Koopman Operator Dynamical Models: Learning, Analysis and Control

Understand

The Koopman operator allows for handling nonlinear systems through a (globally) linear representation.

• In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.
• Although there are principled ways of learning such finite approximations, they are in many instances overlooked in favor of, often ill-posed and unstructured methods.
• Also, Koopman operator theory has long-standing connections to known system-theoretic and dynamical system notions that are not universally recognized.