Nonconvex scenario optimization for data-driven reachability

Elizabeth Dietrich, Alex Devonport, Murat Arcak
Proceedings of the 6th Annual Learning for Dynamics & Control Conference, PMLR 242:514-527, 2024.

Abstract

Many of the popular reachability analysis methods rely on the existence of system models. When system dynamics are uncertain or unknown, data-driven techniques must be utilized instead. In this paper, we propose an approach to data-driven reachability that provides a probabilistic guarantee of correctness for these systems through nonconvex scenario optimization. We pose the problem of finding reachable sets directly from data as a chance-constrained optimization problem, and present two algorithms for estimating nonconvex reachable sets: (1) through the union of partition cells and (2) through the sum of radial basis functions. Additionally, we investigate numerical examples to demonstrate the capability and applicability of the introduced methods to provide nonconvex reachable set approximations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v242-dietrich24a, title = {Nonconvex scenario optimization for data-driven reachability}, author = {Dietrich, Elizabeth and Devonport, Alex and Arcak, Murat}, booktitle = {Proceedings of the 6th Annual Learning for Dynamics & Control Conference}, pages = {514--527}, year = {2024}, editor = {Abate, Alessandro and Cannon, Mark and Margellos, Kostas and Papachristodoulou, Antonis}, volume = {242}, series = {Proceedings of Machine Learning Research}, month = {15--17 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v242/dietrich24a/dietrich24a.pdf}, url = {https://proceedings.mlr.press/v242/dietrich24a.html}, abstract = {Many of the popular reachability analysis methods rely on the existence of system models. When system dynamics are uncertain or unknown, data-driven techniques must be utilized instead. In this paper, we propose an approach to data-driven reachability that provides a probabilistic guarantee of correctness for these systems through nonconvex scenario optimization. We pose the problem of finding reachable sets directly from data as a chance-constrained optimization problem, and present two algorithms for estimating nonconvex reachable sets: (1) through the union of partition cells and (2) through the sum of radial basis functions. Additionally, we investigate numerical examples to demonstrate the capability and applicability of the introduced methods to provide nonconvex reachable set approximations.} }
Endnote
%0 Conference Paper %T Nonconvex scenario optimization for data-driven reachability %A Elizabeth Dietrich %A Alex Devonport %A Murat Arcak %B Proceedings of the 6th Annual Learning for Dynamics & Control Conference %C Proceedings of Machine Learning Research %D 2024 %E Alessandro Abate %E Mark Cannon %E Kostas Margellos %E Antonis Papachristodoulou %F pmlr-v242-dietrich24a %I PMLR %P 514--527 %U https://proceedings.mlr.press/v242/dietrich24a.html %V 242 %X Many of the popular reachability analysis methods rely on the existence of system models. When system dynamics are uncertain or unknown, data-driven techniques must be utilized instead. In this paper, we propose an approach to data-driven reachability that provides a probabilistic guarantee of correctness for these systems through nonconvex scenario optimization. We pose the problem of finding reachable sets directly from data as a chance-constrained optimization problem, and present two algorithms for estimating nonconvex reachable sets: (1) through the union of partition cells and (2) through the sum of radial basis functions. Additionally, we investigate numerical examples to demonstrate the capability and applicability of the introduced methods to provide nonconvex reachable set approximations.
APA
Dietrich, E., Devonport, A. & Arcak, M.. (2024). Nonconvex scenario optimization for data-driven reachability. Proceedings of the 6th Annual Learning for Dynamics & Control Conference, in Proceedings of Machine Learning Research 242:514-527 Available from https://proceedings.mlr.press/v242/dietrich24a.html.

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