Computing Reachable Sets of Semi-Discrete Solid Dynamics Equations with ReachabilityAnalysis.jl

Abstract

Set-Based Solid Dynamics. When uncertainty is present, the initial displacements x(0) and the initial velocities x′(0) belong to the feasible sets X0 and V0, respectively. In [6] a novel approach for time integration of solid dynamics equations based on set-based techniques was presented. The approach allows to compute, in a single integration, the solution sets (or flowpipes) that include all exact trajectories under uncertainties in the initial conditions and applied loads. Such solution sets cannot be obtained using standard numerical integrators, since they are designed to propagate initial points, not sets.