What Is the Koopman Operator? A Simplified Treatment for Discrete-Time Systems

Abstract

This paper provides an introduction to the discrete-time Koopman operator for nonexperts, including a treatment of the basic definitions and properties of the Koopman operator and a numerical method for approximating the Koopman spectrum. Furthermore, the paper stresses the role of compositional completeness for spaces of Koopman observables and gives conditions under which the Lp spaces are compositionally complete. Numerical examples are given to illustrate the basic concepts.