--- _id: '1407' abstract: - lang: eng text: We consider the problem of computing the set of initial states of a dynamical system such that there exists a control strategy to ensure that the trajectories satisfy a temporal logic specification with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and specifications given as formulas of the Generalized Reactivity(1) fragment of Linear Temporal Logic over linear predicates in the states of the system. We propose a solution based on iterative abstraction-refinement, and turn-based 2-player probabilistic games. While the theoretical guarantee of our algorithm after any finite number of iterations is only a partial solution, we show that if our algorithm terminates, then the result is the set of all satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. While the proposed algorithm guarantees progress and soundness in every iteration, it is computationally demanding. We offer an alternative, more efficient solution for the reachability properties that decomposes the problem into a series of smaller problems of the same type. All algorithms are demonstrated on an illustrative case study. article_processing_charge: No author: - first_name: Mária full_name: Svoreňová, Mária last_name: Svoreňová - first_name: Jan full_name: Kretinsky, Jan id: 44CEF464-F248-11E8-B48F-1D18A9856A87 last_name: Kretinsky orcid: 0000-0002-8122-2881 - first_name: Martin full_name: Chmelik, Martin id: 3624234E-F248-11E8-B48F-1D18A9856A87 last_name: Chmelik - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Ivana full_name: Cěrná, Ivana last_name: Cěrná - first_name: Cǎlin full_name: Belta, Cǎlin last_name: Belta citation: ama: 'Svoreňová M, Kretinsky J, Chmelik M, Chatterjee K, Cěrná I, Belta C. Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games. Nonlinear Analysis: Hybrid Systems. 2017;23(2):230-253. doi:10.1016/j.nahs.2016.04.006' apa: 'Svoreňová, M., Kretinsky, J., Chmelik, M., Chatterjee, K., Cěrná, I., & Belta, C. (2017). Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games. Nonlinear Analysis: Hybrid Systems. Elsevier. https://doi.org/10.1016/j.nahs.2016.04.006' chicago: 'Svoreňová, Mária, Jan Kretinsky, Martin Chmelik, Krishnendu Chatterjee, Ivana Cěrná, and Cǎlin Belta. “Temporal Logic Control for Stochastic Linear Systems Using Abstraction Refinement of Probabilistic Games.” Nonlinear Analysis: Hybrid Systems. Elsevier, 2017. https://doi.org/10.1016/j.nahs.2016.04.006.' ieee: 'M. Svoreňová, J. Kretinsky, M. Chmelik, K. Chatterjee, I. Cěrná, and C. Belta, “Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games,” Nonlinear Analysis: Hybrid Systems, vol. 23, no. 2. Elsevier, pp. 230–253, 2017.' ista: 'Svoreňová M, Kretinsky J, Chmelik M, Chatterjee K, Cěrná I, Belta C. 2017. Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games. Nonlinear Analysis: Hybrid Systems. 23(2), 230–253.' mla: 'Svoreňová, Mária, et al. “Temporal Logic Control for Stochastic Linear Systems Using Abstraction Refinement of Probabilistic Games.” Nonlinear Analysis: Hybrid Systems, vol. 23, no. 2, Elsevier, 2017, pp. 230–53, doi:10.1016/j.nahs.2016.04.006.' short: 'M. Svoreňová, J. Kretinsky, M. Chmelik, K. Chatterjee, I. Cěrná, C. Belta, Nonlinear Analysis: Hybrid Systems 23 (2017) 230–253.' date_created: 2018-12-11T11:51:50Z date_published: 2017-02-01T00:00:00Z date_updated: 2023-09-20T09:43:09Z day: '01' department: - _id: ToHe - _id: KrCh doi: 10.1016/j.nahs.2016.04.006 ec_funded: 1 external_id: arxiv: - '1410.5387' isi: - '000390637000014' intvolume: ' 23' isi: 1 issue: '2' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1410.5387 month: '02' oa: 1 oa_version: Preprint page: 230 - 253 project: - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme - _id: 25EE3708-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '267989' name: Quantitative Reactive Modeling - _id: 2581B60A-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '279307' name: 'Quantitative Graph Games: Theory and Applications' - _id: 25832EC2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S 11407_N23 name: Rigorous Systems Engineering - _id: 2584A770-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: P 23499-N23 name: Modern Graph Algorithmic Techniques in Formal Verification - _id: 25863FF4-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S11407 name: Game Theory publication: 'Nonlinear Analysis: Hybrid Systems' publication_status: published publisher: Elsevier publist_id: '5800' quality_controlled: '1' related_material: record: - id: '1689' relation: earlier_version status: public scopus_import: '1' status: public title: Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 23 year: '2017' ...