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J. Cyranka, A. Islam, G. Byrne, P. Jones, S. Smolka, R. Grosu:
"Lagrangian Reachabililty";
Talk: CAV 2017: the 29th International Conference on Computer-Aided Verification, Heidelberg, Germany; 2017-07-24 - 2017-07-28; in: "Proc. of CAV 2017: the 29th International Conference on Computer-Aided Verification", Springer, 10426 (2017), ISBN: 978-3-319-63387-9; 379 - 400.

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.

http://dx.doi.org/10.1007/978-3-319-63387-9_19