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A regularization of Zubov's equation for robust domains of attraction

DOI zum Zitieren der Version auf EPub Bayreuth: https://doi.org/10.15495/EPub_UBT_00005460
URN to cite this document: urn:nbn:de:bvb:703-epub-5460-2

Title data

Camilli, Fabio ; Grüne, Lars ; Wirth, Fabian:
A regularization of Zubov's equation for robust domains of attraction.
Bayreuth , 2000

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Abstract

We derive a method for the computation of robust domains of attraction based on a recent generalization of Zubov's theorem on representing robust domains of attraction for perturbed systems via the viscosity solution of a suitable partial differential equation (available here). While a direct discretization of the equation leads to numerical difficulties due to a singularity at the stable equilibrium, a suitable regularization enables us to apply a standard discretization technique for Hamilton-Jacobi-Bellman equations. We present the resulting fully discrete scheme and show a numerical example.

Further data

Item Type: Preprint, postprint
Additional notes (visible to public): erschienen In:
Isidori, Alberto ; Lamnabhi-Lagarrigue, Françoise ; Respondek, Witold (Hrsg.): Nonlinear control in the Year 2000. Volume 1. - Berlin : Springer , 2001 . - S. 277-290
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Institutions of the University: 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
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)
Language: English
Originates at UBT: Yes
URN: urn:nbn:de:bvb:703-epub-5460-2
Date Deposited: 07 May 2021 06:31
Last Modified: 14 May 2021 09:50
URI: https://epub.uni-bayreuth.de/id/eprint/5460
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