000K  utf8
1100  2024$c2024-10-30
1500  eng
2051  10.1016/j.ifacol.2024.10.187
3000  Gernandt, Hannes
3010  Reis, Timo
4000  Linear-quadratic optimal control for abstract differential-algebraic equations$hElsevier  [Gernandt, Hannes]
4030  Frankfurt$nElsevier
4060  6 Seiten
4209  In this paper, we extend a classical approach to linear quadratic (LQ) optimal control via Popov operators to abstract linear differential-algebraic equations (ADAEs) in Hilbert spaces. To ensure existence of solutions, we assume that the underlying differential-algebraic equation has index one in the pseudo-resolvent sense. This leads to the existence of a degenerate semigroup that can be used to define a Popov operator for our system. It is shown that under a suitable coercivity assumption for the Popov operator the optimal costs can be described by a bounded Riccati operator and that the optimal control input is of feedback form. Furthermore, we characterize exponential stability of ADAEs which is required to solve the infinite horizon LQ problem.
4950  https://doi.org/10.1016/j.ifacol.2024.10.187$xR$3Volltext$534
4961  https://www.db-thueringen.de/receive/dbt_mods_00069094
5051  600
5550  differential-algebraic equations
5550  infinite dimensional systems
5550  linear quadratic regulator
5550  optimal control
5550  stability