Lower Bounds on the Proportion of Leaders Needed for Expected Consensus of 3-D Flocks

摘要: This paper considers the consensus behavior of a spatially distributed 3-D dynamical network composed heterogeneous agents: leaders and followers, in which have preferred information about destination, while followers do not have. All move Euclidean space with given speed their headings updated according to average velocity corresponding neighbors. Compared 2-D model, key point lies how analyze “linear” nonhomogeneous equation where term strongly nonlinearly depends on states all agents. Using structure estimation some characteristics for initial states, we present proper decaying rate then establish lower bounds ratio number that is needed expected by considering two cases: 1) fixed neighborhood radius 2) variable respect population size. Some simulation examples are justify theoretical results.