Computing Aumann's Integral

R. Baier, F. Lempio: Computing Aumann's Integral
in: Modeling Techniques for Uncertain Systems,Proceedings of a Conference held in Sopron, Hungary, July 6-10, 1992, A. B. Kurzhanski, V. M. Veliov (eds.)
Progress in Systems and Control Theory 18, Birkhäuser, Basel, 1994, 71 - 92

MR Nummer: 1287649
Zentralblattnummer: 0828.65021
Keywords: Aumann's integral; reachable set; finite difference methods
Mathematics Subject Classification Code: 34A60 (49M25 65D30 65D32 65L05 93B03)
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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.


1. Introduction
2. Quadrature Formulae for Set-Valued Mappings
3. Approximation of Reachable Sets for Linear Control Problems
4. Test Examples

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