Lagrangian Reachabililty

TitleLagrangian Reachabililty
Publication TypeConference Paper
Year of Publication2017
AuthorsCyranka, Jacek, Islam Md. Ariful, Byrne Greg, Jones Paul L., Smolka Scott A., and Grosu Radu
Conference NameComputer Aided Verification - 29th International Conference, {CAV} 2017 Proceedings, Part {I}

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.