Koopman operators and Extended dynamic mode decomposition for the inverted pendulum

We apply the Koopman operator theory and Extended Dynamic Mode Decomposition in the inverted pendulum model. The inverted pendulum is one of the fundamental problems in the theory of systems and control, due to its theoretical value, along with its practical applications. The inverted pendulum is a nonlinear system, its equation of motion is a nonlinear differential equation. This makes the computation of an appropriate control law a difficult task. Koopman operator captures the dynamics of a nonlinear system, however it is infinite dimensional. In this study, we approximate the inverted pendulum with a data-driven finite dimensional linear system which is defined on some augmented state space. We approximate so the trajectories of the system and obtain an alternative description of the system based on Koopman operator theory, Extended Dynamic Mode Decomposition, and Machine Learning.