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

TL;DR

This paper introduces a Lyapunov-based measure to quantify how data influences the stability and control performance of learning-based control systems, especially for unknown nonlinear dynamics modeled with Gaussian processes.

Contribution

It proposes a novel Lyapunov-based metric linking data quality to certifiable control stability, applicable to a broad class of unknown nonlinear systems.

Findings

The measure effectively assesses data impact on control stability.

Numerical simulations demonstrate the approach's efficacy.

The method provides insights into data value for control performance.

Abstract

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.