mlsanityData to 14 Oct 2026

Stability-certified reinforcement learning: A control-theoretic perspective

arXiv 1810.11505 ↗First posted 26 Oct 2018eess.SY cs.LG cs.SYcited by 31

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Abstract (arXiv)

We investigate the important problem of certifying stability of reinforcement learning policies when interconnected with nonlinear dynamical systems. We show that by regulating the input-output gradients of policies, strong guarantees of robust stability can be obtained based on a proposed semidefinite programming feasibility problem. The method is able to certify a large set of stabilizing controllers by exploiting problem-specific structures; furthermore, we analyze and establish its (non)conservatism. Empirical evaluations on two decentralized control tasks, namely multi-flight formation and power system frequency regulation, demonstrate that the reinforcement learning agents can have high performance within the stability-certified parameter space, and also exhibit stable learning behaviors in the long run.

Key facts. Cited by 31 papers in the map (data through 14 Oct 2026). First posted on arXiv 26 Oct 2018.

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Citing papers per year: 2020: 1; 2021: 4; 2022: 7; 2023: 5; 2024: 7; 2025: 6; 2026: 1.

31 papers.

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  1. 2021Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learningcited by 371
  2. 2020Imitation Learning with Stability and Safety Guaranteescited by 34
  3. 2023Physics-Informed Machine Learning for Modeling and Control of Dynamical Systemscited by 28
  4. 2021Recurrent Neural Network Controllers Synthesis with Stability Guarantees for Partially Observed Systemscited by 16
  5. 2022Chordal Sparsity for Lipschitz Constant Estimation of Deep Neural Networkscited by 15
  6. 2024A Review of Safe Reinforcement Learning Methods for Modern Power Systemscited by 11
  7. 2024Enhancing Efficiency of Safe Reinforcement Learning via Sample Manipulationcited by 9
  8. 2024Novel Quadratic Constraints for Extending LipSDP beyond Slope-Restricted Activationscited by 7
  9. 2024Learning to Boost the Performance of Stable Nonlinear Systemscited by 7
  10. 2025A view on learning robust goal-conditioned value functions: Interplay between RL and MPCcited by 7
  11. 2022Equipping Black-Box Policies with Model-Based Advice for Stable Nonlinear Controlcited by 6
  12. 2022Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Modelscited by 5
19 more
  1. 2024Synthesizing Neural Network Controllers with Closed-Loop Dissipativity Guaranteescited by 4
  2. 2024Ensuring Both Positivity and Stability Using Sector-Bounded Nonlinearity for Systems with Neural Network Controllerscited by 4
  3. 2022Learning Neural Networks under Input-Output Specificationscited by 3
  4. 2023Tempo Adaptation in Non-stationary Reinforcement Learningcited by 3
  5. 2023Stabilizing reinforcement learning control: A modular framework for optimizing over all stable behaviorcited by 3
  6. 2021Learning to Act Safely with Limited Exposure and Almost Sure Certaintycited by 2
  7. 2024LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layerscited by 2
  8. 2025Improved Scalable Lipschitz Bounds for Deep Neural Networkscited by 2
  9. 2025Local Stability and Region of Attraction Analysis for Neural Network Feedback Systems under Positivity Constraintscited by 2
  10. 2023A modular framework for stabilizing deep reinforcement learning controlcited by 1
  11. 2023Stable Modular Control via Contraction Theory for Reinforcement Learningcited by 1
  12. 2025A New Perspective On AI Safety Through Control Theory Methodologiescited by 1
  13. 2021Learning Lipschitz Feedback Policies from Expert Demonstrations: Closed-Loop Guarantees, Generalization and Robustnesscited by 0
  14. 2022Revisiting PGD Attacks for Stability Analysis of Large-Scale Nonlinear Systems and Perception-Based Controlcited by 0
  15. 2022A stabilizing reinforcement learning approach for sampled systems with partially unknown modelscited by 0
  16. 2022Measuring Interventional Robustness in Reinforcement Learningcited by 0
  17. 2025SALSA-RL: Stability Analysis in the Latent Space of Actions for Reinforcement Learningcited by 0
  18. 2025Taxonomy and Trends in Reinforcement Learning for Robotics and Control Systems: A Structured Reviewcited by 0
  19. 2026CMR: Contractive Mapping Embeddings for Robust Humanoid Locomotion on Unstructured Terrainscited by 0