Computing Reachable Sets as Capture-Viability Kernels in Reverse Time

DOI: 10.4236/am.2012.311219   PDF   HTML   XML   2,928 Downloads   4,832 Views   Citations

Abstract

The set SF(x0;T) of states y reachable from a given state x0 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 x0 at T in reverse time of the target {x0} 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.

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

References

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