Necessary and Sufficient Conditions for Complementary Stochastic Quadratic Operators of Finite-Dimensional Simplex

Abdulghafor, Rawad; Turaev, Sherzod; Zeki, Akram M.

doi:10.30537/sjcms.v1i1.2

Cited by 10 publications

(6 citation statements)

References 11 publications

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“…This has allowed us to obtain certain necessary and sufficient conditions for SSQO. These SSQO results extend and complement some existing results on the convergence of classes of quadratic stochastic operators (QSO) [56][57][58][59][60][61].…”

Section: Introductionsupporting

confidence: 80%

A Fast Non-Linear Symmetry Approach for Guaranteed Consensus in Network of Multi-Agent Systems

Abdulghafor

Almotairi

2020

Symmetry

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There has been tremendous work on multi-agent systems (MAS) in recent years. MAS consist of multiple autonomous agents that interact with each order to solve a complex problem. Several applications of MAS can be found in computer networks, smart grids, and the modeling of complex systems. Despite numerous benefits, a significant challenge for MAS is achieving a consensus among agents in a shared target task, which is difficult without applying certain mathematical equations. Non-linear models offer better possibility of resolving consensus for MAS; however, existing non-linear models are considerably complicated and present no guarantees for achieving consensus. This paper proposes a non-linear mathematical model of semi symmetry quadratic operator (SSQO) in order to resolve the issue of consensus in networks of MAS. The model is based on stochastic quadratic operator theory, with added new notations. An important feature for the proposed model is low complexity, fast consensus, and a guaranteed capability to reach a consensus. We present an evaluation of the proposed SSQO model and comparison with other existing models. We demonstrate that an average consensus can be achieved with our model in addition to the emulation effects for the MAS consensus.

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Section: Introductionsupporting

confidence: 80%

A Fast Non-Linear Symmetry Approach for Guaranteed Consensus in Network of Multi-Agent Systems

Abdulghafor

Almotairi

2020

Symmetry

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“…In [14], an application of QSOs in population genetics has been modelled. QSQs are defined on dimensional simplex [15,16] where the simplex is a set of points. The higher dimension is more complicated to study and still an open problem for two-dimensional simplex [17,18].…”

Section: Introductionmentioning

confidence: 99%

The nonlinear limit control of EDSQOs on finite dimensional simplex

et al. 2019

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Consensus problems in multi agent systems (MAS) are theoretical aspect convergence of doubly stochastic quadratic operators. This work has presented the dynamic classifications of extreme doubly stochastic quadratic operators (EDSQOs) on finite-dimensional simplex (FDS) based on the limit behaviour of the trajectories. The limit behaviour of the trajectories of EDSQOs, on FDS is either in state of convergence, or fixed or periodic. This paper aimed at examining the behaviour of these states. The paper modelled the states and proves theoretically the characteristics of each state. The results indicate that convergence operators converge to the centre 1 m , and EDSQOs point are fixed with two or more points whereas periodic states exhibit sinusoidal behaviour. This work has contributed in understanding the limit of EDSQOs of the exterior initial points as fixed and periodic points developed spread attribute toward a fixed point. ARTICLE HISTORY

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“…Vallander succeeded in investigating and producing the results for some cases of QSOs on two-dimensional simplex [62] that were developed on finite-dimensional simplex by Ganikhodzhaev in [59,63]. Subclasses have been investigated from the class of QSOs such as DSQOs [60,64], dissipative doubly stochastic operators [65], and complementary stochastic quadratic operators [66].…”

Section: (A) the Problem Domainmentioning

confidence: 99%

Nonlinear Consensus Protocol Modified from Doubly Stochastic Quadratic Operators in Networks of Dynamic Agents

et al. 2019

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This article explores nonlinear convergence to limit the effects of the consensus problem that usually occurs in multi-agent systems. Most of the existing research essentially considers the outline of linear protocols, using complex mathematical equations in various orders. In this work, however, we designed and developed an alternative nonlinear protocol based on simple and effective mathematical approaches. The designed protocol in this sense was modified from the Doubly Stochastic Quadratic Operators (DSQO) and was aimed at resolving consensus problems. Therefore, we called it Modified Doubly Stochastic Quadratic Operators (MDSQO). The protocol was derived in the context of coordinated systems to overcome the consensus issue related to multi-agent systems. In the process, we proved that by using the proposed nonlinear protocol, the consensus could be reached via a common agreement among the agents (average consensus) in a fast and easy fashion without losing any initial status. Moreover, the investigated nonlinear protocol of MDSQO realized the reaching consensus always as well as DSQO in some cases, which could not reach consensus. Finally, simulation results were given to prove the validity of the theoretical analysis.

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Necessary and Sufficient Conditions for Complementary Stochastic Quadratic Operators of Finite-Dimensional Simplex

Abstract: We define a complementary stochastic quadratic operator on finite-dimensional space as a new sub-class of quadratic stochastic operator. We give necessary and sufficient conditions for complementary stochastic quadratic operator.

Cited by 10 publications

References 11 publications

A Fast Non-Linear Symmetry Approach for Guaranteed Consensus in Network of Multi-Agent Systems

A Fast Non-Linear Symmetry Approach for Guaranteed Consensus in Network of Multi-Agent Systems

The nonlinear limit control of EDSQOs on finite dimensional simplex

Nonlinear Consensus Protocol Modified from Doubly Stochastic Quadratic Operators in Networks of Dynamic Agents

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