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The paper is published in:
Modeling Techniques for Uncertain Systems.
Proceedings of a Conference held in Sopron, Hungary, July 610 1992.
Alexander B. Kurzhanksi, Vladimir V. Veliov (eds.), Progress in Systems and Control Theory 18.
Birkhäuser: BostonBaselBerlin, 1994, pp. 7193.
 MSC:
 34A60 Equations with multivalued righthand sides, See Also
 49M25 Finite difference methods
 65D30 Numerical integration
 65L05 Initial value problems
 93B03 Attainable sets
 Keywords:
 Aumann's integral, reachable set, finite difference methods
 Abstract:

Quadrature formulae for the numerical approximation of Aumann's integral are investigated, which are setvalued
analogues of ordinary quadrature formulae with nonnegative weights, like certain NewtonCotes 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 setvalued integrands which are smooth in an appropriate sense, this approach yields higher order
methods, for setvalued integrands which are not smooth enough, it yields further insight into wellknown 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.
 Table of Contents:

1. Introduction
2. Quadrature Formulae for SetValued 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