Regular Papers

International Journal of Control, Automation and Systems 2017; 15(5): 2320-2328

Published online September 6, 2017

https://doi.org/10.1007/s12555-016-0440-9

© The International Journal of Control, Automation, and Systems

Analysis of the Effects of Communication Delays for Consensus of Networked Multi-Agent Systems

Myrielle Allen-Prince, Christopher Thomas, and Sun Yi*

North Carolina A and T State University

Abstract

Achieving cooperation and coordination in a network of multi-agent systems is key to solving the consensus problem. Synchronization of such systems requires consistent communication between agents to reach a consensus, which is not feasible in the presence of delays, data loss, disturbances, and other unpredictable factors. Communication delays combined with environmental uncertainties can cause adverse effects and negatively change the behavior of the networked system preventing synchronization. In this paper, the stability of the delayed networked systems is analyzed using delay differential equations. Solving these equations has not been feasible, because of the infinite number of characteristic roots. The approach based on the LambertWfunction has the capability of analytically solving delay differential equations. The approach is used to quantify and analyze the stability of the delayed networked systems. The communication between the agents is modeled using the graph theory and the Laplacian matrix. The stability is analyzed by incorporating the Laplacian matrix into the Lambert W function based approach which provides the locus of the eigenvalues of the system as delay changes. Sensitivities and convergence speed with respect to delay for various topologies of the network are presented for comparison. The numerical results and implementation using MATLAB/Simulink are presented for illustration."

Keywords Consensus, delay, multiple-agent systems, sensitivity, stability, topology

Article

Regular Papers

International Journal of Control, Automation and Systems 2017; 15(5): 2320-2328

Published online October 1, 2017 https://doi.org/10.1007/s12555-016-0440-9

Copyright © The International Journal of Control, Automation, and Systems.

Analysis of the Effects of Communication Delays for Consensus of Networked Multi-Agent Systems

Myrielle Allen-Prince, Christopher Thomas, and Sun Yi*

North Carolina A and T State University

Abstract

Achieving cooperation and coordination in a network of multi-agent systems is key to solving the consensus problem. Synchronization of such systems requires consistent communication between agents to reach a consensus, which is not feasible in the presence of delays, data loss, disturbances, and other unpredictable factors. Communication delays combined with environmental uncertainties can cause adverse effects and negatively change the behavior of the networked system preventing synchronization. In this paper, the stability of the delayed networked systems is analyzed using delay differential equations. Solving these equations has not been feasible, because of the infinite number of characteristic roots. The approach based on the LambertWfunction has the capability of analytically solving delay differential equations. The approach is used to quantify and analyze the stability of the delayed networked systems. The communication between the agents is modeled using the graph theory and the Laplacian matrix. The stability is analyzed by incorporating the Laplacian matrix into the Lambert W function based approach which provides the locus of the eigenvalues of the system as delay changes. Sensitivities and convergence speed with respect to delay for various topologies of the network are presented for comparison. The numerical results and implementation using MATLAB/Simulink are presented for illustration."

Keywords: Consensus, delay, multiple-agent systems, sensitivity, stability, topology

IJCAS
April 2024

Vol. 22, No. 4, pp. 1105~1460

Stats or Metrics

Share this article on

  • line

Related articles in IJCAS

IJCAS

eISSN 2005-4092
pISSN 1598-6446