mlsanityData to 7 Oct 2026

Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guarantees

arXiv 2206.01913 ↗First posted 4 Jun 2022eess.SY cs.LG cs.ROcited by 39

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Abstract (arXiv)

Learning for control of dynamical systems with formal guarantees remains a challenging task. This paper proposes a learning framework to simultaneously stabilize an unknown nonlinear system with a neural controller and learn a neural Lyapunov function to certify a region of attraction (ROA) for the closed-loop system. The algorithmic structure consists of two neural networks and a satisfiability modulo theories (SMT) solver. The first neural network is responsible for learning the unknown dynamics. The second neural network aims to identify a valid Lyapunov function and a provably stabilizing nonlinear controller. The SMT solver then verifies that the candidate Lyapunov function indeed satisfies the Lyapunov conditions. We provide theoretical guarantees of the proposed learning framework in terms of the closed-loop stability for the unknown nonlinear system. We illustrate the effectiveness of the approach with a set of numerical experiments.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). Builds on 13 of its 53 references that are in the map. First posted on arXiv 4 Jun 2022.

Builds on

13 of 53 references.

References · 13

  1. 2017Reluplex: An Efficient SMT Solver for Verifying Deep Neural Networkscited by 739
  2. 2017Safe Model-based Reinforcement Learning with Stability Guaranteescited by 347
  3. 2019Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networkscited by 290
  4. 2020Neural Lyapunov Controlcited by 142
  5. 2021Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functionscited by 91
  6. 2018The Lyapunov Neural Network: Adaptive Stability Certification for Safe Learning of Dynamical Systemscited by 87
  7. 2021Lyapunov-stable neural-network controlcited by 66
  8. 2016Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian Processescited by 38
  9. 2020Learning Lyapunov Functions for Hybrid Systemscited by 24
  10. 2021Lyapunov-Net: A Deep Neural Network Architecture for Lyapunov Function Approximationcited by 16
  11. 2021Learning Region of Attraction for Nonlinear Systemscited by 16
  12. 2022Neural Koopman Lyapunov Controlcited by 11
1 more
  1. 2022A Piecewise Learning Framework for Control of Unknown Nonlinear Systems with Stability Guaranteescited by 1

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 9; 2024: 17; 2025: 7; 2026: 6.

39 papers.

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  1. 2024Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulationcited by 23
  2. 2023Neural Lyapunov Control for Discrete-Time Systemscited by 21
  3. 2023Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verificationcited by 20
  4. 2024Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificatescited by 15
  5. 2023Neural Abstractionscited by 11
  6. 2023Neural Operators for PDE Backstepping Control of First-Order Hyperbolic PIDE with Recycle and Delaycited by 11
  7. 2024LyZNet: A Lightweight Python Tool for Learning and Verifying Neural Lyapunov Functions and Regions of Attractioncited by 10
  8. 2023Data-Driven Control with Inherent Lyapunov Stabilitycited by 6
  9. 2024Actor-Critic Physics-informed Neural Lyapunov Controlcited by 6
  10. 2025Two-Stage Learning of Stabilizing Neural Controllers via Zubov Sampling and Iterative Domain Expansioncited by 6
  11. 2023Learning Control-Oriented Dynamical Structure from Datacited by 5
  12. 2024Synthesizing Neural Network Controllers with Closed-Loop Dissipativity Guaranteescited by 4
27 more
  1. 2024Formally Verified Physics-Informed Neural Control Lyapunov Functionscited by 4
  2. 2024Policy Verification in Stochastic Dynamical Systems Using Logarithmic Neural Certificatescited by 3
  3. 2024Transformer-Based Fault-Tolerant Control for Fixed-Wing UAVs Using Knowledge Distillation and In-Context Adaptationcited by 3
  4. 2025Safe Domains of Attraction for Discrete-Time Nonlinear Systems: Characterization and Verifiable Neural Network Estimationcited by 3
  5. 2023FLEX: an Adaptive Exploration Algorithm for Nonlinear Systemscited by 2
  6. 2023MPC-Inspired Reinforcement Learning for Verifiable Model-Free Controlcited by 2
  7. 2024Distributionally Robust Policy and Lyapunov-Certificate Learningcited by 2
  8. 2024Manifold-Guided Lyapunov Control with Diffusion Modelscited by 1
  9. 2024Transfer of Safety Controllers Through Learning Deep Inverse Dynamics Modelcited by 1
  10. 2024Combining Neural Networks and Symbolic Regression for Analytical Lyapunov Function Discoverycited by 1
  11. 2024Stochastic Reinforcement Learning with Stability Guarantees for Control of Unknown Nonlinear Systemscited by 1
  12. 2024Control the GNN: Utilizing Neural Controller with Lyapunov Stability for Test-Time Feature Reconstructioncited by 1
  13. 2024Learning Koopman-based Stability Certificates for Unknown Nonlinear Systemscited by 1
  14. 2025Analytical Lyapunov Function Discovery: An RL-based Generative Approachcited by 1
  15. 2023A Policy Optimization Method Towards Optimal-time Stabilitycited by 0
  16. 2024Structured Deep Neural Network-Based Backstepping Trajectory Tracking Control for Lagrangian Systemscited by 0
  17. 2024(Un)supervised Learning of Maximal Lyapunov Functionscited by 0
  18. 2025Neural Lyapunov Function Approximation with Self-Supervised Reinforcement Learningcited by 0
  19. 2025Application-Specific Component-Aware Structured Pruning of Deep Neural Networks in Control via Soft Coefficient Optimizationcited by 0
  20. 2025Lyapunov Stability Learning with Nonlinear Control via Inductive Biasescited by 0
  21. 2025The Silence that Speaks: Neural Estimation via Communication Gapscited by 0
  22. 2026Conformal Reachability for Safe Control in Unknown Environmentscited by 0
  23. 2026Rigorous Error Certification for Neural PDE Solvers: From Empirical Residuals to Solution Guaranteescited by 0
  24. 2026Verifiable Error Bounds for Physics-Informed Neural Network Solutions of Lyapunov and Hamilton-Jacobi-Bellman Equationscited by 0
  25. 2026Learned Lyapunov Shielding for Adaptive Controlcited by 0
  26. 2026Andy: A Mathematical Agent for Rigorous Proof and Autonomous Researchcited by 0
  27. 2026Learning Provable Neural Network Observer for Uncertain Dynamical Systemscited by 0