# L1-GP: L1 Adaptive Control with Bayesian Learning

arXiv: https://arxiv.org/abs/2004.14594 · HTML: https://mlsanity.com/paper/2004.14594/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Apr 2020.

## Built on by (most cited first, 11 of 11)

- [Safe Learning in Robotics: From Learning-Based Control to Safe Reinforcement Learning](https://mlsanity.com/paper/2108.06266/) (2021)
- [A Review of Safe Reinforcement Learning: Methods, Theory and Applications](https://mlsanity.com/paper/2205.10330/) (2022)
- [Active Learning of Discrete-Time Dynamics for Uncertainty-Aware Model Predictive Control](https://mlsanity.com/paper/2210.12583/) (2022)
- [Adaptive Control of SE(3) Hamiltonian Dynamics with Learned Disturbance Features](https://mlsanity.com/paper/2109.09974/) (2021)
- [Bridging Model-based Safety and Model-free Reinforcement Learning through System Identification of Low Dimensional Linear Models](https://mlsanity.com/paper/2205.05787/) (2022)
- [Physically Consistent Learning of Conservative Lagrangian Systems with Gaussian Processes](https://mlsanity.com/paper/2206.12272/) (2022)
- [Networked Online Learning for Control of Safety-Critical Resource-Constrained Systems based on Gaussian Processes](https://mlsanity.com/paper/2202.11491/) (2022)
- [Learning to Reach, Swim, Walk and Fly in One Trial: Data-Driven Control with Scarce Data and Side Information](https://mlsanity.com/paper/2106.10533/) (2021)
- [Bayesian inference for data-efficient, explainable, and safe robotic motion planning: A review](https://mlsanity.com/paper/2307.08024/) (2023)
- [Error-Aware Policy Learning: Zero-Shot Generalization in Partially Observable Dynamic Environments](https://mlsanity.com/paper/2103.07732/) (2021)
- [Robustifying Reinforcement Learning Policies with L1 Adaptive Control](https://mlsanity.com/paper/2106.02249/) (2021)

## Abstract (arXiv)

We present L1-GP, an architecture based on L1 adaptive control and Gaussian Process Regression (GPR) for safe simultaneous control and learning. On one hand, the L1 adaptive control provides stability and transient performance guarantees, which allows for GPR to efficiently and safely learn the uncertain dynamics. On the other hand, the learned dynamics can be conveniently incorporated into the L1 control architecture without sacrificing robustness and tracking performance. Subsequently, the learned dynamics can lead to less conservative designs for performance/robustness tradeoff. We illustrate the efficacy of the proposed architecture via numerical simulations.