Strict dissipativity for generalized linear-quadratic problems in infinite dimensions

Titelangaben

Grüne, Lars ; Philipp, Friedrich ; Schaller, Manuel:
Strict dissipativity for generalized linear-quadratic problems in infinite dimensions.
In: IFAC-PapersOnLine. Bd. 55 (2022) Heft 30 . - S. 311-316.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2022.11.071

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Abstract

We analyze strict dissipativity of generalized linear quadratic optimal control problems on Hilbert spaces. Here, the term "generalized" refers to cost functions containing both quadratic and linear terms. We characterize strict pre-dissipativity with a quadratic storage function via coercivity of a particular Lyapunov-like quadratic form. Further, we show that under an additional algebraic assumption, strict pre-dissipativity can be strengthened to strict dissipativity. Last, we relate the obtained characterizations of dissipativity with exponential detectability.