This paper proposes 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.
Abstract
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.
A theoretical analysis of the closed-loop properties of a data-driven kernel-based predictive control (DDKPC) scheme developed solely from input-output data proves that the DDKPC scheme guarantees recursive feasibility and closed-loop stability.
Wenjie Liu, Yifei Li, Gang Wang et al.· 0 citations
This paper presents a data-driven stable manifold (DD-SM) method, which integrates Koopman operator representation learning with the geometric stable manifold approach to Hamilton-Jacobi-Bellman (HJB) equations, enabling end-to-end optimal feedback control synthesis from raw trajectory data without prior knowledge of system dynamics. We construct an augmented control system under a unified symmetric subspace decomposition (SSD) and extended dynamic mode decomposition (EDMD) framework for joint approximation of the drift field, control matrix and their spatial derivatives, and derive probabilistic finite-sample error bounds for invariant and non-invariant dictionary spaces to yield a provably accurate approximate characteristic system of HJB equation. Via Lyapunov-Perron operator and ODE perturbation analysis, we prove the data-driven stable manifold achieves monotonically decreasing semi-global error with growing training data. We further establish closed-loop exponential stability and quantify the optimality gap, both tightenable by refining model accuracy. An efficient algorithm pipeline with adaptive data generation and deep neural approximation is developed, outputting control signals within 1 millisecond. Experiments on a modified van der Pol oscillator verify the effectiveness of our method.
A central methodological question in data-driven control is whether to adopt a direct or indirect approach. Direct methods infer a controller or certificate directly from data, while indirect methods first identify a system model and then apply model-based control techniques. Recent developments of the direct method have led to finite-sample guarantees for the data-driven stability analysis of switched linear systems under various settings. However, for the indirect method, such guarantees remain largely elusive. In this paper, we provide a novel framework for the stability analysis of switched linear systems from noisy state measurements, using the indirect approach and quadratic Lyapunov analysis. Our framework comes with finite-sample guarantees on the convergence rate of the system. For that, we combine generalization bounds from machine learning and system identification with sensitivity analysis from quadratic Lyapunov analysis. To enable comparison, we also extend existing direct data-driven methods to handle measurement noise beyond the bounded noise case currently available in the literature. Finally, we compare the two approaches through numerical experiments, revealing that under moderate-to-high noise levels the indirect approach yields tighter probabilistic guarantees as well as greater robustness to noise and outliers than the direct approach
Alexis Vuille, Guillaume O. Berger, Raphael M. Jungers· 0 citations
This work proposes a data-driven predictive control framework for nonlinear systems that incorporates data column preferences according to their proximity to the current operating point through a weighted norm regularization, thereby localizing the predictor without discarding any data.
F. Engeln, S. Zieglmeier, Marta A. Zagorowska et al.· 0 citations