This paper focuses on synthesizing control policies for discrete-time stochastic control systems together with a lower bound on the probability that the systems satisfy the complex temporal properties. The desired properties of the system are expressed as linear temporal logic (LTL) specifications over finite traces. In particular, our approach decomposes the given specification into simpler reachability tasks based on its automata representation. We then propose the use of so-called \emph{control barrier certificate} to solve those simpler reachability tasks along with computing the corresponding controllers and probability bounds. Finally, we combine those controllers to obtain a hybrid control policy solving the considered problem. Under some assumptions, we also provide two systematic approaches for uncountable and finite input sets to search for control barrier certificates. We demonstrate the effectiveness of the proposed approach on a room temperature control and lane-keeping of a vehicle modeled as a four-dimensional single-track kinematic model. We compare our results with the discretization-based methods in the literature.

中文翻译：

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通过控制障碍证书正式合成随机系统

本文重点介绍离散时间随机控制系统的控制策略以及系统满足复杂时间特性的概率的下界。系统的所需属性表示为有限轨迹上的线性时序逻辑 (LTL) 规范。特别是，我们的方法根据其自动机表示将给定的规范分解为更简单的可达性任务。然后，我们建议使用所谓的 \emph {控制屏障证书} 来解决那些更简单的可达性任务以及计算相应的控制器和概率界限。最后，我们结合这些控制器以获得解决所考虑问题的混合控制策略。在一些假设下，我们还为不可数和有限输入集提供了两种系统的方法来搜索控制屏障证书。我们证明了所提出的方法对建模为四维单轨运动学模型的车辆的室温控制和车道保持的有效性。我们将我们的结果与文献中基于离散化的方法进行比较。