TY - JOUR
T1 - Nonlinear Convergence Algorithm
T2 - Structural Properties with Doubly Stochastic Quadratic Operators for Multi-Agent Systems
AU - Abdulghafor, Rawad
AU - Turaev, Sherzod
AU - Zeki, Akram
AU - Abubaker, Adamu
N1 - Funding Information:
We woflld like to thank Kfllliyyah of Information and Commflnication Technology and the Research Management Center of the International Islamic University Malaysia (IIUM) for their sflp-port. This work is sflpported by the MOHE throflgh IIUM Research Initiative Grant Scheme RIGS1fi-3fi8-0532.
Publisher Copyright:
© 2018 Rawad Abdulghafor et al., published by De Gruyter Open 2018.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - 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.
AB - 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.
KW - consensus problem
KW - doubly stochastic quadratic operators
KW - multi-agent systems
KW - nonlinear convergence algorithm
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U2 - 10.1515/jaiscr-2018-0003
DO - 10.1515/jaiscr-2018-0003
M3 - Article
AN - SCOPUS:85033402857
SN - 2083-2567
VL - 8
SP - 49
EP - 61
JO - Journal of Artificial Intelligence and Soft Computing Research
JF - Journal of Artificial Intelligence and Soft Computing Research
IS - 1
ER -