Abstract
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.
Highlights
The consensus problem for distributed systems has developed increasingly growing attention in various research areas
We have presented our modified nonlinear protocol for a consensus problem in multi-agent systems (MASs), which we will call modified doubly stochastic quadratic operators (MDSQOs)
Let x be the row vector containing the status of all agents and Y be the matrix of interactions in the current state
Summary
The consensus problem for distributed systems has developed increasingly growing attention in various research areas. One of the essential problems linked to multi-agent systems (MASs) is the consensus in convergence to a common value via a mathematical distributed model of discrete-time. Such problems are solved by linear and nonlinear consensus algorithms. The input that is necessary to overcoming the behaviour orientation problem of robots is bounded, and the controls of required inputs cannot be secured by linear protocols Another disadvantage of the linear protocols lies in the fact that they cannot limit the data transmission rate as characterized by flexible communications and exact transfer data among agents [22]. The proven efficiency of the nonlinear models shields them from the weaknesses inherent to the processes applied in linear models
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