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Conditions for strict dissipativity of infinite-dimensional generalized linear-quadratic problems

Title data

Grüne, Lars ; Muff, David ; Schaller, Manuel:
Conditions for strict dissipativity of infinite-dimensional generalized linear-quadratic problems.
Bayreuth ; Ilmenau , 2021 . - 9 p.

Official URL: Volltext

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Abstract in another language

We derive sufficient conditions for strict dissipativity for optimal control of linear evolution equations on Hilbert spaces with a cost functional including linear and quadratic terms. We show that strict dissipativity with a particular storage function is equivalent to ellipticity of a Lyapunov-like operator. Further we prove under a spectral decomposition assumption of the underlying generator and an orthogonality condition of the resulting subspaces that this ellipticity property holds under a detectability assumption. We illustrate our result by means of an example involving a heat equation on a one-dimensional domain.

Further data

Item Type: Preprint, postprint
Refereed: Yes
Keywords: Optimal control; Dissipativity; Infinite-dimensional system; Detectability; Ellipticity; Lyapunov inequality; Necessary optimality condition
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 22 Apr 2021 07:05
Last Modified: 22 Apr 2021 07:05
URI: https://eref.uni-bayreuth.de/id/eprint/64882