Convergence of the Forward Euler Method for Nonconvex Differential Inclusions

Abstract

The convergence of reachable sets for nonconvex differential inclusions is considered. When the right-hand side in the differential inclusion is a compact-valued, Lipschitz continuous set-valued function it is shown that the convergence in Hausdorff distance of reachable sets for a forward Euler discretization is linear in the time step.