@Article{dbt_mods_00069127,
  author = 	{Schaller, Manuel
		and Worthmann, Karl
		and Philipp, Friedrich
		and Peitz, Sebastian
		and N{\"u}ske, Feliks
		and {12. IFAC Symposium on Nonlinear Control Systems (NOLCOS 2022) (Canberra, 04.-06.01.2023)}},
  title = 	{Towards reliable data-based optimal and predictive control using extended DMD},
  journal = 	{IFAC-PapersOnLine},
  year = 	{2023},
  month = 	{Mar},
  day = 	{16},
  publisher = 	{Elsevier},
  address = 	{Frankfurt; Frankfurt ; M{\"u}nchen [u.a.]},
  volume = 	{56},
  number = 	{1},
  pages = 	{169--174},
  keywords = 	{Approximation error; data-based; dictionary size; eDMD; estimation error; finite data; Koopman; optimal control; predicted control; projection error},
  abstract = 	{While Koopman-based techniques like extended Dynamic Mode Decomposition are nowadays ubiquitous in the data-driven approximation of dynamical systems, quantitative error estimates were only recently established. To this end, both sources of error resulting from a finite dictionary and only finitely-many data points in the generation of the surrogate model have to be taken into account. We generalize the rigorous analysis of the approximation error to the control setting while simultaneously reducing the impact of the curse of dimensionality by using a recently proposed bilinear approach. In particular, we establish uniform bounds on the approximation error of state-dependent quantities like constraints or a performance index enabling data-based optimal and predictive control with guarantees.},
  note = 	{Fortsetzung von: Internationale F{\"o}rderung f{\"u}r Automatische Lenkung: IFAC Proceedings Volumes},
  issn = 	{2405-8963},
  doi = 	{10.1016/j.ifacol.2023.02.029},
  url = 	{https://www.db-thueringen.de/receive/dbt_mods_00069127},
  url = 	{http://uri.gbv.de/document/gvk:ppn:1876272104},
  url = 	{http://uri.gbv.de/document/gvk:ppn:839396090},
  url = 	{https://doi.org/10.1016/j.ifacol.2023.02.029},
  url = 	{https://doi.org/10.1016/j.ifacol},
  file = 	{:https://www.db-thueringen.de/servlets/MCRFileNodeServlet/dbt_derivate_00070492/2405-8963_56_2023_1_169-174.pdf:PDF},
  language = 	{en}
}