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

Mária Svoreňová, Jan Křetínský, Martin Chmelík, Krishnendu Chatterjee, Ivana Černá, Calin Belta
2015 Proceedings of the 18th International Conference on Hybrid Systems Computation and Control - HSCC '15  
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
more » ... inement, 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.
doi:10.1145/2728606.2728608 dblp:conf/hybrid/SvorenovaKCCCB15 fatcat:kwmvhhavhzcq5lktx4az3mvbjq