# Stability Enhancement in Reinforcement Learning via Adaptive Control Lyapunov Function

arXiv: https://arxiv.org/abs/2504.19473 · HTML: https://mlsanity.com/paper/2504.19473/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Safe and constrained RL, one of 15 directions in Deep reinforcement learning methods.
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 18 Jan 2025.

## Placed in

- Deep reinforcement learning methods / [Safe and constrained RL](https://mlsanity.com/deeprl/safe-and-constrained-rl/)

## Builds on (most cited first, 13 of 13)

- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Playing Atari with Deep Reinforcement Learning](https://mlsanity.com/paper/1312.5602/) (2013)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [AirSim: High-Fidelity Visual and Physical Simulation for Autonomous Vehicles](https://mlsanity.com/paper/1705.05065/) (2017)
- [Sim-to-Real Transfer in Deep Reinforcement Learning for Robotics: a Survey](https://mlsanity.com/paper/2009.13303/) (2020)
- [Safe Model-based Reinforcement Learning with Stability Guarantees](https://mlsanity.com/paper/1705.08551/) (2017)
- [Control Barrier Function Based Quadratic Programs for Safety Critical Systems](https://mlsanity.com/paper/1609.06408/) (2016)
- [A Review of Safe Reinforcement Learning: Methods, Theory and Applications](https://mlsanity.com/paper/2205.10330/) (2022)
- [A General Safety Framework for Learning-Based Control in Uncertain Robotic Systems](https://mlsanity.com/paper/1705.01292/) (2017)
- [Safe Reinforcement Learning for Legged Locomotion](https://mlsanity.com/paper/2203.02638/) (2022)
- [Torque Saturation in Bipedal Robotic Walking through Control Lyapunov Function Based Quadratic Programs](https://mlsanity.com/paper/1302.7314/) (2013)
- [DeepSafeMPC: Deep Learning-Based Model Predictive Control for Safe Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2403.06397/) (2024)

## Built on by (most cited first, 1 of 1)

- [MSACL: Multi-Step Actor-Critic Learning with Lyapunov Certificates for Exponentially Stabilizing Control](https://mlsanity.com/paper/2512.24955/) (2025)

## Abstract (arXiv)

Reinforcement Learning (RL) has shown promise in control tasks but faces significant challenges in real-world applications, primarily due to the absence of safety guarantees during the learning process. Existing methods often struggle with ensuring safe exploration, leading to potential system failures and restricting applications primarily to simulated environments. Traditional approaches such as reward shaping and constrained policy optimization can fail to guarantee safety during initial learning stages, while model-based methods using Control Lyapunov Functions (CLFs) or Control Barrier Functions (CBFs) may hinder efficient exploration and performance. To address these limitations, this paper introduces Soft Actor-Critic with Control Lyapunov Function (SAC-CLF), a framework that enhances stability and safety through three key innovations: (1) a task-specific CLF design method for safe and optimal performance; (2) dynamic adjustment of constraints to maintain robustness under unmodeled dynamics; and (3) improved control input smoothness while ensuring safety. Experimental results on a classical nonlinear system and satellite attitude control demonstrate the effectiveness of SAC-CLF in overcoming the shortcomings of existing methods.