Dynamic connectivity maintenance problems in networks of multi‐agent systems via nearest neighbor‐based methods

Abstract Connectivity maintenance is crucial for the real‐world deployment of multi‐agent systems, as it ultimately allows the agents to communicate, coordinate, and perform tasks in a collaborative way. In this paper, a new problem called the dynamic connectivity maintenance problem is considered, which aims to model the scenario where part agents have already broken away from the original communication range but still could be communicated by the other agents. To this end, nearest neighbor‐based methods are proposed in this paper to ensure that the graphs of multi‐agent systems have a spanning tree at all times. Considering that it takes time during the dynamic connectivity maintenance process, this paper also considers the impact of non‐uniform time‐varying time delays on communication and obtains a solution to the gain under the maximum time delay through the Lyapunov method when achieving a consensus. A new approach based on a chain‐type transformation to investigate the consensus problem is proposed. Some sufficient conditions are established. Finally, the developed approaches are validated through a simulation of unmanned surface vessels and a task of autonomous driving truck fleet.