This article is concerned with a compositional approach for the construction of control barrier certificates for large-scale interconnected stochastic systems while synthesizing hybrid controllers against high-level logic properties. Our proposed methodology involves decomposition of interconnected systems into smaller subsystems and leverages the notion of control sub-barrier certificates of subsystems, enabling one to construct control barrier certificates of interconnected systems by employing some max\max-type small-gain conditions. The main goal is to synthesize hybrid controllers enforcing complex logic properties, including the ones represented by the accepting language of deterministic finite automata, while providing probabilistic guarantees on the satisfaction of given specifications in bounded-time horizons. To do so, we propose a systematic approach to first decompose high-level specifications into simple reachability tasks by utilizing automata corresponding to the complement of specifications. We then construct control sub-barrier certificates and synthesize local controllers for those simpler tasks and combine them to obtain a hybrid controller that ensures satisfaction of the complex specification with some lower bound on the probability of satisfaction. We finally apply our proposed techniques to a fully-interconnected Kuramoto network composed of 100 nonlinear oscillators.

中文翻译：

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从小增益理论到大规模随机系统障碍证书的组合构造


本文关注的是一种为大规模互连随机系统构建控制屏障证书的组合方法，同时根据高级逻辑属性合成混合控制器。我们提出的方法涉及将互连系统分解为更小的子系统，并利用子系统控制子屏障证书的概念，使人们能够通过采用一些最大\最大型小增益条件来构造互连系统的控制屏障证书。主要目标是综合执行复杂逻辑属性的混合控制器，包括由确定性有限自动机的接受语言表示的逻辑属性，同时提供在有限时间范围内满足给定规范的概率保证。为此，我们提出了一种系统方法，首先利用与规范补集相对应的自动机将高级规范分解为简单的可达性任务。然后，我们构建控制子屏障证书并为那些更简单的任务合成本地控制器，并将它们组合起来以获得混合控制器，该混合控制器确保满足复杂的规范，并且满足概率的下限。我们最终将我们提出的技术应用于由 100 个非线性振荡器组成的完全互连的 Kuramoto 网络。