Computing Reachable Sets as Capture-Viability Kernels in Reverse Time

Abstract

The set*S*_{F}(*x*_{0};*T*) of states *y* reachable from a given state *x*_{0} at time *T* under a set-valued dynamic *x*’(*t*)∈*F*(*x* (*t*)) and under constraints *x*(*t*)∈*K* where *K* is a closed set, is also the capture-viability kernel of *x*_{0} at *T* in reverse time of the target {*x*_{0}} while remaining in *K*. In dimension up to three, Saint-Pierre’s viability algorithm is well-adapted; for higher dimensions, Bonneuil’s viability algorithm is better suited. It is used on a large-dimensional example.

The set

Cite this paper

N. Bonneuil, "Computing Reachable Sets as Capture-Viability Kernels in Reverse Time,"*Applied Mathematics*, Vol. 3 No. 11, 2012, pp. 1593-1597. doi: 10.4236/am.2012.311219.

N. Bonneuil, "Computing Reachable Sets as Capture-Viability Kernels in Reverse Time,"

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