---
_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'
...