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Robert Baier, Frank Lempio

Approximating Reachable Sets by Extrapolation Methods

The paper is published in:
P.J. Laurent, A. Le Mehaute and L.L. Schumaker (eds.):
Curves and Surfaces in Geometric Design,
Wellesley: A K Peters, 1994, pp. 9-18.

MSC:
65L05 Initial value problems
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections, See Also {26E25, 54C60, 54C65, 90A14}
34A60 Equations with multivalued right-hand sides, See Also

Keywords:
order of convergence; Hausdorff distance; Aumann's integral; extrapolation method; Romberg's method; reachable sets; linear differential inclusions; linear control problems

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 order of convergence.

Table of Contents:
1. Introduction
2. Set-Valued Integration
3. Approximation of Reachable Sets
4. Concluding Remarks


© Robert Baier
Last modified: Thu May 28 14:57:20 MDT 1998