Open AccessAsymptotical rotating consensus algorithm with processing delay
Author(s) -
Fen Nie,
Xiaojun Duan,
Yicheng Liu
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1334/1/012008
Subject(s) - laplacian matrix , rotation (mathematics) , eigenvalues and eigenvectors , algorithm , laplace operator , mathematics , matrix (chemical analysis) , topology (electrical circuits) , logarithm , geometry , mathematical analysis , physics , combinatorics , materials science , quantum mechanics , composite material
In this paper, we studied some consensus algorithms for the collective rotating motions of a team of agents, which has been widely studied in different disciplines ranging from physics, networks and engineering. Both discrete and continues consensus algorithm with processing delays are investigated. There are three motion patterns determined by the information exchange topology of systems and rotation angle of rotation matrices. The asymptotic consensus appears when 0 is an simple eigenvalue of Laplacian matrix and the rotation angle is less than the critical value, and the rotating consensus achieves when the rotation angle is equal to the critical value. At this point, all agents move on circular orbits and the relative radii of orbits are equal to the relative magnitudes of the components of a right eigenvector associated with 0 eigenvalue of the non-symmetric Laplacian matrix. Finally, all agents move along logarithmic spiral curves with a fixed center when the rotation angle is larger than the critical value.