Data-driven feedback optimization for particle accelerator application

For many engineering problems involving control systems, finding a good working point for steady-state operation is crucial. Therefore, this paper presents an application of steady-state optimization with feedback on particle accelerators, specifically the European X-ray free-electron laser. In simulation studies, we demonstrate that feedback optimization is able to reach a near-optimal steady-state operation in the presence of uncertainties, even without relying on a priori known model information but purely data-driven through input-output measurements. Additionally, we discuss the importance of including second-order information in the optimization to ensure a satisfactory convergence speed and propose an approximated Hessian representation for problems without second-order knowledge on the plant.