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J. Cyranka, A. Islam, S. Smolka, S. Gao, R. Grosu:
"Tight Continuous-Time Reachtubes for Lagrangian Reachability";
Talk: 57th IEEE Conference on Decision and Control, Miami, Florida, USA; 2018-12-17 - 2018-12-19; in: "57th IEEE Conference on Decision and Control", IEEE, 2018 IEEE Conference on Decision and Control (CDC) (2018), ISSN: 2576-2370; 6854 - 6861.

We introduce continuous Lagrangian reachability (CLRT), a new algorithm for the computation of a tight, conservative and continuous-time reachtube for the solution flows of a nonlinear, time-variant dynamical system. CLRT employs finite strain theory to determine the deformation of the solution set from time ti to time ti+1. We have developed simple explicit analytic formulas for the optimal metric for this deformation; this is superior to prior work, which used semi-definite programming. CLRT also uses infinitesimal strain theory to derive an optimal time increment hi between ti and ti+1, nonlinear optimization to minimally bloat (i.e., using a minimal radius) the state set at time ti such that it includes all the states of the solution flow in the interval [ti; ti+1]. We use delta-satisfiability to ensure the correctness of the bloating. Our results on a series of benchmarks show that CLRT performs favorably compared to state-of-the-art tools such as CAPD in terms of the continuous reachtube volumes they compute.

http://dx.doi.org/10.1109/CDC.2018.8619647