Leveraging neural networks and the Koopman operator for controlled dynamical systems and linear model predictive control

In this thesis, we present a novel network architecture using an encoder-decoder neural network, inspired by Lusch et al. [15], to directly obtain the eigenfunctions of the Koopman operator, which globally linearize the dynamics of nonlinear systems. By extending this approach to account for control inputs, we enable the application of well-established control synthesis techniques for obtaining optimal policies, while ensuring that control constraints remain convex for globally optimal solutions. This method overcomes the limitations of traditional Koopman operator approximations and provides improved prediction and control performance. We demonstrate the efficacy of our approach on a range of simulated controlled dynamical systems and show its potential for real-world applications in fields like robotics, and process control.