Application of Koopman Direct Encoding-Based Model Predictive Control to Nonlinear Electromechanical Systems

Abstract

The Koopman operator framework has shown promising results in enabling the analysis of nonlinear dynamics into an infinite-dimensional linear representation. Koopman direct encoding (KDE) is a model-based approach that utilizes inner products and compositions in a Hilbert space to compute the Koopman operator. However, it has primarily been applied to autonomous systems and simulation environments. Here, we extend the application of KDE to nonautonomous systems and real-world environments by introducing Koopman direct encoding-based model predictive control (KDE-MPC). It was validated on nonlinear electromechanical systems with segmented dynamic conditions, such as contact-noncontact transitions, which pose challenges for modeling and control. Simulation results demonstrate a more stable and smoother position profile compared to proportional-integral-derivative control, particularly at discontinuous boundaries. KDE-MPC was also applied to real-world systems, achieving similar position tracking performance to simulation results. We anticipate that KDE-MPC will offer a viable solution for complex robotic control challenges.