arXiv Machine Learning By Max Beier, Nicolas Hoischen, Sandra Hirche, Petar Bevanda

Demystifying Linear Operator Learning for Control Systems

Read the original on arXiv Machine Learning →

The paper introduces a structured method for learning linear operators in control systems using data. It leverages the framework of (semi)groups for evolution equations to establish structural assumptions and applies inverse‑problems theory to analyze learning algorithms, revealing error decompositions, convergence guarantees, and optimal regularization. Focusing on bounded operators on Hilbert spaces, the authors derive a convergent estimator for time‑varying systems, illustrating the practical power of their approach.

Machine-generated by The Flow from the publisher's headline and feed description — not written or checked by a human. The full article lives at arXiv Machine Learning.

arXiv Machine Learning
Aug 26

Sequential operator learning under dependent data

The paper presents time‑uniform self‑normalized concentration bounds for stochastic processes in Hilbert spaces with vector‑valued noise, enabling regression‑error guarantees for both linear and nonlinear parametric operators. These results apply to possibly infinite‑dimensional inputs and outputs without requiring independence or mixing assumptions, and are derived in the context of sequentially collected, dependent data such as adaptive experimental design and dynamical‑system modelling.

By Rafael Oliveira
arXiv Machine Learning
Jul 7

Nonparametric Control Koopman Operators

arXiv:2405. 07312v5 Announce Type: replace-cross Abstract: This paper presents a novel Koopman composition operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations.

By Petar Bevanda, Bas Driessen, Lucian Cristian Iacob, Stefan Sosnowski, Roland T\'oth, Sandra Hirche