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Robert Baier, Frank Lempio

Computing Aumann's Integral

The paper is published in:
Modeling Techniques for Uncertain Systems.
Proceedings of a Conference held in Sopron, Hungary, July 6-10 1992.
Alexander B. Kurzhanksi, Vladimir V. Veliov (eds.), Progress in Systems and Control Theory 18.
Birkhäuser: Boston-Basel-Berlin, 1994, pp. 71-93.

34A60 Equations with multivalued right-hand sides, See Also
49M25 Finite difference methods
65D30 Numerical integration
65L05 Initial value problems
93B03 Attainable sets

Aumann's integral, reachable set, finite difference methods

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

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

The results are used to define higher order methods for the approximation of reachable sets of certain classes of linear
control problems.

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

© Robert Baier
Last modified: Thu May 28 14:47:02 MDT 1998