Multilayer Extended Dynamic Mode Decomposition for Coupled Van der Pol Oscillators

Abstract

Extended dynamic mode decomposition (EDMD), which is the data-driven method based on the Koopman operator approach, is one of the valuable methods when treating nonlinear dynamical systems. However, the accuracy of linearization deteriorates when the technique is applied to a high-dimensional nonlinear dynamical system such as robots and flying vehicles. To overcome the problem, we propose the multilayer extended dynamic mode decomposition (MEDMD) for the high-dimensional nonlinear system divided into low-dimensional subsystems. The proposed method is applied to a mathematical system model that consists of subsystems in numerical simulation. The results show that MEDMD has good linear accuracy compared to conventional EDMD.