# Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems

arXiv: https://arxiv.org/abs/1903.01577 · HTML: https://mlsanity.com/paper/1903.01577/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Mar 2019.

## Built on by (most cited first, 19 of 19)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview](https://mlsanity.com/paper/2110.00675/) (2021)
- [Learning Barrier Certificates: Towards Safe Reinforcement Learning with Zero Training-time Violations](https://mlsanity.com/paper/2108.01846/) (2021)
- [Reinforcement Learning for Safe Robot Control using Control Lyapunov Barrier Functions](https://mlsanity.com/paper/2305.09793/) (2023)
- [Model-Free Reinforcement Learning for Symbolic Automata-encoded Objectives](https://mlsanity.com/paper/2202.02404/) (2022)
- [Bounded nonlinear forecasts of partially observed geophysical systems with physics-constrained deep learning](https://mlsanity.com/paper/2202.05750/) (2022)
- [Random Features Approximation for Control-Affine Systems](https://mlsanity.com/paper/2406.06514/) (2024)
- [Learning Contraction Policies from Offline Data](https://mlsanity.com/paper/2112.05911/) (2021)
- [Decomposing Control Lyapunov Functions for Efficient Reinforcement Learning](https://mlsanity.com/paper/2403.12210/) (2024)
- [Recursively Feasible Probabilistic Safe Online Learning with Control Barrier Functions](https://mlsanity.com/paper/2208.10733/) (2022)
- [Meta-Learning-Based Adaptive Stability Certificates for Dynamical Systems](https://mlsanity.com/paper/2312.15340/) (2023)
- [Distributionally Robust Policy and Lyapunov-Certificate Learning](https://mlsanity.com/paper/2404.03017/) (2024)
- [Robust Model Based Reinforcement Learning Using L1 Adaptive Control](https://mlsanity.com/paper/2403.14860/) (2024)
- [Safe Learning Reference Governor: Theory and Application to Fuel Truck Rollover Avoidance](https://mlsanity.com/paper/2101.09298/) (2021)
- [Learning to Control an Unstable System with One Minute of Data: Leveraging Gaussian Process Differentiation in Predictive Control](https://mlsanity.com/paper/2103.04548/) (2021)
- [ProBF: Learning Probabilistic Safety Certificates with Barrier Functions](https://mlsanity.com/paper/2112.12210/) (2021)
- [Learning to Stabilize Online Reinforcement Learning in Unbounded State Spaces](https://mlsanity.com/paper/2306.01896/) (2023)
- [CaRT: Certified Safety and Robust Tracking in Learning-based Motion Planning for Multi-Agent Systems](https://mlsanity.com/paper/2307.08602/) (2023)
- [Real-Time Model Checking for Closed-Loop Robot Reactive Planning](https://mlsanity.com/paper/2508.19186/) (2025)

## Abstract (arXiv)

Many modern nonlinear control methods aim to endow systems with guaranteed properties, such as stability or safety, and have been successfully applied to the domain of robotics. However, model uncertainty remains a persistent challenge, weakening theoretical guarantees and causing implementation failures on physical systems. This paper develops a machine learning framework centered around Control Lyapunov Functions (CLFs) to adapt to parametric uncertainty and unmodeled dynamics in general robotic systems. Our proposed method proceeds by iteratively updating estimates of Lyapunov function derivatives and improving controllers, ultimately yielding a stabilizing quadratic program model-based controller. We validate our approach on a planar Segway simulation, demonstrating substantial performance improvements by iteratively refining on a base model-free controller.