有向网络下二阶线性多个体动力学系统的渐近性

摘要

This paper investigates the asymptotical behavior of second-order linear multi-agent dynamic systems in a direct communication network, and the configuration relation between those systems and the system structure. We use the notion of inertia in classical mechanism to describe the asymptotic behavior of second-order systems. When the parameters of position-control and the parameters of velocity-control of the system satisfy some conditions, the system approaches to the inertia-state. Meanwhile, the basic independent systems uniformly approach to the individual inertia-states which are determined by system initial-conditions and Laplacian left-eigenvectors associated with the zero eigenvalue; while the dependent systems reach some inertia-states in the convex-combination of individual inertia-states of independent systems.%本文探讨任意有向通讯网络条件下二阶线性多个体动力学系统的渐近性质及其与系统结构的关系.二阶多个体系统的平衡态可以用惯性概念描述.当系统位置控制系数与速度控制系数满足一定的关系时系统将趋于惯性状态.独立基本子系统趋于自身的位置一致惯性状态,这一状态由子系统状态初值以及其Laplacian零特征根左特征向量所确定;非独立子系统中个体的惯性状态在独立基本子系统位置一致惯性状态所决定的凸集内.