Direct Data Driven Natural Gradient Descent for Control

This paper introduces a novel direct data-driven control framework based on Natural Gradient Descent (NGD) to design interpretable and robust closed-loop policies without requiring explicit model identification. We propose two data-driven NGD formulations that incorporate the closed-loop covariance matrix through the Fisher Information Matrix (FIM), allowing gradient updates to be preconditioned according to the system's intrinsic uncertainty. Leveraging two distinct data-based parameterizations of the closed-loop system, our method enables stability-guaranteed policy synthesis directly from data. We provide theoretical guarantees for contraction and convergence using semidefinite programs (SDPs) and validate our framework in both simulations and on hardware on a ROSbot XL platform. The results demonstrate intuitive features compared to linear-quadratic regulator (LQR) and standard data-driven baselines, particularly in terms of convergence speed, robustness, and control interpretability. This work bridges the gap between trajectory-oriented natural gradient methods and practical data-driven control design.