Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 28, Issue 11, Pages 2555-2565Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2016.2598576
Keywords
3-D flocking model; expected consensus; leader-follower model; lower bound
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Funding
- National Natural Science Foundation of China [61273221, 61473189]
- Research Fund for the Doctoral Program of Higher Education of China
- National Key Basic Research Program of China (973 program) [2014CB845302]
- Australian Research Council's Discovery Projects funding scheme [DP130101658]
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This paper considers the consensus behavior of a spatially distributed 3-D dynamical network composed of heterogeneous agents: leaders and followers, in which the leaders have the preferred information about the destination, while the followers do not have. All followers move in a 3-D Euclidean space with a given speed and with their headings updated according to the average velocity of the corresponding neighbors. Compared with the 2-D model, a key point lies in how to analyze the dynamical behavior of a linear nonhomogeneous equation where the nonhomogeneous term strongly nonlinearly depends on the states of all agents. Using the network structure and the estimation of some characteristics for the initial states, we present a proper decaying rate for the nonhomogeneous term and then establish lower bounds on the ratio of the number of leaders to the number of followers that is needed for the expected consensus by considering two cases: 1) fixed speed and neighborhood radius and 2) variable speed and neighborhood radius with respect to the population size. Some simulation examples are given to justify the theoretical results.
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