Data-Driven Reachability Analysis Using Matrix Zonotopes

Amr Alanwar, Anne Koch, Frank Allgöwer, Karl Henrik Johansson
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:163-175, 2021.

Abstract

In this paper, we propose a data-driven reachability analysis approach for an unknown control system. Reachability analysis is an essential tool for guaranteeing safety properties. However, most current reachability analysis heavily relies on the existence of a suitable system model, which is often not directly available in practice. We instead propose a reachability analysis approach based on noisy data. More specifically, we first provide an algorithm for over-approximating the reachable set of a linear time-invariant system using matrix zonotopes. Then we introduce an extension for nonlinear systems. We provide theoretical guarantees in both cases. Numerical examples show the potential and applicability of the introduced methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-alanwar21a, title = {Data-Driven Reachability Analysis Using Matrix Zonotopes}, author = {Alanwar, Amr and Koch, Anne and Allg\"ower, Frank and Johansson, Karl Henrik}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {163--175}, year = {2021}, editor = {Jadbabaie, Ali and Lygeros, John and Pappas, George J. and A. Parrilo, Pablo and Recht, Benjamin and Tomlin, Claire J. and Zeilinger, Melanie N.}, volume = {144}, series = {Proceedings of Machine Learning Research}, month = {07 -- 08 June}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v144/alanwar21a/alanwar21a.pdf}, url = {https://proceedings.mlr.press/v144/alanwar21a.html}, abstract = {In this paper, we propose a data-driven reachability analysis approach for an unknown control system. Reachability analysis is an essential tool for guaranteeing safety properties. However, most current reachability analysis heavily relies on the existence of a suitable system model, which is often not directly available in practice. We instead propose a reachability analysis approach based on noisy data. More specifically, we first provide an algorithm for over-approximating the reachable set of a linear time-invariant system using matrix zonotopes. Then we introduce an extension for nonlinear systems. We provide theoretical guarantees in both cases. Numerical examples show the potential and applicability of the introduced methods.} }
Endnote
%0 Conference Paper %T Data-Driven Reachability Analysis Using Matrix Zonotopes %A Amr Alanwar %A Anne Koch %A Frank Allgöwer %A Karl Henrik Johansson %B Proceedings of the 3rd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2021 %E Ali Jadbabaie %E John Lygeros %E George J. Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire J. Tomlin %E Melanie N. Zeilinger %F pmlr-v144-alanwar21a %I PMLR %P 163--175 %U https://proceedings.mlr.press/v144/alanwar21a.html %V 144 %X In this paper, we propose a data-driven reachability analysis approach for an unknown control system. Reachability analysis is an essential tool for guaranteeing safety properties. However, most current reachability analysis heavily relies on the existence of a suitable system model, which is often not directly available in practice. We instead propose a reachability analysis approach based on noisy data. More specifically, we first provide an algorithm for over-approximating the reachable set of a linear time-invariant system using matrix zonotopes. Then we introduce an extension for nonlinear systems. We provide theoretical guarantees in both cases. Numerical examples show the potential and applicability of the introduced methods.
APA
Alanwar, A., Koch, A., Allgöwer, F. & Johansson, K.H.. (2021). Data-Driven Reachability Analysis Using Matrix Zonotopes. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:163-175 Available from https://proceedings.mlr.press/v144/alanwar21a.html.

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