scholarly journals A Nonlinear Convergence Consensus: Extreme Doubly Stochastic Quadratic Operators for Multi-Agent Systems

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 540 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Sultan Almotairi ◽  
Hamad Almohamedh ◽  
Badr Almutairi ◽  
Abdullah Bajahzar ◽  
...  
Keyword(s):  
Stochastic Matrix ◽  
Extreme Points ◽  
Interaction Network ◽  
Low Complexity ◽  
Fast Time ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Common Value ◽  
Doubly Stochastic ◽  
Multi Agent

We investigate a novel nonlinear consensus from the extreme points of doubly stochastic quadratic operators (EDSQO), based on majorization theory and Markov chains for time-varying multi-agent distributed systems. We describe a dynamic system that has a local interaction network among agents. EDSQO has been applied for distributed agent systems, on a finite dimensional stochastic matrix. We prove that multi-agent systems converge at a center (common value) via the extreme waited value of doubly stochastic quadratic operators (DSQO), which are only 1 or 0 or 1/2 1 2 if the exchanges of each agent member has no selfish communication. Applying this rule means that the consensus is nonlinear and low-complexity computational for fast time convergence. The investigated nonlinear model of EDSQO follows the structure of the DeGroot linear (DGL) consensus model. However, EDSQO is nonlinear and faster convergent than the DGL model and is of lower complexity than DSQO and cubic stochastic quadratic operators (CSQO). The simulation result and theoretical proof are illustrated.

scholarly journals Learning to Reach Agreement in a Continuous Ultimatum Game

2008 ◽  
Vol 33 ◽  
pp. 551-574 ◽  
Author(s):  
S. De Jong ◽  
S. Uyttendaele ◽  
K. Tuyls
Keyword(s):  
Ultimatum Game ◽  
Social Dilemmas ◽  
Interaction Network ◽  
Multi Agent Systems ◽  
Scale Free ◽  
Agent Systems ◽  
Strategy Games ◽  
Common Strategy ◽  
Multi Agent ◽  
Free Interaction

It is well-known that acting in an individually rational manner, according to the principles of classical game theory, may lead to sub-optimal solutions in a class of problems named social dilemmas. In contrast, humans generally do not have much difficulty with social dilemmas, as they are able to balance personal benefit and group benefit. As agents in multi-agent systems are regularly confronted with social dilemmas, for instance in tasks such as resource allocation, these agents may benefit from the inclusion of mechanisms thought to facilitate human fairness. Although many of such mechanisms have already been implemented in a multi-agent systems context, their application is usually limited to rather abstract social dilemmas with a discrete set of available strategies (usually two). Given that many real-world examples of social dilemmas are actually continuous in nature, we extend this previous work to more general dilemmas, in which agents operate in a continuous strategy space. The social dilemma under study here is the well-known Ultimatum Game, in which an optimal solution is achieved if agents agree on a common strategy. We investigate whether a scale-free interaction network facilitates agents to reach agreement, especially in the presence of fixed-strategy agents that represent a desired (e.g. human) outcome. Moreover, we study the influence of rewiring in the interaction network. The agents are equipped with continuous-action learning automata and play a large number of random pairwise games in order to establish a common strategy. From our experiments, we may conclude that results obtained in discrete-strategy games can be generalized to continuous-strategy games to a certain extent: a scale-free interaction network structure allows agents to achieve agreement on a common strategy, and rewiring in the interaction network greatly enhances the agents' ability to reach agreement. However, it also becomes clear that some alternative mechanisms, such as reputation and volunteering, have many subtleties involved and do not have convincing beneficial effects in the continuous case.

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

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1519 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Sultan Almotairi ◽  
Hamad Almohamedh ◽  
Sherzod Turaev ◽  
Badr Almutairi
Keyword(s):  
Theoretical Analysis ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
Consensus Protocol ◽  
Agent Systems ◽  
Doubly Stochastic ◽  
Average Consensus ◽  
Multi Agent ◽  
Mathematical Equations ◽  
Simulation Results

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.

Bounded consensus tracking control of second-order multi-agent systems with active leader and jointly connected topology

2016 ◽  
Vol 40 (2) ◽  
pp. 504-513 ◽  
Author(s):  
Lei Chen ◽  
Kaiyu Qin ◽  
Jiangping Hu
Keyword(s):  
Tracking Control ◽  
Sufficient Conditions ◽  
Interaction Network ◽  
Second Order ◽  
Multi Agent System ◽  
Multi Agent Systems ◽  
Agent System ◽  
Agent Systems ◽  
Strongly Connected ◽  
Multi Agent

In this paper, we investigate a tracking control problem for second-order multi-agent systems. Here, the leader is self-active and cannot be completely measured by all the followers. The interaction network associated with the leader–follower multi-agent system is described by a jointly connected topology, where the topology switches over time and is not strongly connected during each time subinterval. We consider a consensus control of the multi-agent system with or without time delay and propose two categories of neighbour-based control rules for every agent to track the leader, then provide sufficient conditions to ensure that all agents follow the leader, and meanwhile, the tracking errors can be estimated. Finally, some simulation results are presented to demonstrate our theoretical results.

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

2018 ◽  
Vol 8 (1) ◽  
pp. 49-61 ◽  
Author(s):  
Rawad Abdulghafor ◽  
Sherzod Turaev ◽  
Akram Zeki ◽  
Adamu Abubaker
Keyword(s):  
Nonlinear Operator ◽  
Stochastic Matrices ◽  
Multi Agent Systems ◽  
Quadratic Operator ◽  
Dimensional Simplex ◽  
Agent Systems ◽  
Doubly Stochastic ◽  
Degroot Model ◽  
Multi Agent ◽  
Time Required

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.

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

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1692
Author(s):  
Rawad Abdulghafor ◽  
Sultan Almotairi
Keyword(s):  
Smart Grids ◽  
Autonomous Agents ◽  
Linear Models ◽  
Low Complexity ◽  
Complex Problem ◽  
Multi Agent Systems ◽  
Quadratic Operator ◽  
Agent Systems ◽  
Non Linear ◽  
Multi Agent

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.

Nonlinear Consensus for Multi-Agent Systems using Positive Intractions of Doubly Stochastic Quadratic Operators

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Rawad Abdulghafor ◽  
SHERZOD TURAEV ◽  
Mohd Izzuddin
Keyword(s):  
Technical Note ◽  
Positive Interactions ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Doubly Stochastic ◽  
Multi Agent

This technical note addresses a new nonlinear protocol class based on doubly stochasticquadratic operators (DSQO) for a consensus problem in multi-agent systems (MAS). In this technical note, afaster consensus is achieved for MAS by the rules of DSQO with the positive interactions among agents.

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