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.
arXiv:2608.30431v1 Announce Type: cross Abstract: By focusing on algorithmic stability as a means of establishing out-of-sample bounds, we provide a system-theoretic interpretation of generalization...
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.
arXiv:2606. 23827v1 Announce Type: cross Abstract: A data-driven method is developed for approximating value functions in deterministic optimal control problems with nonlinear control-affine dynamics.
arXiv:2607. 01819v1 Announce Type: cross Abstract: The Koopman operator has gained considerable attention due to its ability to provide a global linear representation of highly complex dynamical systems.
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.
arXiv:2603. 14762v3 Announce Type: replace-cross Abstract: We study supervisory switching control for partially-observed linear dynamical systems.
arXiv:2609.22338v1 Announce Type: cross Abstract: This tutorial provides a unified view of the emerging area of bilinear learning and control. Using linear systems as a benchmark, it explains what fu...
arXiv:2504.18184v5 Announce Type: replace Abstract: We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert sp...
The paper investigates continuous‑time stochastic control problems with unknown drift and running reward functions, using an exploratory reinforcement learning framework that incorporates relaxed controls and entropy regularization. It develops policy‑iteration algorithms based on probabilistic representations of the optimal value function and its gradient, proving convergence and demonstrating performance through numerical examples. The study also extends to a special case with control‑dependent diffusion, requiring a Hessian representation.
arXiv:2607. 07468v1 Announce Type: cross Abstract: We study the recovery of sparse functions from finite, noisy, and indirect observations in the framework of statistical inverse learning.
The paper investigates the Lyapunov solution operator, which maps a vector field to its corresponding Lyapunov function via a dissipation-based PDE. It proves that this operator is well-defined, unique, and continuous on compact subsets of the domain of attraction under exponential stability, enabling uniform approximation across families of nonlinear systems. Using Fourier Neural Operators, the authors demonstrate that a single trained operator can accurately approximate Lyapunov functions for parameterized dynamics, showcasing the potential of neural operators in stability analysis.
arXiv:2606. 09047v1 Announce Type: cross Abstract: A classical universal stabilization formula offers the practitioner no design freedom: it is a single, parameter-free object.