Inner approximated reachability analysis

Eric Goubault (1) , Olivier Mullier (2) , Sylvie Putot (1) , Michel Kieffer (3)

1 LIST (CEA) - Laboratoire d'Intégration des Systèmes et des Technologies
2 LMeASI - Laboratoire Modélisation et Analyse de Systèmes en Interaction
3 L2S - Laboratoire des signaux et systèmes

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.

Domains: Computer Science [cs]; Automatic Control Engineering; Computer Science [cs]; Numerical Analysis [cs.NA]; Computer Science [cs]; Signal and Image Processing

Eric Goubault, Olivier Mullier, Sylvie Putot, Michel Kieffer. Inner approximated reachability analysis. HSCC '14, Apr 2014, Berlin, Germany. pp.163-172, ⟨10.1145/2562059.2562113⟩. ⟨hal-01073731⟩