具有非通用交互、时滞和通信故障的一阶与二阶Cucker-Smale模型
First and second-order Cucker-Smale models with non-universal interaction, time delay and communication failures
AI总结：
本文针对智能体间非通用交互、时滞及通信故障问题，引入图拓扑并基于持续激励条件，证明当交互有向图强连通时，一阶与二阶Cucker-Smale模型均指数收敛至一致性。
摘要：
本文研究具有非通用交互、时滞以及智能体间可能缺乏连接的一阶和二阶对齐模型。具体而言，我们分析系统中智能体不向所有其他智能体传输信息，且相互连接的智能体在特定时间可暂停交互的情况；此外，还考虑了交互中可能存在的时滞。为处理所考虑的“非通用”连接，需引入模型结构的图拓扑。在所谓的持续激励条件下，当描述智能体间交互的有向图强连通时，我们证明了两种模型均指数收敛至一致性。
英文摘要：
In this paper, we deal with first and second-order alignment models with non-universal interaction, time delay and possible lack of connection between the agents. More precisely, we analyze the situation in which the system's agents do not transmit information to all the other agents and also agents that are linked to each other can suspend their interaction at certain times. Moreover, we take into account of possible time lags in the interactions. To deal with the considered "non-universal" connection, a graph topology over the structure of the model has to be considered. Under a so-called Persistence Excitation Condition, we establish the exponential convergence to consensus for both models whenever the digraph that describes the interaction between the agents is strongly connected.
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