Physics Informed Fully Embedded Koopman Operator-based Optimal Control of Two-Link Robotic System

This paper presents a data-driven framework utilising neural networks to approximate the Koopman operator for a discrete-time representation of an electrically actuated two-link mechanical system, enabling the application of linear control techniques. A validated dynamic model is used to generate training data. The Physics Informed Fully Embedded Koopman (PIFEK) framework embeds the original state space directly into the Koopman space, leading to sensible tuning of the controllers. The tuning was done using bandwidth analysis of the Koopman dynamics, yielding estimates of the true dynamics. This resulted in satisfactory control performance, including accurate tracking of a trajectory. Comparisons with a conventional PI controller show that while performance is similar, the data-driven PIFEK approach requires significantly less system-specific knowledge, underscoring its potential for efficient control design.