在本文中，我们研究了随机控制屏障功能（SCBF），以在存在不确定性的情况下实现概率安全实时控制器的设计，并基于嘈杂的测量。我们的目标是设计控制器，该控制器将系统故障的概率与给定的所需值相结合。为此，我们首先使用扩展的卡尔曼滤波器从嘈杂测量估计系统状态，并计算过滤错误上的置信区间。然后，我们根据估计的状态归因于过滤错误并在控制输入上导出足够的条件，以绑定系统的实际状态在有限时间间隔内输入不安全区域的概率。我们表明，这些充足的条件是对控制输入的线性约束，因此，除了可达性等其他性能之外，它们可以用于实现安全性以实现安全性，以及稳定性。我们的方法是使用浓密交通的高速公路上的车道改变情景进行了评估。

In this paper, we reduce the complexity of approximating the correlation clustering problem from $O(m\times\left( 2+ \alpha (G) \right)+n)$ to $O(m+n)$ for any given value of $\varepsilon$ for a complete signed graph with $n$ vertices and $m$ positive edges where $\alpha(G)$ is the arboricity of the graph. Our approach gives the same output as the original algorithm and makes it possible to implement the algorithm in a full dynamic setting where edge sign flipping and vertex addition/removal are allowed. Constructing this index costs $O(m)$ memory and $O(m\times\alpha(G))$ time. We also studied the structural properties of the non-agreement measure used in the approximation algorithm. The theoretical results are accompanied by a full set of experiments concerning seven real-world graphs. These results shows superiority of our index-based algorithm to the non-index one by a decrease of %34 in time on average.