论文标题
层次循环追踪：包含拉普拉斯光谱的代数曲线
Hierarchical Cyclic Pursuit: Algebraic Curves Containing the Laplacian Spectra
论文作者
论文摘要
本文解决了具有常规定向环结构的网络中多代理通信的问题。这些可以看作是经典循环追求拓扑的层次扩展。我们表明，相应的拉普拉斯矩阵的光谱允许在复杂平面上精确定位。此外，我们得出了此类矩阵的特征多项式的一般形式，分析了其根部属于其根的代数曲线，并提出了一种获得其封闭形式方程的方法。结合高阶SISO线性剂的频域共识标准，这些曲线使人们能够分析具有不同代理数量的网络中共识的可行性。
The paper addresses the problem of multi-agent communication in networks with regular directed ring structure. These can be viewed as hierarchical extensions of the classical cyclic pursuit topology. We show that the spectra of the corresponding Laplacian matrices allow exact localization on the complex plane. Furthermore, we derive a general form of the characteristic polynomial of such matrices, analyze the algebraic curves its roots belong to, and propose a way to obtain their closed-form equations. In combination with frequency domain consensus criteria for high-order SISO linear agents, these curves enable one to analyze the feasibility of consensus in networks with varying number of agents.
