Maintaining connectivity for networked mobile systems in the presence of agent loss

Connectivity is a fundamental property in many networked systems for communication and coordination among the agents. Removal of any agent from a network may destroy its connectivity. In order to maintain the connectivity of mobile networked systems in agent loss, one can design a robust network topology such that the network is tolerant to a finite number of agent losses, and/or develop a control strategy, such that the network reconfigures itself until the connectivity requirements are satisfied. In this paper, we introduce a decentralized control scheme based on a sequence of replacements, each of which occurs between an agent and one of its neighbors. The proposed scheme always maintains the graph connectivity, and it does not rely on any gathering of global information either a priori or at the intermediate steps of a mission. Moreover, the proposed scheme does not cause any increase in the total number of edges and the maximum node degree in a graph, thus it assures no increase in the overall communication cost due to the topological changes. In this study, we validate the control strategy by means of an analytical proof and simulation results.