Computing Aumann's Integral

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Baier, Robert ; Lempio, Frank:
Computing Aumann's Integral.
Bayreuth , 1994

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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.