Finite-data error bounds for PDE-based Koopman methods

Establish finite-data approximation error bounds for Koopman-based methods applied to systems governed by partial differential equations, to enable rigorous data-driven control of distributed parameter systems.

Background

While Koopman theory has been explored for autonomous PDEs and used in control of PDE-governed systems, existing results largely focus on spectral analysis or assume exact lifted representations. Finite-data error bounds analogous to those for ODE systems are lacking.

Such bounds are crucial to support robust controller design with guarantees for distributed parameter systems where model learning must be performed from limited data.