Nonlinear Convergence Algorithm: Structural Properties with Doubly Stochastic Quadratic Operators for Multi-Agent Systems

Rawad Abdulghafor, Sherzod Turaev, Akram Zeki, Adamu Abubaker

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

This paper proposes nonlinear operator of extreme doubly stochastic quadratic operator (EDSQO) for convergence algorithm aimed at solving consensus problem (CP) of discrete-time for multi-agent systems (MAS) on n-dimensional simplex. The first part undertakes systematic review of consensus problems. Convergence was generated via extreme doubly stochastic quadratic operators (EDSQOs) in the other part. However, this work was able to formulate convergence algorithms from doubly stochastic matrices, majorization theory, graph theory and stochastic analysis. We develop two algorithms: 1) the nonlinear algorithm of extreme doubly stochastic quadratic operator (NLAEDSQO) to generate all the convergent EDSQOs and 2) the nonlinear convergence algorithm (NLCA) of EDSQOs to investigate the optimal consensus for MAS. Experimental evaluation on convergent of EDSQOs yielded an optimal consensus for MAS. Comparative analysis with the convergence of EDSQOs and DeGroot model were carried out. The comparison was based on the complexity of operators, number of iterations to converge and the time required for convergences. This research proposed algorithm on convergence which is faster than the DeGroot linear model.

Original languageEnglish
Pages (from-to)49-61
Number of pages13
JournalJournal of Artificial Intelligence and Soft Computing Research
Volume8
Issue number1
DOIs
Publication statusPublished - Jan 1 2018
Externally publishedYes

Keywords

  • consensus problem
  • doubly stochastic quadratic operators
  • multi-agent systems
  • nonlinear convergence algorithm

ASJC Scopus subject areas

  • Information Systems
  • Modelling and Simulation
  • Hardware and Architecture
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence

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