Open Access

ARTICLE

Average Convergence for Directed & Undirected Graphs in Distributed Systems

by Ali Mustafa^1,2, M Najam ul Islam¹, Salman Ahmed^1,3,*

1 Bahria University, Islamabad, 44000, Pakistan
2 Comsats University Islamabad, Attock campus, 43600, Pakistan
3 University of Engineering & Technology, Peshawar, 25000, Pakistan

* Corresponding Author: Salman Ahmed. Email:

Computer Systems Science and Engineering 2021, 37(3), 399-413. https://doi.org/10.32604/csse.2021.015575

Received 28 November 2020; Accepted 06 January 2021; Issue published 08 March 2021

Abstract

Consensus control of multi-agent systems is an innovative paradigm for the development of intelligent distributed systems. This has fascinated numerous scientific groups for their promising applications as they have the freedom to achieve their local and global goals and make their own decisions. Network communication topologies based on graph and matrix theory are widely used in a various real-time applications ranging from software agents to robotics. Therefore, while sustaining the significance of both directed and undirected graphs, this research emphases on the demonstration of a distributed average consensus algorithm. It uses the harmonic mean in the domain of multi-agent systems with directed and undirected graphs under static topologies based on a control input scheme. The proposed agreement protocol focuses on achieving a constant consensus on directional and undirected graphs using the exchange of information between neighbors to update their status values and to be able to calculate the total number of agents that contribute to the communication network at the same time. The proposed method is implemented for the identical networks that are considered under the directional and non-directional communication links. Two different scenarios are simulated and it is concluded that the undirected approach has an advantage over directed graph communication in terms of processing time and the total number of iterations required to achieve convergence. The same network parameters are introduced for both orientations of the communication graphs. In addition, the results of the simulation and the calculation of various matrices are provided at the end to validate the effectiveness of the proposed algorithm to achieve consensus.

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