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[SKCCCB16] M. Svorenova, J. Kretinsky, M. Chmelik, K. Chatterjee, I. Cerna, C. Belta. Temporal Logic Control for Stochastic Linear Systems using Abstraction Refinement of Probabilistic Games. Nonlinear Analysis: Hybrid Systems, 23, pages 230-253, Elsevier. February 2017. [bib]
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Notes: Available online at: http://authors.elsevier.com/sd/article/S1751570X16300218
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 specifi cation with probability 1 (almost-surely). We focus on discrete-time, stochastic linear dynamics and speci fications 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-refi nement, 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 speci fication. While the proposed algorithm guarantees progress and soundness in every iteration, it is computationally demanding. We o ffer 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.