This paper introduces a new framework for representing control systems using Koopman composition operators within reproducing kernel Hilbert spaces (RKHSs). This approach eliminates the need for explicit dictionary or input parametrizations, bridging the gap between control system operator learning and infinite-dimensional regression. The framework enables accurate finite-rank approximations in infinite-dimensional spaces and finite-dimensional predictors without pre-defined function or input spans. To enhance scalability for high-dimensional control systems, the method incorporates sketching techniques, demonstrating superior prediction accuracy over bilinear EDMD in numerical experiments, particularly in high dimensions. The learned models are also shown to be compatible with linear-parameter-varying techniques for model predictive control. AI
IMPACT This research could advance control system design by enabling more accurate and scalable modeling, potentially impacting areas like robotics and autonomous systems.
RANK_REASON Academic paper detailing a novel framework for control systems. [lever_c_demoted from research: ic=1 ai=0.4]
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