Hierarchical Cyclic Pursuit: Algebraic Curves Containing the Laplacian Spectra

by   Sergei E. Parsegov, et al.
Mail.Ru Group

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.


page 2

page 11

page 13


Second-Order Agents on Ring Digraphs

The paper addresses the problem of consensus seeking among second-order ...

Finite-time Heterogeneous Cyclic Pursuit with Application to Target Interception

This paper presents a finite-time heterogeneous cyclic pursuit scheme th...

The spectra of generalized Paley graphs and their associated irreducible cyclic codes

For q=p^m with p prime and k| q-1, we consider the generalized Paley gra...

Guidance of Agents in Cyclic Pursuit

This report studies the emergent behavior of systems of agents performin...

Eigenvalues of the laplacian matrices of the cycles with one weighted edge

In this paper we study the eigenvalues of the laplacian matrices of the ...

REDCHO: Robust Exact Dynamic Consensus of High Order

This article addresses the problem of average consensus in a multi-agent...

Please sign up or login with your details

Forgot password? Click here to reset