Efficient approximation of the Koopman operator for large-scale nonlinear systems

Implementing Model Predictive Control (MPC) for large-scale nonlinear systems is often computationally challenging due to the intensive online optimization required. To address this, various reduced-order linearization techniques have been developed. The Koopman operator linearizes a nonlinear system by mapping it into an infinite-dimensional space of observables, enabling the application of linear control strategies. While Artificial Neural Networks (ANNs) can approximate the Koopman operator in a data-driven manner, training these networks becomes computationally intensive for high-dimensional systems as the lifting into a higher-dimensional observable space significantly increases data size and complexity. In this work, we propose a technique, combining Proper Orthogonal Decomposition (POD) with an efficient ANN structure to reduce the training time of ANN for large order systems. By first applying POD, we obtain a low order projection of the system. Subsequently, we train the ANN with an efficient structure to approximate the Koopman operator, significantly decreasing training time without sacrificing accuracy.