# Stability-certified reinforcement learning: A control-theoretic perspective

arXiv: https://arxiv.org/abs/1810.11505 · HTML: https://mlsanity.com/paper/1810.11505/

## Key facts

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

## Built on by (most cited first, 30 of 31)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Imitation Learning with Stability and Safety Guarantees](https://mlsanity.com/paper/2012.09293/) (2020)
- [Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems](https://mlsanity.com/paper/2306.13867/) (2023)
- [Recurrent Neural Network Controllers Synthesis with Stability Guarantees for Partially Observed Systems](https://mlsanity.com/paper/2109.03861/) (2021)
- [Chordal Sparsity for Lipschitz Constant Estimation of Deep Neural Networks](https://mlsanity.com/paper/2204.00846/) (2022)
- [A Review of Safe Reinforcement Learning Methods for Modern Power Systems](https://mlsanity.com/paper/2407.00304/) (2024)
- [Enhancing Efficiency of Safe Reinforcement Learning via Sample Manipulation](https://mlsanity.com/paper/2405.20860/) (2024)
- [Novel Quadratic Constraints for Extending LipSDP beyond Slope-Restricted Activations](https://mlsanity.com/paper/2401.14033/) (2024)
- [Learning to Boost the Performance of Stable Nonlinear Systems](https://mlsanity.com/paper/2405.00871/) (2024)
- [A view on learning robust goal-conditioned value functions: Interplay between RL and MPC](https://mlsanity.com/paper/2502.06996/) (2025)
- [Equipping Black-Box Policies with Model-Based Advice for Stable Nonlinear Control](https://mlsanity.com/paper/2206.01341/) (2022)
- [Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Models](https://mlsanity.com/paper/2205.05787/) (2022)
- [Synthesizing Neural Network Controllers with Closed-Loop Dissipativity Guarantees](https://mlsanity.com/paper/2404.07373/) (2024)
- [Ensuring Both Positivity and Stability Using Sector-Bounded Nonlinearity for Systems with Neural Network Controllers](https://mlsanity.com/paper/2406.12744/) (2024)
- [Learning Neural Networks under Input-Output Specifications](https://mlsanity.com/paper/2202.11246/) (2022)
- [Tempo Adaptation in Non-stationary Reinforcement Learning](https://mlsanity.com/paper/2309.14989/) (2023)
- [Stabilizing reinforcement learning control: A modular framework for optimizing over all stable behavior](https://mlsanity.com/paper/2310.14098/) (2023)
- [Learning to Act Safely with Limited Exposure and Almost Sure Certainty](https://mlsanity.com/paper/2105.08748/) (2021)
- [LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layers](https://mlsanity.com/paper/2410.22258/) (2024)
- [Improved Scalable Lipschitz Bounds for Deep Neural Networks](https://mlsanity.com/paper/2503.14297/) (2025)
- [Local Stability and Region of Attraction Analysis for Neural Network Feedback Systems under Positivity Constraints](https://mlsanity.com/paper/2505.22889/) (2025)
- [A modular framework for stabilizing deep reinforcement learning control](https://mlsanity.com/paper/2304.03422/) (2023)
- [Stable Modular Control via Contraction Theory for Reinforcement Learning](https://mlsanity.com/paper/2311.03669/) (2023)
- [A New Perspective On AI Safety Through Control Theory Methodologies](https://mlsanity.com/paper/2506.23703/) (2025)
- [Learning Lipschitz Feedback Policies from Expert Demonstrations: Closed-Loop Guarantees, Generalization and Robustness](https://mlsanity.com/paper/2103.16629/) (2021)
- [Revisiting PGD Attacks for Stability Analysis of Large-Scale Nonlinear Systems and Perception-Based Control](https://mlsanity.com/paper/2201.00801/) (2022)
- [A stabilizing reinforcement learning approach for sampled systems with partially unknown models](https://mlsanity.com/paper/2208.14714/) (2022)
- [Measuring Interventional Robustness in Reinforcement Learning](https://mlsanity.com/paper/2209.09058/) (2022)
- [SALSA-RL: Stability Analysis in the Latent Space of Actions for Reinforcement Learning](https://mlsanity.com/paper/2502.15512/) (2025)
- [Taxonomy and Trends in Reinforcement Learning for Robotics and Control Systems: A Structured Review](https://mlsanity.com/paper/2510.21758/) (2025)

## 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.