# The Impact of Data on the Stability of Learning-Based Control- Extended Version

arXiv: https://arxiv.org/abs/2011.10596 · HTML: https://mlsanity.com/paper/2011.10596/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Nov 2020.

## Built on by (most cited first, 6 of 6)

- [Koopman Kernel Regression](https://mlsanity.com/paper/2305.16215/) (2023)
- [Pointwise Feasibility of Gaussian Process-based Safety-Critical Control under Model Uncertainty](https://mlsanity.com/paper/2106.07108/) (2021)
- [Experimental Design for Linear Functionals in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2205.13627/) (2022)
- [Nonparametric Control Koopman Operators](https://mlsanity.com/paper/2405.07312/) (2024)
- [Neural Observer with Lyapunov Stability Guarantee for Uncertain Nonlinear Systems](https://mlsanity.com/paper/2208.13006/) (2022)
- [Adaptive Low-Pass Filtering using Sliding Window Gaussian Processes](https://mlsanity.com/paper/2111.03617/) (2021)

## Abstract (arXiv)

Despite the existence of formal guarantees for learning-based control approaches, the relationship between data and control performance is still poorly understood. In this paper, we propose a Lyapunov-based measure for quantifying the impact of data on the certifiable control performance. By modeling unknown system dynamics through Gaussian processes, we can determine the interrelation between model uncertainty and satisfaction of stability conditions. This allows us to directly asses the impact of data on the provable stationary control performance, and thereby the value of the data for the closed-loop system performance. Our approach is applicable to a wide variety of unknown nonlinear systems that are to be controlled by a generic learning-based control law, and the results obtained in numerical simulations indicate the efficacy of the proposed measure.