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.

Leader-following consensus of heterogeneous linear multi-agent systems: New results based on linear transformation method

2021 ◽  
pp. 014233122110582
Author(s):  
Yangzhou Chen ◽  
Guangyue Xu ◽  
Jingyuan Zhan
Keyword(s):  
Linear Transformation ◽  
Design Method ◽  
Transformation Method ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
Consensus Protocol ◽  
Agent Systems ◽  
Hurwitz Stability ◽  
Leader Following ◽  
Multi Agent

This paper studies the leader-following state consensus problem for heterogeneous linear multi-agent systems under fixed directed communication topologies. First, we propose a consensus protocol consisting of four parts for high-order multi-agent systems, in which different agents are allowed to have different gain matrices so as to increase the degree of design freedom. Then, we adopt a state linear transformation, which is constructed based on the incidence matrix of a directed spanning tree of the communication topology, to equivalently transform the state consensus problem into a partial variable stability problem. Meanwhile, the results of the partial variable stability theory are used to derive a sufficient and necessary consensus criterion, expressed as the Hurwitz stability of a real matrix. Then, this criterion is further expressed as a bilinear matrix inequality condition, and, based on this condition, an iterative algorithm is proposed to find the gain matrices of the protocol. Finally, numerical examples are provided to verify the effectiveness of the proposed protocol design method.

scholarly journals Consensus Analysis for High-Order Multi-Agent Systems without or with Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Zhengxin Wang ◽  
Yang Cao
Keyword(s):  
Partial Information ◽  
Sufficient Conditions ◽  
High Order ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
Consensus Protocol ◽  
Consensus Analysis ◽  
Agent Systems ◽  
Multi Agent ◽  
Necessary And Sufficient

This paper studies the consensus problem for a high-order multi-agent systems without or with delays. Consensus protocols, which only depend on the own partial information of agents and partial relative information with its neighbors, are proposed for consensus and quasi-consensus, respectively. Firstly, some lemmas are presented, and then a necessary and sufficient condition for guaranteeing the consensus is established under the consensus protocol without delays. Furthermore, communication delays are considered. Some necessary and sufficient conditions for solving quasi-consensus problem with delays are obtained. Finally, some simulations are given to verify the theoretical results.

A generalized hierarchical nearly cyclic pursuit for the leader-following consensus problem in multi-agent systems

2017 ◽  
Vol 40 (5) ◽  
pp. 1529-1537 ◽  
Author(s):  
Muhammad Iqbal ◽  
John Leth ◽  
Trung D Ngo
Keyword(s):  
Convergence Rate ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Cyclic Pursuit ◽  
Leader Following ◽  
Multi Agent ◽  
Simulation Results ◽  
Pursuit Strategy

In this paper, we solve the leader-following consensus problem using a hierarchical nearly cyclic pursuit (HNCP) strategy for multi-agent systems. We extend the nearly cyclic pursuit strategy and the two-layer HNCP to the generalized L-layer HNCP that enables the agents to rendezvous at a point dictated by a beacon. We prove that the convergence rate of the generalized L-layer HNCP for the leader-following consensus problem is faster than that of the nearly cyclic pursuit. Simulation results demonstrate the effectiveness of the proposed method.

Consensus of Discrete-Time Second-Order Multi-Agent Systems with Partial Information Transmission

2013 ◽  
Vol 457-458 ◽  
pp. 1069-1073
Author(s):  
Lei Ding
Keyword(s):  
Information Transmission ◽  
Partial Information ◽  
Necessary Condition ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
Consensus Protocol ◽  
Position Information ◽  
Agent Systems ◽  
Multi Agent ◽  
Sufficient And Necessary Condition

This paper investigates the consensus problem of multi-agent systems with partial information transmission under an undirected topology. A distributed consensus protocol is proposed with local velocity feedback and the position information from neighbors. The consensus problem is converted to the stabilization problem by transforming the original systems into a reduced order state system. Then, by using graph theory and Jurys stability test, a sufficient and necessary condition for consensus of multi-agent systems is derived. An example is given to illustrate the effectiveness of the presented results.

Distributed Event-Triggered Quantizer in Multi-Agent Systems

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Huaqiang Zhang ◽  
Yu Ren ◽  
Xinsheng Wang
Keyword(s):  
Theoretical Analysis ◽  
Control Strategy ◽  
Numerical Results ◽  
Control Input ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Consensus Strategy ◽  
Multi Agent ◽  
Event Triggered

This paper investigates a kind of consensus problem in multi-agent systems, revises an existing control input for consensus by dynamic quantizers, and also gives a visible distributed event-triggered rule to update the parameters for dynamic quantizers. In other words, distributed event-triggered dynamic quantizers are firstly proposed and employed when designing a consensus strategy for multi-agent systems by this paper. Meanwhile, the overall steps of the control strategy are included. The numerical results come to agreement with the theoretical analysis, and shows that the proposed strategy can get faster convergence speed in comparison with an existing one.

Consensus Analysis for a Class of Heterogeneous Multi-Agent Systems in Directed Graph

2014 ◽  
Vol 599-601 ◽  
pp. 1930-1933
Author(s):  
Yi Jie Sun ◽  
Guo Liang Zhang ◽  
Jing Zeng
Keyword(s):  
Directed Graph ◽  
Matrix Theory ◽  
Sufficient Condition ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
Consensus Protocol ◽  
Consensus Analysis ◽  
Agent Systems ◽  
First Order ◽  
Multi Agent

This paper investigates the consensus problem for heterogeneous multi-agent systems in directed graph. The system includes first-order and second-order agents. A linear consensus protocol is proposed for solving such a consensus problem. A sufficient condition for the consensus problem is established by applying graph theory and matrix theory. Finally, a numerical simulation is provided to illustrate the effectiveness of the theoretical result.

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