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


Author(s): Svoreňová, Mária; Křetínský, Jan; Chmelík, Martin; Chatterjee, Krishnendu; Cěrná, Ivana; Belta, Cǎlin A
Title: Temporal logic control for stochastic linear systems using abstraction refinement of probabilistic games
Affiliation IST Austria
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.
Keywords: probabilistic games; abstraction refinement; Algorithms; Temporal logic; Hybrid systems; Linear temporal logic; Abstracting; Control strategies; Specifications; Dynamical systems; Iterative methods; Linear systems; Stochastic systems; Stochastic linear dynamics; Stochastic linear systems; Temporal logic specifications; Theoretical guarantees
Conference Title: HSCC: Hybrid Systems - Computation and Control
Publisher: Springer  
Date Published: 2015-04-14
Start Page: 259
End Page: 268
URL:
DOI: 10.1145/2728606.2728608
Notes: This work was partially supported by Czech Science Foundation grant 15-17564S, People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement 291734, ERC grant 267989 (QUAREM) and Start grant (279307: Graph Games), Austrian Science Fund (FWF) grants S11402-N23 (RiSE), P23499-N23 and S11407-N23 (RiSE), Czech Ministry of Education Youth and Sports grant LH11065, and NSF grants CMMI-1400167 and CNS-1035588.
Open access: yes (repository)
IST Austria Authors
  1. Martin Chmelik
    23 Chmelik
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