Koopman Operator Learning Using Neural Networks for Data-driven Control

Willems' Fundamental Lemma from behavioral theory establishes the conditions for a non-parametric representation of the linear time-invariant (LTI) systems. How to extent the Fundamental Lemma to nonlinear systems has seen a surge of interest in recent years. The Koopman operator can embed the system states into higher-dimensional space using lifting function. There is still no universal method for the design of lifting functions. We propose an invertible neural network (INN) for the Koopman operator as lifting function. The INN is designed for data-driven controller and ensures the linearity and reconstructionability. Then the proposed network is demonstrated on a typical nonlinear system, validating its efficiency and compared with kernel methods.