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

Author(s): Svoreňová, Mária; Křetínský, Jan; Chmelík, Martin; Chatterjee, Krishnendu; Cěrná, Ivana; Belta, Cǎlin A
Article 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 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.
Keywords: abstraction refinement; Temporal logic; games; Control; Linear stochastic system
Journal Title: Nonlinear Analysis: Hybrid Systems
Volume: 23
ISSN: 1751-570X
Publisher: Elsevier  
Date Published: 2017-02-01
Start Page: 230
End Page: 253
DOI: 10.1016/j.nahs.2016.04.006
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, European Research Council (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, Czech Science Foundation Grant No.15-08772S, and National Science Foundation (NSF) grants CMMI-1400167 and CNS-1035588.
Open access: yes (repository)
IST Austria Authors
  1. Martin Chmelik
    23 Chmelik
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