Lagrangian reachtubes: The next generation

Gruenbacher S, Cyranka J, Lechner M, Islam MA, Smolka SA, Grosu R. 2020. Lagrangian reachtubes: The next generation. Proceedings of the 59th IEEE Conference on Decision and Control. CDC: Conference on Decision and Control vol. 2020, 1556–1563.


Conference Paper | Published | English

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Author
Gruenbacher, Sophie; Cyranka, Jacek; Lechner, MathiasIST Austria; Islam, Md Ariful; Smolka, Scott A.; Grosu, Radu
Department
Abstract
We introduce LRT-NG, a set of techniques and an associated toolset that computes a reachtube (an over-approximation of the set of reachable states over a given time horizon) of a nonlinear dynamical system. LRT-NG significantly advances the state-of-the-art Langrangian Reachability and its associated tool LRT. From a theoretical perspective, LRT-NG is superior to LRT in three ways. First, it uses for the first time an analytically computed metric for the propagated ball which is proven to minimize the ball’s volume. We emphasize that the metric computation is the centerpiece of all bloating-based techniques. Secondly, it computes the next reachset as the intersection of two balls: one based on the Cartesian metric and the other on the new metric. While the two metrics were previously considered opposing approaches, their joint use considerably tightens the reachtubes. Thirdly, it avoids the "wrapping effect" associated with the validated integration of the center of the reachset, by optimally absorbing the interval approximation in the radius of the next ball. From a tool-development perspective, LRT-NG is superior to LRT in two ways. First, it is a standalone tool that no longer relies on CAPD. This required the implementation of the Lohner method and a Runge-Kutta time-propagation method. Secondly, it has an improved interface, allowing the input model and initial conditions to be provided as external input files. Our experiments on a comprehensive set of benchmarks, including two Neural ODEs, demonstrates LRT-NG’s superior performance compared to LRT, CAPD, and Flow*.
Publishing Year
Date Published
2020-12-14
Proceedings Title
Proceedings of the 59th IEEE Conference on Decision and Control
Acknowledgement
The authors would like to thank Ramin Hasani and Guillaume Berger for intellectual discussions about the research which lead to the generation of new ideas. ML was supported in part by the Austrian Science Fund (FWF) under grant Z211-N23 (Wittgenstein Award). Smolka’s research was supported by NSF grants CPS-1446832 and CCF-1918225. Gruenbacher is funded by FWF project W1255-N23. JC was partially supported by NAWA Polish Returns grant PPN/PPO/2018/1/00029.
Volume
2020
Page
1556-1563
Conference
CDC: Conference on Decision and Control
Conference Location
Jeju Islang, Korea (South)
Conference Date
2020-12-14 – 2020-12-18
ISSN
IST-REx-ID

Cite this

Gruenbacher S, Cyranka J, Lechner M, Islam MA, Smolka SA, Grosu R. Lagrangian reachtubes: The next generation. In: Proceedings of the 59th IEEE Conference on Decision and Control. Vol 2020. IEEE; 2020:1556-1563. doi:10.1109/CDC42340.2020.9304042
Gruenbacher, S., Cyranka, J., Lechner, M., Islam, M. A., Smolka, S. A., & Grosu, R. (2020). Lagrangian reachtubes: The next generation. In Proceedings of the 59th IEEE Conference on Decision and Control (Vol. 2020, pp. 1556–1563). Jeju Islang, Korea (South): IEEE. https://doi.org/10.1109/CDC42340.2020.9304042
Gruenbacher, Sophie, Jacek Cyranka, Mathias Lechner, Md Ariful Islam, Scott A. Smolka, and Radu Grosu. “Lagrangian Reachtubes: The next Generation.” In Proceedings of the 59th IEEE Conference on Decision and Control, 2020:1556–63. IEEE, 2020. https://doi.org/10.1109/CDC42340.2020.9304042.
S. Gruenbacher, J. Cyranka, M. Lechner, M. A. Islam, S. A. Smolka, and R. Grosu, “Lagrangian reachtubes: The next generation,” in Proceedings of the 59th IEEE Conference on Decision and Control, Jeju Islang, Korea (South), 2020, vol. 2020, pp. 1556–1563.
Gruenbacher S, Cyranka J, Lechner M, Islam MA, Smolka SA, Grosu R. 2020. Lagrangian reachtubes: The next generation. Proceedings of the 59th IEEE Conference on Decision and Control. CDC: Conference on Decision and Control vol. 2020, 1556–1563.
Gruenbacher, Sophie, et al. “Lagrangian Reachtubes: The next Generation.” Proceedings of the 59th IEEE Conference on Decision and Control, vol. 2020, IEEE, 2020, pp. 1556–63, doi:10.1109/CDC42340.2020.9304042.
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