Computing Reachable Sets as Capture-Viability Kernels in Reverse Time

The set of states y reachable from a given state 0;FS x T 0x at time under a set-valued dynamic T x t F x t and under constraints x t K where is a closed set, is also the capture-viability kernel K - 0,CaptTF K x of 0x at T in reverse time of the target 0x 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