chapter
R. Baier and F. Lemp io
Pages 10

We concentrate on a special approach for the numerical approximation of reachable sets of linear differential inclusions which is based on the compu­ tation of Aumann’s integral for set-valued mappings. It consists in exploiting ordinary quadrature formulae with nonnegative weights for the numerical ap­ proximation of the dual representation of Aumann’s integral via its support functional. Theoretical roots of this approach could be traced back via [11] to [5]. The paper [4] is the first one with explicit numerical computations, exploiting mainly composite closed Newton-Cotes formulae for set-valued in­ tegrands, and including an outline of proof techniques for error estimates with respect to Hausdorff distance, which avoid the embedding of families of convex sets into abstract spaces (cf. [13,14]). All proofs are based on error es­ timates using weak assumptions on the regularity of single-valued integrands (see [15,7,8,4]).