Data-Driven Abstraction of Monotone Systems

Anas Makdesi, Antoine Girard, Laurent Fribourg
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:803-814, 2021.

Abstract

In this paper, we introduce an approach for data-driven abstraction of monotone dynamical systems. First, we present an approach to find the optimal approximation of the dynamics of an unknown system by a set-valued map based on a set of transitions generated by the system. Then we show that the dynamical system induced by the introduced map is equivalent (in the sense of alternating bisimulation) to a finite state transition system which can be used to synthesize controllers using the well-established symbolic control techniques. We show the effectiveness of the approach on a safety controller synthesis problem.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-makdesi21a, title = {Data-Driven Abstraction of Monotone Systems}, author = {Makdesi, Anas and Girard, Antoine and Fribourg, Laurent}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {803--814}, 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/makdesi21a/makdesi21a.pdf}, url = {https://proceedings.mlr.press/v144/makdesi21a.html}, abstract = {In this paper, we introduce an approach for data-driven abstraction of monotone dynamical systems. First, we present an approach to find the optimal approximation of the dynamics of an unknown system by a set-valued map based on a set of transitions generated by the system. Then we show that the dynamical system induced by the introduced map is equivalent (in the sense of alternating bisimulation) to a finite state transition system which can be used to synthesize controllers using the well-established symbolic control techniques. We show the effectiveness of the approach on a safety controller synthesis problem.} }
Endnote
%0 Conference Paper %T Data-Driven Abstraction of Monotone Systems %A Anas Makdesi %A Antoine Girard %A Laurent Fribourg %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-makdesi21a %I PMLR %P 803--814 %U https://proceedings.mlr.press/v144/makdesi21a.html %V 144 %X In this paper, we introduce an approach for data-driven abstraction of monotone dynamical systems. First, we present an approach to find the optimal approximation of the dynamics of an unknown system by a set-valued map based on a set of transitions generated by the system. Then we show that the dynamical system induced by the introduced map is equivalent (in the sense of alternating bisimulation) to a finite state transition system which can be used to synthesize controllers using the well-established symbolic control techniques. We show the effectiveness of the approach on a safety controller synthesis problem.
APA
Makdesi, A., Girard, A. & Fribourg, L.. (2021). Data-Driven Abstraction of Monotone Systems. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:803-814 Available from https://proceedings.mlr.press/v144/makdesi21a.html.

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