Temporal Logic Control for Stochastic Linear Systems using Abstraction Refinement of Probabilistic Games
| Autor: | Krishnendu Chatterjee, Mária Svoreňová, Calin Belta, Martin Chmelík, Ivana Černá, Jan Křetínský |
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| Rok vydání: | 2014 |
| Předmět: |
Soundness
0209 industrial biotechnology Mathematical optimization Computation tree logic Interval temporal logic Linear system Probabilistic logic 0102 computer and information sciences 02 engineering and technology Systems and Control (eess.SY) 01 natural sciences Computer Science Applications 020901 industrial engineering & automation Linear temporal logic Fragment (logic) Control and Systems Engineering 010201 computation theory & mathematics FOS: Electrical engineering electronic engineering information engineering Computer Science - Systems and Control Temporal logic Finite set Algorithm Analysis Mathematics |
| Zdroj: | HSCC |
| DOI: | 10.48550/arxiv.1410.5387 |
| Popis: | 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. Comment: Technical report accompanying HSCC'15 paper |
| Databáze: | OpenAIRE |
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