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Séminaire du département Automatique du 22/04/2013 à 14h00

 

Reachability of Hybrid Systems using Support Functions over Continuous Time

Intervenant : G. Frehse, Verimag, University Joseph Fourier

Lieu : Salle des séminaires du DAUTO

 

Résumé : Computing the reachable states of a hybrid system is hard, in part because efficient algorithms are available mainly for convex sets, while the states reachable by time elapse, so-called flowpipes, are generally nonconvex. When the dynamics are piecewise affine, the nonconvexity takes a particular form: when drawn along a time axis, the flowpipe is convex at any point in time. We exploit this property to lift efficient approximation techniques from convex sets to flowpipes. The approximation consists of a set of piecewise linear scalar functions over continuous time, which define at each time point a polyhedral inner- and outer approximation. Reachability operations that are difficult to carry out on nonconvex sets correspond to simple operations on these scalar functions. The resulting reachability algorithm is precise, scalable, and provides good error measurements. We present an implementation in the SpaceEx verification platform and showcase the performance on several examples.


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