Error analysis of kernel EDMD for prediction and control in the Koopman framework

Understand

Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the Koopman operator for deterministic and stochastic (control) systems.

• This operator is linear and encompasses full information on the (expected stochastic) dynamics.
• In this paper, we analyze a kernel-based EDMD algorithm, known as kEDMD, where the dictionary consists of the canonical kernel features at the data points.
• The latter are acquired by i.i.d.