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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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.

Contents:

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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