https://www.db-thueringen.de/receive/dbt_mods_00069094https://www.db-thueringen.de/servlets/MCRFileNodeServlet/dbt_derivate_00070459/2405-8963_58_2024_17_310-315.pdfhttps://www.db-thueringen.de/rsc/thumbnail/dbt_mods_00069094.png article 58 17 310 315 text continuingjournal IFAC-PapersOnLine IFAC papers online journal Internationale Förderung für Automatische Lenkung isb Issuing body 1746-2 2015 Frankfurt ; München [u.a.] Elsevier en 600 10.1016/j.ifacol http://uri.gbv.de/document/gvk:ppn:839396090 2405-8963 2839185-8 his Host institution Fortsetzung von: Internationale Förderung für Automatische Lenkung: IFAC Proceedings Volumes text article Linear-quadratic optimal control for abstract differential-algebraic equations Gernandt, Hannes aut Author Gernandt Hannes Reis, Timo aut Author 132186276 0000-0003-0721-8494 Reis Timo 26. International Symposium on Mathematical Theory of Networks and Systems (MTNS) (Cambridge, 19.-23.08.2024) 2024-10-30 Frankfurt Elsevier 2026-01-29 6 Seiten en 600 10.1016/j.ifacol.2024.10.187 his Host institution differential-algebraic equations infinite dimensional systems linear quadratic regulator optimal control stability In this paper, we extend a classical approach to linear quadratic (LQ) optimal control via Popov operators to abstract linear differential-algebraic equations (ADAEs) in Hilbert spaces. To ensure existence of solutions, we assume that the underlying differential-algebraic equation has index one in the pseudo-resolvent sense. This leads to the existence of a degenerate semigroup that can be used to define a Popov operator for our system. It is shown that under a suitable coercivity assumption for the Popov operator the optimal costs can be described by a bounded Riccati operator and that the optimal control input is of feedback form. Furthermore, we characterize exponential stability of ADAEs which is required to solve the infinite horizon LQ problem. dbt_mods_00069094https://www.db-thueringen.de/receive/dbt_mods_00069094