Temporal Logic Control for Nonlinear Stochastic Systems Under Unknown Disturbances

Ibon Gracia, Luca Laurenti, Manuel Mazo Jr, Alessandro Abate, Morteza Lahijanian
Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, PMLR 283:1537-1549, 2025.

Abstract

In this paper, we present a novel framework to synthesize robust strategies for discrete-time non-linear systems with and random disturbances that are unknown and non-additive, against temporal logic specifications. The proposed framework is data-driven and abstraction-based: leveraging observations of the system, our approach learns a high-confidence abstraction of the system in the form of an uncertain Markov decision process (UMDP). The uncertainty in the resulting UMDP is used to formally account for both the error in abstracting the system and for the uncertainty coming from the data. Critically, we show that for any given state-action pair in the resulting UMDP, the uncertainty in the transition probabilities can be represented as a convex polytope obtained by a 2-layer state discretization and concentration inequalities. This allows us to obtain tighter uncertainty estimates compared to existing approaches, and guarantees efficiency, as we tailor a synthesis algorithm exploiting the structure of this UMDP. We empirically validate our approach on several case studies, showing substantially improved empirical performance compared to the state-of-the-art.

Cite this Paper

BibTeX
@InProceedings{pmlr-v283-gracia25a, title = {Temporal Logic Control for Nonlinear Stochastic Systems Under Unknown Disturbances}, author = {Gracia, Ibon and Laurenti, Luca and Jr, Manuel Mazo and Abate, Alessandro and Lahijanian, Morteza}, booktitle = {Proceedings of the 7th Annual Learning for Dynamics \& Control Conference}, pages = {1537--1549}, year = {2025}, editor = {Ozay, Necmiye and Balzano, Laura and Panagou, Dimitra and Abate, Alessandro}, volume = {283}, series = {Proceedings of Machine Learning Research}, month = {04--06 Jun}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v283/main/assets/gracia25a/gracia25a.pdf}, url = {https://proceedings.mlr.press/v283/gracia25a.html}, abstract = {In this paper, we present a novel framework to synthesize robust strategies for discrete-time non-linear systems with and random disturbances that are unknown and non-additive, against temporal logic specifications. The proposed framework is data-driven and abstraction-based: leveraging observations of the system, our approach learns a high-confidence abstraction of the system in the form of an uncertain Markov decision process (UMDP). The uncertainty in the resulting UMDP is used to formally account for both the error in abstracting the system and for the uncertainty coming from the data. Critically, we show that for any given state-action pair in the resulting UMDP, the uncertainty in the transition probabilities can be represented as a convex polytope obtained by a 2-layer state discretization and concentration inequalities. This allows us to obtain tighter uncertainty estimates compared to existing approaches, and guarantees efficiency, as we tailor a synthesis algorithm exploiting the structure of this UMDP. We empirically validate our approach on several case studies, showing substantially improved empirical performance compared to the state-of-the-art.} }
Endnote
%0 Conference Paper %T Temporal Logic Control for Nonlinear Stochastic Systems Under Unknown Disturbances %A Ibon Gracia %A Luca Laurenti %A Manuel Mazo Jr %A Alessandro Abate %A Morteza Lahijanian %B Proceedings of the 7th Annual Learning for Dynamics \& Control Conference %C Proceedings of Machine Learning Research %D 2025 %E Necmiye Ozay %E Laura Balzano %E Dimitra Panagou %E Alessandro Abate %F pmlr-v283-gracia25a %I PMLR %P 1537--1549 %U https://proceedings.mlr.press/v283/gracia25a.html %V 283 %X In this paper, we present a novel framework to synthesize robust strategies for discrete-time non-linear systems with and random disturbances that are unknown and non-additive, against temporal logic specifications. The proposed framework is data-driven and abstraction-based: leveraging observations of the system, our approach learns a high-confidence abstraction of the system in the form of an uncertain Markov decision process (UMDP). The uncertainty in the resulting UMDP is used to formally account for both the error in abstracting the system and for the uncertainty coming from the data. Critically, we show that for any given state-action pair in the resulting UMDP, the uncertainty in the transition probabilities can be represented as a convex polytope obtained by a 2-layer state discretization and concentration inequalities. This allows us to obtain tighter uncertainty estimates compared to existing approaches, and guarantees efficiency, as we tailor a synthesis algorithm exploiting the structure of this UMDP. We empirically validate our approach on several case studies, showing substantially improved empirical performance compared to the state-of-the-art.
APA
Gracia, I., Laurenti, L., Jr, M.M., Abate, A. & Lahijanian, M.. (2025). Temporal Logic Control for Nonlinear Stochastic Systems Under Unknown Disturbances. Proceedings of the 7th Annual Learning for Dynamics \& Control Conference, in Proceedings of Machine Learning Research 283:1537-1549 Available from https://proceedings.mlr.press/v283/gracia25a.html.

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