Temporal Logic Control for Stochastic Linear Systems using
Abstraction Refinement of Probabilistic Games

D 2015

Temporal Logic Control for Stochastic Linear Systems using Abstraction Refinement of Probabilistic Games

SVOREŇOVÁ, Mária, Jan KŘETÍNSKÝ, Martin CHMELÍK, Krishnendu CHATTERJEE, Ivana ČERNÁ et. al.

Basic information

Original name

Temporal Logic Control for Stochastic Linear Systems using Abstraction Refinement of Probabilistic Games

Authors

SVOREŇOVÁ, Mária (703 Slovakia, belonging to the institution), Jan KŘETÍNSKÝ (203 Czech Republic), Martin CHMELÍK (203 Czech Republic), Krishnendu CHATTERJEE (40 Austria), Ivana ČERNÁ (203 Czech Republic, belonging to the institution) and Calin BELTA (840 United States of America)

Edition

Seattle, Washington, USA, Proceedings of ACM international conference on Hybrid Systems: Computation and Control, p. 259-268, 10 pp. 2015

Publisher

Association for Computing Machinery (ACM)

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

electronic version available online

RIV identification code

RIV/00216224:14330/15:00080610

Organization unit

Faculty of Informatics

ISBN

978-1-4503-3433-4

DOI

http://dx.doi.org/10.1145/2728606.2728608

Keywords in English

control; linear temporal logic (LTL); linear stochastic system; games

Abstract

V originále

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 satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. We demonstrate our approach on an illustrative case study.

Links

GA15-17564S, research and development project

Name: Teorie her jako prostředek pro formální analýzu a verifikaci počítačových systémů

Investor: Czech Science Foundation

LH11065, research and development project

Name: Řízení a ověřování vlastností komplexních hybridních systémů (Acronym: Řízení a ověřování vlastností komplexních hybridní)

Investor: Ministry of Education, Youth and Sports of the CR

MUNI/A/1159/2014, interní kód MU

Name: Rozsáhlé výpočetní systémy: modely, aplikace a verifikace IV.

Investor: Masaryk University, Category A

MUNI/A/1206/2014, interní kód MU

Name: Zapojení studentů Fakulty informatiky do mezinárodní vědecké komunity (Acronym: SKOMU)

Investor: Masaryk University, Category A

Citovat

SVOREŇOVÁ, Mária, Jan KŘETÍNSKÝ, Martin CHMELÍK, Krishnendu CHATTERJEE, Ivana ČERNÁ and Calin BELTA. Temporal Logic Control for Stochastic Linear Systems using Abstraction Refinement of Probabilistic Games. Online. In Proceedings of ACM international conference on Hybrid Systems: Computation and Control. Seattle, Washington, USA: Association for Computing Machinery (ACM), 2015, p. 259-268. ISBN 978-1-4503-3433-4. Available from: https://dx.doi.org/10.1145/2728606.2728608.

@inproceedings{1206052,
   author = {Svoreňová, Mária and Křetínský, Jan and Chmelík, Martin and Chatterjee, Krishnendu and Černá, Ivana and Belta, Calin},
   address = {Seattle, Washington, USA},
   booktitle = {Proceedings of ACM international conference on Hybrid Systems: Computation and Control},
   doi = {http://dx.doi.org/10.1145/2728606.2728608},
   keywords = {control; linear temporal logic (LTL); linear stochastic system; games},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Seattle, Washington, USA},
   isbn = {978-1-4503-3433-4},
   pages = {259-268},
   publisher = {Association for Computing Machinery (ACM)},
   title = {Temporal Logic Control for Stochastic Linear Systems using Abstraction Refinement of Probabilistic Games},
   year = {2015}
}

TY  - JOUR
ID  - 1206052
AU  - Svoreňová, Mária - Křetínský, Jan - Chmelík, Martin - Chatterjee, Krishnendu - Černá, Ivana - Belta, Calin
PY  - 2015
TI  - Temporal Logic Control for Stochastic Linear Systems using Abstraction Refinement of Probabilistic Games
PB  - Association for Computing Machinery (ACM)
CY  - Seattle, Washington, USA
SN  - 9781450334334
KW  - control
KW  - linear temporal logic (LTL)
KW  - linear stochastic system
KW  - games
N2  - 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 satisfying initial states. Moreover, for any (partial) solution our algorithm synthesizes witness control strategies to ensure almost-sure satisfaction of the temporal logic specification. We demonstrate our approach on an illustrative case study.
ER  -

SVOREŇOVÁ, Mária, Jan KŘETÍNSKÝ, Martin CHMELÍK, Krishnendu CHATTERJEE, Ivana ČERNÁ and Calin BELTA. Temporal Logic Control for Stochastic Linear Systems using Abstraction Refinement of Probabilistic Games. Online. In \textit{Proceedings of ACM international conference on Hybrid Systems: Computation and Control}. Seattle, Washington, USA: Association for Computing Machinery (ACM), 2015, p.~259-268. ISBN~978-1-4503-3433-4. Available from: https://dx.doi.org/10.1145/2728606.2728608.

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