Inner approximated reachability analysis

Abstract : Computing a tight inner approximation of the range of a function over some set is notoriously di cult, 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 a ne 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.
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Eric Goubault, Olivier Mullier, Sylvie Putot, Michel Kieffer. Inner approximated reachability analysis. HSCC '14, Apr 2014, Berlin, Germany. Proceedings of the 17th international conference on Hybrid systems: computation and control, pp.163-172, 2014, 〈10.1145/2562059.2562113〉. 〈hal-01073731〉

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