mlsanityData to 7 Oct 2026

Lyapunov-stable Neural Control for State and Output Feedback: A Novel Formulation

arXiv 2404.07956 ↗First posted 11 Apr 2024cs.LG cs.AI cs.ROcited by 23

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Abstract (arXiv)

Learning-based neural network (NN) control policies have shown impressive empirical performance in a wide range of tasks in robotics and control. However, formal (Lyapunov) stability guarantees over the region-of-attraction (ROA) for NN controllers with nonlinear dynamical systems are challenging to obtain, and most existing approaches rely on expensive solvers such as sums-of-squares (SOS), mixed-integer programming (MIP), or satisfiability modulo theories (SMT). In this paper, we demonstrate a new framework for learning NN controllers together with Lyapunov certificates using fast empirical falsification and strategic regularizations. We propose a novel formulation that defines a larger verifiable region-of-attraction (ROA) than shown in the literature, and refines the conventional restrictive constraints on Lyapunov derivatives to focus only on certifiable ROAs. The Lyapunov condition is rigorously verified post-hoc using branch-and-bound with scalable linear bound propagation-based NN verification techniques. The approach is efficient and flexible, and the full training and verification procedure is accelerated on GPUs without relying on expensive solvers for SOS, MIP, nor SMT. The flexibility and efficiency of our framework allow us to demonstrate Lyapunov-stable output feedback control with synthesized NN-based controllers and NN-based observers with formal stability guarantees, for the first time in literature. Source code at https://github.com/Verified-Intelligence/Lyapunov_Stable_NN_Controllers

Key facts. Cited by 23 papers in the map (data through 7 Oct 2026). Builds on 29 of its 49 references that are in the map. First posted on arXiv 11 Apr 2024.

Builds on

29 of 49 references.

References · 29

  1. 2017Towards Deep Learning Models Resistant to Adversarial Attackscited by 6,326
  2. 2018QT-Opt: Scalable Deep Reinforcement Learning for Vision-Based Robotic Manipulationcited by 730
  3. 2018Efficient Neural Network Robustness Certification with General Activation Functionscited by 439
  4. 2019Algorithms for Verifying Deep Neural Networkscited by 221
  5. 2020Fast and Complete: Enabling Complete Neural Network Verification with Rapid and Massively Parallel Incomplete Verifierscited by 183
  6. 2022General Cutting Planes for Bound-Propagation-Based Neural Network Verificationcited by 102
  7. 2019Safety Verification and Robustness Analysis of Neural Networks via Quadratic Constraints and Semidefinite Programmingcited by 100
  8. 2021Safe Nonlinear Control Using Robust Neural Lyapunov-Barrier Functionscited by 91
  9. 2021Lyapunov-stable neural-network controlcited by 66
  10. 2020Learning Certified Control using Contraction Metriccited by 48
  11. 2020Stability Analysis using Quadratic Constraints for Systems with Neural Network Controllerscited by 42
  12. 2015Learning Deep Control Policies for Autonomous Aerial Vehicles with MPC-Guided Policy Searchcited by 41
17 more
  1. 2021Reachability Analysis of Neural Feedback Loopscited by 41
  2. 2022Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guaranteescited by 39
  3. 2020Neural Certificates for Safe Control Policiescited by 35
  4. 2023Provably Bounding Neural Network Preimagescited by 28
  5. 2022Safe Control Under Input Limits with Neural Control Barrier Functionscited by 27
  6. 2020Learning Lyapunov Functions for Hybrid Systemscited by 24
  7. 2022Safety Certification for Stochastic Systems via Neural Barrier Functionscited by 22
  8. 2022IBP Regularization for Verified Adversarial Robustness via Branch-and-Boundcited by 21
  9. 2023Neural Lyapunov Control for Discrete-Time Systemscited by 21
  10. 2022Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systemscited by 18
  11. 2022Convex synthesis and verification of control-Lyapunov and barrier functions with input constraintscited by 14
  12. 2022Joint Differentiable Optimization and Verification for Certified Reinforcement Learningcited by 11
  13. 2022Reachable Polyhedral Marching (RPM): An Exact Analysis Tool for Deep-Learned Control Systemscited by 6
  14. 2022DRIP: Domain Refinement Iteration with Polytopes for Backward Reachability Analysis of Neural Feedback Loopscited by 6
  15. 2023A General Framework for Verification and Control of Dynamical Models via Certificate Synthesiscited by 6
  16. 2015Counter-Example Guided Synthesis of Control Lyapunov Functions for Switched Systemscited by 4
  17. 2023Approximate Optimal Controller Synthesis for Cart-Poles and Quadrotors via Sums-of-Squarescited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 7; 2025: 10; 2026: 6.

23 papers.

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  1. 2024Scalable Neural Network Verification with Branch-and-bound Inferred Cutting Planescited by 33
  2. 2024Verification of Neural Control Barrier Functions with Symbolic Derivative Bounds Propagationcited by 12
  3. 2025Clip-and-Verify: Linear Constraint-Driven Domain Clipping for Accelerating Neural Network Verificationcited by 9
  4. 2025Two-Stage Learning of Stabilizing Neural Controllers via Zubov Sampling and Iterative Domain Expansioncited by 6
  5. 2024SoundnessBench: A Soundness Benchmark for Neural Network Verifierscited by 5
  6. 2025Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systemscited by 5
  7. 2024Formally Verified Physics-Informed Neural Control Lyapunov Functionscited by 4
  8. 2024Certified Training with Branch-and-Bound for Lyapunov-stable Neural Controlcited by 3
  9. 2025Provably-Safe Neural Network Training Using Hybrid Zonotope Reachability Analysiscited by 3
  10. 2025Safe Domains of Attraction for Discrete-Time Nonlinear Systems: Characterization and Verifiable Neural Network Estimationcited by 3
  11. 2026Parallel Differentiable Reachability for Learning and Planning with Certified Neural Dynamics and Controllerscited by 2
  12. 2024Combining Neural Networks and Symbolic Regression for Analytical Lyapunov Function Discoverycited by 1
11 more
  1. 2024Kernel-Based Optimal Control: An Infinitesimal Generator Approachcited by 1
  2. 2025Analytical Lyapunov Function Discovery: An RL-based Generative Approachcited by 1
  3. 2025Learning Verifiable Control Policies Using Relaxed Verificationcited by 1
  4. 2026Bridging Control with Neural Network Verifier alpha-beta-CROWN: A Tutorialcited by 1
  5. 2025Neural Lyapunov Function Approximation with Self-Supervised Reinforcement Learningcited by 0
  6. 2025Certifying Stability of Reinforcement Learning Policies using Generalized Lyapunov Functionscited by 0
  7. 2025Verifying Closed-Loop Contractivity of Learning-Based Controllers via Partitioningcited by 0
  8. 2026Learned Lyapunov Shielding for Adaptive Controlcited by 0
  9. 2026Efficient Verification of Neural Control Barrier Functions with Smooth Nonlinear Activationscited by 0
  10. 2026A Survey on the Verification of Reinforcement Learning Policiescited by 0
  11. 2026Learning Provable Neural Network Observer for Uncertain Dynamical Systemscited by 0