## 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

Review: |

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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.