2021
DOI: 10.48550/arxiv.2104.11803
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Automata-based Controller Synthesis for Stochastic Systems: A Game Framework via Approximate Probabilistic Relations

Abstract: In this work, we propose an abstraction and refinement methodology for the controller synthesis of discrete-time stochastic systems to enforce complex logical properties expressed by deterministic finite automata (a.k.a. DFA). Our proposed scheme is based on a notion of so-called ( , δ)-approximate probabilistic relations, allowing one to quantify the similarity between stochastic systems modeled by discrete-time stochastic games and their corresponding finite abstractions. Leveraging this type of relations, t… Show more

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Cited by 1 publication
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“…Therefore, we have V ρ ,λ * (ρ ) H (x 0 , q0 ) ≤ η whenapplying the supervisor as in Definition 3.7. According to[27, Theorem 5.10], one has P Ω y ωH |= A ≤ η, which completes the proof.…”
mentioning
confidence: 57%
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“…Therefore, we have V ρ ,λ * (ρ ) H (x 0 , q0 ) ≤ η whenapplying the supervisor as in Definition 3.7. According to[27, Theorem 5.10], one has P Ω y ωH |= A ≤ η, which completes the proof.…”
mentioning
confidence: 57%
“…Accordingly, the formal safety guarantee for the desired safety specification is provided based on an ( , δ)-approximate probabilistic relation between D and D. To establish such a relation, one can employ existing results (e.g. [26,Section 4], [27,Section 4]). Due to lack of space, we are not providing details of those results.…”
Section: Design Of Safe-visor Architecturementioning
confidence: 99%
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