Approximating Reachable Sets by Extrapolation Methods

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Baier, Robert ; Lempio, Frank:
Approximating Reachable Sets by Extrapolation Methods.
Bayreuth , 1994

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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.