Approximating Reachable Sets by Extrapolation Methods

R. Baier, F. Lempio: Approximating Reachable Sets by Extrapolation Methods
in: 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, P. J. Laurent, A. Le Méhauteé, L. L. Schumaker (eds.)
A K Peters, Wellesley, 1994, 9 - 18

MR Nummer: 1302177
Zentralblattnummer: 0813.65099
Keywords: Aumann's integral; reachable set; extrapolation method
Mathematics Subject Classification Code: 34A60 (49M25 65D30 65L05 93B03)
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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.


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

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