In this article, we formulate and solve the probabilistic security problem , defined as the probability that a multirobot system (MRS) with probabilistic interaction graphs has realizations that are secure from adversarial attacks. The concept of security is based on the control-theoretic notion of left invertibility, which depends on the existence of disjoint paths and subcuts in the topology describing robot interactions. To model uncertainties in interactions, we associate the existence of edges with a probability distribution. We, then, derive a probability expression based on disjoint paths and subcuts that defines the probability of security of the MRS. The exact probability is computed using the concept of binary decision diagrams (BDDs), a graphical method used to represent Boolean functions. To improve computational complexity, we formulate a combinatorial optimization problem that aims to bound the probability of security. Since MRSs are inherently dynamic, we leverage the graphical properties of BDDs to adapt to any topological changes. To demonstrate the validity of our results, we first track the probability of security of an MRS performing an environmental monitoring task, with Monte Carlo simulations as a baseline for comparison. Finally, we study the behavior of a probabilistic MRS when under attack in three different scenarios.

中文翻译：

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多机器人系统的概率安全性

在本文中，我们制定并解决了 概率安全问题 ，定义为具有概率交互图的多机器人系统（MRS）具有可抵抗对抗攻击的实现的概率。安全性的概念基于左可逆性的控制理论概念，该概念取决于拓扑中描述机器人交互作用的不相交路径和子切口的存在。为了对相互作用中的不确定性进行建模，我们将边的存在与概率分布关联起来。然后，我们基于不相交的路径和子路口得出概率表达式，该表达式定义了MRS的安全性概率。准确概率是使用二进制决策图（BDD）（一种用于表示布尔函数的图形方法）的概念来计算的。为了提高计算复杂度，我们制定了一个组合优化问题，旨在界安全的可能性。由于MRS本质上是动态的，所以我们利用BDD的图形属性来适应任何拓扑变化。为了证明我们的结果的有效性，我们首先以蒙特卡洛模拟为比较基准，跟踪执行环境监测任务的MRS的安全性概率。最后，我们研究了概率MRS在三种不同情况下受到攻击时的行为。