Computing Aumann's Integral

Titelangaben

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

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Abstract

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.