10.1145/2728606.2728608
Svoreňová, Mária
Mária
Svoreňová
Kretinsky, Jan
Jan
Kretinsky0000-0002-8122-2881
Chmelik, Martin
Martin
Chmelik
Chatterjee, Krishnendu
Krishnendu
Chatterjee0000-0002-4561-241X
Cěrná, Ivana
Ivana
Cěrná
Belta, Cǎlin
Cǎlin
Belta
Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games
ACM
2015
2018-12-11T11:53:29Z
2020-01-17T09:24:58Z
conference
https://research-explorer.app.ist.ac.at/record/1689
https://research-explorer.app.ist.ac.at/record/1689.json
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.