guided Imitation Learning for Robotic Systemscited by 13
  18. 2024FREA: Feasibility-Guided Generation of Safety-Critical Scenarios with Reasonable Adversarialitycited by 13
  19. 2021SHARP: Shielding-Aware Robust Planning for Safe and Efficient Human-Robot Interactioncited by 12
  20. 2024Gameplay Filters: Robust Zero-Shot Safety through Adversarial Imaginationcited by 12
  21. 2022Generating Formal Safety Assurances for High-Dimensional Reachabilitycited by 11
  22. 2022Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systemscited by 11
  23. 2024The Role of Predictive Uncertainty and Diversity in Embodied AI and Robot Learningcited by 11
  24. 2024Hamilton-Jacobi Reachability in Reinforcement Learning: A Surveycited by 11
  25. 2025SafeFlowMatcher: Safe and Fast Planning using Flow Matching with Control Barrier Functionscited by 11
  26. 2021Efficient Reachability Analysis of Closed-Loop Systems with Neural Network Controllerscited by 10
  27. 2021Scalable Learning of Safety Guarantees for Autonomous Systems using Hamilton-Jacobi Reachabilitycited by 10
  28. 2022End-to-End Imitation Learning with Safety Guarantees using Control Barrier Functionscited by 10
  29. 2025Real-Time Out-of-Distribution Failure Prevention via Multi-Modal Reasoningcited by 10
  30. 2025Preemptive Detection and Steering of LLM Misalignment via Latent Reachabilitycited by 10
  31. 2021LS3: Latent Space Safe Sets for Long-Horizon Visuomotor Control of Sparse Reward Iterative Taskscited by 9
  32. 2022Backward Reachability Analysis for Neural Feedback Loopscited by 9
  33. 2023Efficient Interaction-Aware Interval Analysis of Neural Network Feedback Loopscited by 9
  34. 2023Deception Game: Closing the Safety-Learning Loop in Interactive Robot Autonomycited by 9
  35. 2023Data-Driven Reachability Analysis of Stochastic Dynamical Systems with Conformal Inferencecited by 9
  36. 2023State-Wise Safe Reinforcement Learning With Pixel Observationscited by 9
  37. 2021Analyzing Human Models that Adapt Onlinecited by 8
  38. 2021Robust Value Iteration for Continuous Control Taskscited by 8

50 most cited of 186 All 186 (JSON)