Second-Order Sampling-Based Stability Guarantee for Data-Driven Control Systems

This study presents a sampling-based method to guarantee robust stability of general control systems with uncertainty. The method allows the system dynamics and controllers to be represented by various data-driven models, such as Gaussian processes and deep neural networks. For nonlinear systems, stability conditions involve inequalities over an infinite number of states in a state space. Sampling-based approaches can simplify these hard conditions into inequalities discretized over a finite number of states. However, this simplification requires margins to compensate for discretization residuals. Large margins degrade the accuracy of stability evaluation, and obtaining appropriate margins for various systems is challenging. This study addresses this challenge by deriving second-order margins for various nonlinear systems containing data-driven models. Because the size of the derived margins decrease quadratically as the discretization interval decreases, the stability evaluation is more accurate than with first-order margins. Furthermore, this study designs feedback controllers by integrating the sampling-based approach with an optimization problem. As a result, the controllers can guarantee stability while simultaneously considering control performance.