Approximation of Reachable Sets using Optimal Control Algorithms
نویسندگان
چکیده
We investigate and analyze a computational method for the approximation of reachable sets for nonlinear dynamic systems. The method uses grids to cover the region of interest and the distance function to the reachable set evaluated at grid points. A convergence analysis is provided and shows the convergence of three different types of discrete set approximations to the reachable set. The distance functions can be computed numerically by suitable optimal control problems in combination with direct discretization techniques which allows adaptive calculations of reachable sets. Several numerical examples with nonconvex reachable sets are presented. MSC classification: 49J15, 49M25, 93B03, 93C10 (90C30) keywords: reachable set; optimal control; direct discretization partially supported by the Hausdorff Research Institute for Mathematics, Bonn, within the HIM Junior Semester Program ”Computational Mathematics” from February to April 2008 supported by the European Union under the 7th Framework Programme FP7– PEOPLE–2010–ITN, Grant agreement number 264735–SADCO
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