The Impact of Data on the Stability of Learning-Based Control- Extended Version
This work addresses the poorly understood relationship between data and control performance for learning-based control systems, which is a problem for control engineers and researchers.
This paper proposes a Lyapunov-based measure to quantify how data impacts the certifiable control performance of learning-based control systems. By modeling unknown system dynamics with Gaussian processes, the authors assess the relationship between model uncertainty and stability conditions, providing a direct measure of data's value for stationary control performance.
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.