aiqbench analysis
This research advances the theoretical foundations of learning linear operators within control systems by integrating semigroup frameworks and inverse problem analysis. By establishing convergence guarantees and optimal regularization strategies, the study provides a rigorous pathway for developing robust data-driven estimators for time-varying dynamics. The work bridges structural assumptions in evolution equations with practical machine learning algorithms, offering provably advantageous methods for system identification.
Demystifying Linear Operator Learning for Control Systems
arXiv:2609.19428v1 Announce Type: cross Abstract: 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.
Abstract: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.
Systems and Control (eess.SY); Machine Learning (cs.LG)
arXiv:2609.19428 [eess.SY]
(or arXiv:2609.19428v1 [eess.SY] for this version)
https://doi.org/10.48550/arXiv.2609.19428 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 240 words
