1. Hierarchical Cyclic Pursuit: Algebraic Curves Containing the Laplacian Spectra
- Author
-
Parsegov, Sergei E., Chebotarev, Pavel Yu., Shcherbakov, Pavel S., and Ibáñez, Federico M.
- Subjects
Computer Science - Multiagent Systems ,Mathematics - Combinatorics ,Mathematics - Optimization and Control ,93B70 93C95 37N35 - Abstract
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., Comment: 12 pages, 20 figures. Submitted to the IEEE for possible publication
- Published
- 2022