P. Saint-Pierre, “Approximation of the Viability Kernel,” Applied Mathematics and Optimization, Vol. 29, No. 2, 1994, pp. 187-209. doi:10.1007/BF01204182

has been cited by the following article:

• 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.