Inner approximated reachability analysis
Éric Goubault, Olivier Mullier, Sylvie Putot, Michel Kieffer · 2014
Computing a tight inner approximation of the range of a function over some set is notoriously difficult, way beyond obtaining outer approximations. We propose here a new method to compute a tight inner approximation of the set of reachable states of non-linear dynamical systems on a bounded time interval. This approach involves affine forms and Kaucher arithmetic, plus a number of extra ingredients from set-based methods. An implementation of the method is discussed, and illustrated on representative numerical schemes, discrete-time and continuous-time dynamical systems.