mlsanityData to 13 Oct 2026

Neural Lyapunov Control

arXiv 2005.00611 ↗First posted 1 May 2020cs.LG cs.NE cs.ROcited by 142

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Abstract (arXiv)

We propose new methods for learning control policies and neural network Lyapunov functions for nonlinear control problems, with provable guarantee of stability. The framework consists of a learner that attempts to find the control and Lyapunov functions, and a falsifier that finds counterexamples to quickly guide the learner towards solutions. The procedure terminates when no counterexample is found by the falsifier, in which case the controlled nonlinear system is provably stable. The approach significantly simplifies the process of Lyapunov control design, provides end-to-end correctness guarantee, and can obtain much larger regions of attraction than existing methods such as LQR and SOS/SDP. We show experiments on how the new methods obtain high-quality solutions for challenging control problems.

Key facts. Cited by 142 papers in the map (data through 13 Oct 2026). First posted on arXiv 1 May 2020.

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Citing papers per year: 2021: 26; 2022: 26; 2023: 22; 2024: 31; 2025: 19; 2026: 18.

142 papers.

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  1. 2021Learning Safe Multi-Agent Control with Decentralized Neural Barrier Certificatescited by 71
  2. 2022Enforcing Hard Constraints with Soft Barriers: Safe Reinforcement Learning in Unknown Stochastic Environmentscited by 54
  3. 2022LyaNet: A Lyapunov Framework for Training Neural ODEscited by 43
  4. 2021Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overviewcited by 42
  5. 2022Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guaranteescited by 40
  6. 2021On the Sample Complexity of Stability Constrained Imitation Learningcited by 38
  7. 2021Adaptive-Control-Oriented Meta-Learning for Nonlinear Systemscited by 38
  8. 2023Iterative Reachability Estimation for Safe Reinforcement Learningcited by 35
  9. 2021Enforcing Policy Feasibility Constraints through Differentiable Projection for Energy Optimizationcited by 31
  10. 2021Offline Reinforcement Learning for Autonomous Driving with Safety and Exploration Enhancementcited by 29
  11. 2024Global Lyapunov functions: a long-standing open problem in mathematics, with symbolic transformerscited by 29
  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. 2021Joint Synthesis of Safety Certificate and Safe Control Policy using Constrained Reinforcement Learningcited by 25
  3. 2021Stability Verification in Stochastic Control Systems via Neural Network Supermartingalescited by 24
  4. 2022Safety Certification for Stochastic Systems via Neural Barrier Functionscited by 22
  5. 2023Neural Lyapunov Control for Discrete-Time Systemscited by 22
  6. 2022Learning Control Policies for Stochastic Systems with Reach-avoid Guaranteescited by 21
  7. 2023Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verificationcited by 20
  8. 2025Steering Dialogue Dynamics for Robustness against Multi-turn Jailbreaking Attackscited by 20
  9. 2025Dexterous Manipulation through Imitation Learning: A Surveycited by 20
  10. 2021Learning Robust Output Control Barrier Functions from Safe Expert Demonstrationscited by 19
  11. 2021Value Iteration in Continuous Actions, States and Timecited by 18
  12. 2022Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systemscited by 18
  13. 2021Learning Stable Deep Dynamics Models for Partially Observed or Delayed Dynamical Systemscited by 17
  14. 2022SABLAS: Learning Safe Control for Black-box Dynamical Systemscited by 17
  15. 2022Control-oriented meta-learningcited by 17
  16. 2021Neural Termination Analysiscited by 16
  17. 2021Almost Surely Stable Deep Dynamicscited by 16
  18. 2021Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximationcited by 16
  19. 2023AutoCost: Evolving Intrinsic Cost for Zero-violation Reinforcement Learningcited by 16
  20. 2023In-Distribution Barrier Functions: Self-Supervised Policy Filters that Avoid Out-of-Distribution Statescited by 16
  21. 2023Neural Operators of Backstepping Controller and Observer Gain Functions for Reaction-Diffusion PDEscited by 16
  22. 2023Fossil 2.0: Formal Certificate Synthesis for the Verification and Control of Dynamical Modelscited by 15
  23. 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificatescited by 15
  24. 2021Infinite Time Horizon Safety of Bayesian Neural Networkscited by 13
  25. 2021Learning over All Stabilizing Nonlinear Controllers for a Partially-Observed Linear Systemcited by 13
  26. 2022Policy Optimization with Advantage Regularization for Long-Term Fairness in Decision Systemscited by 13
  27. 2023Compositional Policy Learning in Stochastic Control Systems with Formal Guaranteescited by 12
  28. 2024Hamilton-Jacobi Reachability in Reinforcement Learning: A Surveycited by 12
  29. 2024Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagationcited by 12
  30. 2025Systems Security Foundations for Agentic Computingcited by 12
  31. 2021Learning Density Distribution of Reachable States for Autonomous Systemscited by 11
  32. 2022Neural Koopman Lyapunov Controlcited by 11
  33. 2022Joint Differentiable Optimization and Verification for Certified Reinforcement Learningcited by 11
  34. 2022Statistical Safety and Robustness Guarantees for Feedback Motion Planning of Unknown Underactuated Stochastic Systemscited by 11
  35. 2023Neural Abstractionscited by 11
  36. 2021Youla-REN: Learning Nonlinear Feedback Policies with Robust Stability Guaranteescited by 10
  37. 2024LyZNet: A Lightweight Python Tool for Learning and Verifying Neural Lyapunov Functions and Regions of Attractioncited by 10
  38. 2021Robust Value Iteration for Continuous Control Taskscited by 8

50 most cited of 142 All 142 (JSON)