R. Baier, M. Gerdts and I. Xausa, “Approximation of Reachable Sets Using Optimal Control Algorithms,” 2011. http://num.math.uni-bayreuth.de/en/publications/2012/baier_gerdts_xausa_approx_reach_sets_2011/index.html

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.