Sep 16, 2026 · eess.SYJ/K move · Enter open · S save
Max Beier, Nicolas Hoischen, Sandra Hirche, Petar Bevanda
Chair of Information-Oriented Control, School of Computation, Information and Technology, Technical University of Munich, 80333 Munich, Germany
This paper proposes a structured approach to learning linear operators for control systems from data. We address both structural and learning-theoretic aspects of the problem. To derive structural assumptions, we propose using the well-established framework of (semi)groups for evolution equations, as operators in control systems are of the same type. Further, we propose analyzing learning algorithms through the lens of the inverse problems framework. This reveals how a learned model depends on the data via error decompositions, convergence guarantees, and optimal regularization -- enabling us to compare existing methods and derive provably advantageous algorithms. In order to obtain these results, we restrict our scope to bounded operators on Hilbert spaces. Although this may appear restrictive, existing approaches often make this assumption implicitly to obtain matrix-like representations. We demonstrate the power of using these frameworks by deriving a convergent estimator for time-varying systems.