Demystifying Linear Operator Learning for Control Systems

arXiv:2609.19428 · eess.SY, cs.LG, cs.SY · Submitted 2026-09-16 · Read on arXiv

eess.SY, cs.LG, cs.SY

Submitted: 2026-09-16

Updated: 2026-09-16

Comments: accepted to the 65th IEEE Conference on Decision and Control; authors' version

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Hilbert Space — 18× in this paper · explained in 2 episodes
• Inverse Problem — 17× in this paper · explained in 2 episodes
• Regularization — 16× in this paper · explained in 3 episodes
• Error Decomposition — 9× in this paper · explained in 3 episodes
• Embeddings — 4× in this paper · explained in 2 episodes
• Convergence Guarantees — 3× in this paper · explained in 3 episodes
• Reproducing Kernel Hilbert Space (RKHS) — 2× in this paper · explained in 3 episodes
• Abstraction — 1× in this paper · explained in 1 episode
• Core — 1× in this paper · explained in 2 episodes
• Generalization — 1× in this paper · explained in 13 episodes

Sources

• Nonparametric Control Koopman Operators
• Koopman Operator Dynamical Models: Learning, Analysis and Control
• From Biased to Unbiased Dynamics: An Infinitesimal Generator Approach
• Modeling Nonlinear Control Systems via Koopman Control Family: Universal Forms and Subspace Invariance Proximity
• A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition

Related papers

• One Request, Multiple Experts: LLM Orchestrates Domain Specific Models via Adaptive Task Routing
• A Geometric Decision Procedure for STL Feasibility and Repair
• Submodular Multi-Agent Policy Learning for Online Distributed Task Allocation in Open Multi-Agent Systems
• Policy-Level Recursive Self-Improvement for Embodied AI with a Criticality World Model
• Minimal Experiments for Robust Stabilization: Information, Spectral Geometry, and Duration
• Decentralized Power-Optimal Coordination for Spacecraft Swarms Using Time-Varying Magnetorquer Actuation