Earlier Version

Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games

M. Svoreňová, J. Kretinsky, M. Chmelik, K. Chatterjee, I. Cěrná, C. Belta, in:, Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control, ACM, 2015, pp. 259–268.


Conference Paper | Published | English
Author
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Abstract
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.
Publishing Year
Date Published
2015-04-14
Proceedings Title
Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control
Page
259 - 268
Conference
HSCC: Hybrid Systems - Computation and Control
Conference Location
Seattle, WA, United States
Conference Date
2015-04-14 – 2015-04-16
IST-REx-ID

Cite this

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. In: Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control. ACM; 2015:259-268. doi:10.1145/2728606.2728608
Svoreňová, M., Kretinsky, J., Chmelik, M., Chatterjee, K., Cěrná, I., & Belta, C. (2015). Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games. In Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control (pp. 259–268). Seattle, WA, United States: ACM. https://doi.org/10.1145/2728606.2728608
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.” In Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control, 259–68. ACM, 2015. https://doi.org/10.1145/2728606.2728608.
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,” in Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control, Seattle, WA, United States, 2015, pp. 259–268.
Svoreňová M, Kretinsky J, Chmelik M, Chatterjee K, Cěrná I, Belta C. 2015. Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games. Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control. HSCC: Hybrid Systems - Computation and Control 259–268.
Svoreňová, Mária, et al. “Temporal Logic Control for Stochastic Linear Systems Using Abstraction Refinement of Probabilistic Games.” Proceedings of the 18th International Conference on Hybrid Systems: Computation and Control, ACM, 2015, pp. 259–68, doi:10.1145/2728606.2728608.

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