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.