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Computing Aumann's Integral

Title data

Baier, Robert ; Lempio, Frank:
Computing Aumann's Integral.
In: Kuržanskij, Aleksandr B. ; Veliov, Vladimir M. (ed.): Modeling Techniques for Uncertain Systems : Proceedings of a Conference held in Sopron, Hungary, July 6-10, 1992. - Basel : Birkhäuser , 1994 . - pp. 71-92 . - (Progress in Systems and Control Theory ; 18 )
ISBN 3-7643-3746-X

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Abstract in another language

Quadrature formulae for the numerical approximation of Aumann's integral are investigated, which are set-valued analogues of ordinary quadrature formulae with nonnegative weights, like certain Newton-Cotes formulae or Romberg integration.
Essentially, the approach consists in the numerical approximation of the support functional of Aumann's integral by ordinary quadrature formulae. For set-valued integrands which are smooth in an appropriate sense, this approach yields higher order methods, for set-valued integrands which are not smooth enough, it yields further insight into well-known order reduction phenomena.
The results are used to define higher order methods for the approximation of reachable sets of certain classes of linear control problems.

Further data

Item Type: Article in a book
Refereed: Yes
Keywords: Aumann's integral; reachable set; finite difference methods
Subject classification: Mathematics Subject Classification Code: 34A60 (49M25 65D30 65D32 65L05 93B03)
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 > Former Professors
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
Result of work at the UBT: Yes
DDC Subjects: 500 Science
500 Science > 510 Mathematics
Date Deposited: 17 Feb 2021 07:57
Last Modified: 05 May 2021 10:00
URI: https://eref.uni-bayreuth.de/id/eprint/63146