<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Collage of Information and Communication Technology

Journal of Artificial Intelligence and Soft Computing Research

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

This paper proposes nonlinear operator of extreme doubly stochastic quadratic operator (EDSQO) for convergence algorithm aimed at solving consensus problem...

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

Published Online: Nov 01, 2017

Page range: 49 - 61

Received: May 26, 2016

Accepted: May 21, 2017

DOI: https://doi.org/10.1515/jaiscr-2018-0003

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

© 2018 Rawad Abdulghafor et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Nov 01, 2017

Page range: 49 - 61

Received: May 26, 2016

Accepted: May 21, 2017

DOI: https://doi.org/10.1515/jaiscr-2018-0003

Keywordsdoubly stochastic quadratic operators, nonlinear convergence algorithm, consensus problem, multi-agent systems

© 2018 Rawad Abdulghafor et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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