%0 Journal Article
%T Computing Reachable Sets as Capture-Viability Kernels in Reverse Time
%A No£¿l Bonneuil
%J Applied Mathematics
%P 1593-1597
%@ 2152-7393
%D 2012
%I Scientific Research Publishing
%R 10.4236/am.2012.311219
%X The set <i>S<sub>F</sub></i>(<i>x</i><sub>0</sub>;<i>T</i>) of states <i>y</i> reachable from a given state <i>x</i><sub>0</sub> at time <i>T</i> under a set-valued dynamic <i>x</i>¡¯(<i>t</i>)¡Ê<i>F</i>(<i>x</i> (<i>t</i>)) and under constraints <i>x</i>(<i>t</i>)¡Ê<i>K</i> where <i>K</i> is a closed set, is also the capture-viability kernel of <i>x</i><sub>0</sub> at <i>T</i> in reverse time of the target {<i>x</i><sub>0</sub>} while remaining in <i>K</i>. 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.
%K Set-Valued Analysis
%K Reachable Set
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=24329