Closed-Loop System Identification of an Unstable Nonlinear System Using Koopman Operator

This paper presents a novel methodology for closed-loop system identification of unstable nonlinear systems using the Koopman operator with Extended Dynamic Mode Decomposition with control (EDMDc). The study highlights the critical role of selecting appropriate observable functions to develop accurate and efficient Koopman models. We demonstrate that the resulting Koopman models exhibit excellent fitting and validation properties and retain the stabilizability of the original nonlinear systems. These models are verified through time and frequency responses under closed-loop control using a Linear Quadratic Regulator (LQR), confirming their effectiveness. Future work will extend this framework to more complex systems and incorporate machine learning techniques to refine the selection of observable functions. This approach aims further to enhance the adaptability and robustness of Koopman-based control strategies.