Author(s)

Noël Bonneuil

National Institute of Demographic Studies, Paris, France.

The set S_F(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.

Set-Valued Analysis; Reachable Set

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.