TITLE:
Computing Reachable Sets as Capture-Viability Kernels in Reverse Time
AUTHORS:
Noël Bonneuil
KEYWORDS:
Set-Valued Analysis; Reachable Set
JOURNAL NAME:
Applied Mathematics,
Vol.3 No.11,
November
7,
2012
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.