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首页> 外文期刊>Neural Networks and Learning Systems, IEEE Transactions on >Lower Bounds on the Proportion of Leaders Needed for Expected Consensus of 3-D Flocks
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Lower Bounds on the Proportion of Leaders Needed for Expected Consensus of 3-D Flocks

机译：对3D鸡群的预期共识所需的领导者比例下限

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摘要

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.
机译：本文考虑了由异构主体（领导者和跟随者）组成的空间分布3-D动力学网络的共识行为，其中领导者拥有关于目的地的首选信息，而跟随者则没有。所有跟随者均以给定速度在3-D欧几里得空间中移动，并且其标题根据相应邻居的平均速度进行更新。与二维模型相比，关键在于如何分析“线性”非齐次方程的动力学行为，其中非齐次项强烈非线性地取决于所有主体的状态。使用网络结构和初始状态的某些特征的估计，我们为非齐次项提供了适当的衰减率，然后确定了预期共识所需的领导者数量与跟随者数量之比的下限考虑两种情况：1）固定速度和邻域半径，以及2）关于人口规模的可变速度和邻域半径。给出了一些仿真实例来证明理论结果是正确的。

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