Error bounds under noisy output measurements

Develop finite-data error bounds for Koopman-based surrogate models that explicitly account for noisy output measurements, enabling rigorous closed-loop guarantees for Koopman-based control of nonlinear systems trained on noisy data.

Background

Current finite-data error bounds used for robust Koopman-based control typically assume noise-free data or impose strong invariance conditions that are rarely met. While some methods attempt to learn Koopman models under noise by assuming invariant finite-dimensional dictionaries, these assumptions are often unrealistic.

A principled framework that incorporates noisy output measurements into finite-data error bounds is needed to ensure that controllers designed from such surrogates maintain stability and performance guarantees for the true nonlinear system.