We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that
conservatively approximates the set of reachable states of a nonlinear
dynamical system. LRT makes use of the Cauchy-Green stretching factor (SF),
which is derived from an over-approximation of the gradient of the solution
flows. The SF measures the discrepancy between two states propagated by the
system solution from two initial states lying in a well-defined region, thereby
allowing LRT to compute a reachtube with a ball-overestimate in a metric where
the computed enclosure is as tight as possible. To evaluate its performance, we
implemented a prototype of LRT in C++/Matlab, and ran it on a set of
well-established benchmarks. Our results show that LRT compares very favorably
with respect to the CAPD and Flow* tools.Comment: Accepted to CAV 201