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• W4384080509 abstract "The essential step of abstraction-based control synthesis for nonlinear systems to satisfy a given specification is to obtain a finite-state abstraction of the original systems. The complexity of the abstraction is usually the dominating factor that determines the efficiency of the algorithm. For the control synthesis of discrete-time nonlinear stochastic systems modelled by nonlinear stochastic difference equations, recent literature has demonstrated the soundness of abstractions in preserving robust probabilistic satisfaction of <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$omega$</tex-math></inline-formula> -regular linear-time properties. However, unnecessary transitions exist within the abstractions, which are difficult to quantify, and the completeness of abstraction-based control synthesis in the stochastic setting remains an open theoretical question. In this paper, we address this fundamental question from the topological view of metrizable space of probability measures, and propose constructive finite-state abstractions for control synthesis of probabilistic linear temporal specifications. Such abstractions are both sound and approximately complete. That is, given a concrete discrete-time stochastic system and an arbitrarily small <inline-formula xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink><tex-math notation=LaTeX>$mathcal {L}^{1}$</tex-math></inline-formula> -perturbation of this system, there exists a family of finite-state controlled Markov chains that both abstracts the concrete system and is abstracted by the slightly perturbed system. In other words, given an arbitrarily small prescribed precision, an abstraction always exists to decide whether a control strategy exists for the concrete system to satisfy the probabilistic specification." @default.
• W4384080509 created "2023-07-13" @default.
• W4384080509 creator A5024005879 @default.
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• W4384080509 date "2023-01-01" @default.
• W4384080509 modified "2023-09-26" @default.
• W4384080509 title "Robustly Complete Finite-State Abstractions for Control Synthesis of Stochastic Systems" @default.
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• W4384080509 doi "https://doi.org/10.1109/ojcsys.2023.3294829" @default.
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