Approximating Reachable Sets by Extrapolation Methods

Titelangaben

Baier, Robert ; Lempio, Frank:
Approximating Reachable Sets by Extrapolation Methods.
In: Laurent, Pierre-Jean ; Le Méhauteé, Alain ; Schumaker, Larry L. (Hrsg.): Curves and Surfaces in Geometric Design : Papers from the Second International Conference on Curves and Surfaces, held in Chamonix-Mont-Blanc, France, July 10-16, 1993. - Wellesley, Mass. : Peters , 1994 . - S. 9-18
ISBN 1-56881-039-3

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Abstract

Order of convergence results with respect to Hausdorff distance are summarized for the numerical approximation of Aumann's integral by an extrapolation method which is the set-valued analogue of Romberg's method. This method is applied to the discrete approximation of reachable sets of linear differential inclusions. For a broad class of linear control problems, it yields at least second order of convergence, for problems with additional implicit smoothness properties even higher orders of convergence.