As modern systems become ever more connected with complex dynamic coupling relationships, the development of safe control methods for such networked systems becomes paramount. In this paper, we define a general networked model with coupled dynamics and local control and discuss the relationship of node-level safety definitions for individual agents with local neighborhood dynamics. We define a node-level barrier function (NBF), node-level control barrier function (NCBF), and collaborative node-level barrier function (cNCBF) and provide conditions under which sets defined by these functions will be forward invariant. We use collaborative node-level barrier functions to construct a novel distributed algorithm for the safe control of collaborating network agents and provide conditions under which the algorithm is guaranteed to converge to a viable set of safe control actions for all agents or a terminally infeasible state for at least one agent. We introduce the notion of non-compliance of network neighbors as a metric of robustness for collaborative safety for a given network state and chosen barrier function hyper-parameters. We illustrate these results on a networked susceptible-infected-susceptible (SIS) model.

翻译：随着现代系统日益互联并具有复杂的动态耦合关系，为这类网络化系统开发安全控制方法变得至关重要。本文定义了一个包含耦合动力学和局部控制的一般性网络模型，并探讨了具有局部邻域动态的单个智能体节点级安全定义之间的关系。我们提出了节点级障碍函数（NBF）、节点级控制障碍函数（NCBF）以及协作节点级障碍函数（cNCBF），并给出了这些函数所定义集合保持前向不变的条件。利用协作节点级障碍函数，我们构建了一种新颖的分布式算法，用于协作网络智能体的安全控制，并提供了算法保证收敛到所有智能体可行安全控制动作集或至少一个智能体终端不可行状态的条件。我们引入网络邻居不遵从度的概念，作为给定网络状态和选定障碍函数超参数下协作安全鲁棒性的度量。最后，我们在网络化易感-感染-易感（SIS）模型上展示了这些结果。