Hespe, ChristianChristianHespeKaiser, JanJanKaiserLübsen, JannisJannisLübsenMayet, FrankFrankMayetScholz, MatthiasMatthiasScholzEichler, AnnikaAnnikaEichler2025-07-172025-07-172025-06-01At Automatisierungstechnik 73 (6): 429-440 (2025)https://hdl.handle.net/11420/56255For 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.en2196-677X20256429440De Gruyterhttps://creativecommons.org/licenses/by/4.0/feedback optimization | particle accelerators | recursive least-squares estimation | steady-state controlTechnology::629: Other Branches::629.8: Control and Feedback Control SystemsTechnology::620: EngineeringNatural Sciences and Mathematics::519: Applied Mathematics, ProbabilitiesJournal Articlehttps://doi.org/10.15480/882.1540010.1515/auto-2024-017010.15480/882.15400Journal Article