scholarly journals Consensus Analysis of Second-Order Multiagent Systems with General Topology and Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bo Liu ◽  
Guangming Xie ◽  
Yanping Gao ◽  
Jiaxi Wu ◽  
Jianguo Zhang ◽  
...  
Keyword(s):  
Time Delay ◽  
Multiagent Systems ◽  
Nearest Neighbor ◽  
Laplacian Matrix ◽  
Second Order ◽  
General Topology ◽  
Consensus Analysis ◽  
Laplace Transform Technique ◽  
Eigenvalues Of The Laplacian ◽  
Nearest Neighbor Rule

This paper addresses the consensus of second-order multiagent systems with general topology and time delay based on the nearest neighbor rule. By using the Laplace transform technique, it is proved that the second-order multi-agent system in the presence of time-delay can reach consensus if the network topology contains a globally reachable node and time delay is bounded. The bound of time-delay only depends on eigenvalues of the Laplacian matrix of the system. The main contribution of this paper is that the accurate state of the consensus center and the upper bound of the communication delay to make the agents reach consensus are given. Some numerical simulations are given to illustrate the theoretical results.

scholarly journals Optimizing Pinned Nodes to Maximize the Convergence Rate of Multiagent Systems with Digraph Topologies

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Yujuan Han ◽  
Wenlian Lu ◽  
Tianping Chen ◽  
Changkai Sun
Keyword(s):  
Convergence Rate ◽  
Multiagent Systems ◽  
Spanning Trees ◽  
Laplacian Matrix ◽  
Pinning Control ◽  
Left Eigenvector ◽  
Underlying Network ◽  
Eigenvalues Of The Laplacian ◽  
Eigenvalue Zero ◽  
Theoretical Results

This paper investigates how to choose pinned node set to maximize the convergence rate of multiagent systems under digraph topologies in cases of sufficiently small and large pinning strength. In the case of sufficiently small pinning strength, perturbation methods are employed to derive formulas in terms of asymptotics that indicate that the left eigenvector corresponding to eigenvalue zero of the Laplacian measures the importance of node in pinning control multiagent systems if the underlying network has a spanning tree, whereas for the network with no spanning trees, the left eigenvectors of the Laplacian matrix corresponding to eigenvalue zero can be used to select the optimal pinned node set. In the case of sufficiently large pinning strength, by the similar method, a metric based on the smallest real part of eigenvalues of the Laplacian submatrix corresponding to the unpinned nodes is used to measure the stabilizability of the pinned node set. Different algorithms that are applicable for different scenarios are develped. Several numerical simulations are given to verify theoretical results.

scholarly journals Consensus Analysis for a Class of Heterogeneous Multiagent Systems with Time Delay Based on Frequency Domain Method

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yi-Jie Sun ◽  
Guo-liang Zhang ◽  
Jing Zeng
Keyword(s):  
Time Delay ◽  
Frequency Domain ◽  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Frequency Domain Method ◽  
Consensus Protocol ◽  
Consensus Analysis ◽  
Domain Method ◽  
Communication Topology ◽  
System Coupling

The consensus problem of heterogeneous multiagent systems composed of first-order and second-order agent is investigated. A linear consensus protocol is proposed. Based on frequency domain method, the sufficient conditions of achieving consensus are obtained. If communication topology contains spanning tree and some conditions can be satisfied on control gains, consensus can be achieved. Then, a linear consensus protocol with time delay is proposed. In this case, consensus is dependent only on system coupling strength, each agent input time delay, but independent of communication delay. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical result.

scholarly journals Consensus Analysis for Third-Order Multiagent Systems in Directed Networks

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Yanfen Cao ◽  
Yuangong Sun
Keyword(s):  
Dynamical Systems ◽  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Laplacian Matrix ◽  
Consensus Problem ◽  
Third Order ◽  
Consensus Analysis ◽  
Necessary And Sufficient ◽  
The Relationship ◽  
Theoretical Results

We investigate consensus problem for third-order multiagent dynamical systems in directed graph. Necessary and sufficient conditions to consensus of third-order multiagent systems have been established under three different protocols. Compared with existing results, we focus on the relationship between the scaling strengths and the eigenvalues of the involved Laplacian matrix, which guarantees consensus of third-order multiagent systems. Finally, some simulation examples are given to illustrate the theoretical results.

scholarly journals Consensus of Discrete Time Second-Order Multiagent Systems with Time Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Zhu
Keyword(s):  
Time Delay ◽  
Convergence Rate ◽  
Theoretical Result ◽  
Multiagent Systems ◽  
Discrete Time ◽  
Second Order ◽  
Sufficient Condition ◽  
Consensus Problem ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

The consensus problem for discrete time second-order multiagent systems with time delay is studied. Some effective methods are presented to deal with consensus problems in discrete time multiagent systems. A necessary and sufficient condition is established to ensure consensus. The convergence rate for reaching consensus is also estimated. It is shown that arbitrary bounded time delay can safely be tolerated. An example is presented to illustrate the theoretical result.

Consensus Analysis and Formation Control of Second-Order Multiagent Systems Via Nonlinear Protocol

2013 ◽  
Vol 8 (3) ◽  
Author(s):  
Huan Pan ◽  
Xiaohong Nian ◽  
Ling Guo
Keyword(s):  
Multiagent Systems ◽  
Invariance Principle ◽  
Control Strategy ◽  
Formation Control ◽  
Multiagent System ◽  
Sufficient Conditions ◽  
Second Order ◽  
General Linear ◽  
Communication Graph ◽  
Consensus Analysis

This paper mainly investigates consensus and formation control of second-order multiagent system with undirected communication graph. A nonlinear protocol is proposed as an extension of general linear protocols that have been widely studied. In order to achieve formation control, a formation control strategy corresponding to the nonlinear protocol is designed too. The sufficient conditions of consensus and formation are derived based on LaSalle's invariance principle. Simulation examples are provided to illustrate that the second-order multiagent with the nonlinear protocol can achieve consensus and formation.

scholarly journals Weighted Couple-Group Consensus Analysis of Heterogeneous Multiagent Systems with Cooperative-Competitive Interactions and Time Delays

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Xingcheng Pu ◽  
Chaowen Xiong ◽  
Lianghao Ji ◽  
Longlong Zhao
Keyword(s):  
Time Delay ◽  
Multiagent Systems ◽  
Time Delays ◽  
Multiagent System ◽  
Experimental Simulation ◽  
Group Consensus ◽  
Consensus Protocol ◽  
Consensus Analysis ◽  
Communication Time ◽  
Nyquist Criterion

In this paper, the weighted couple-group consensus of continuous-time heterogeneous multiagent systems with input and communication time delay is investigated. A novel weighted couple-group consensus protocol based on cooperation and competition interaction is designed, which can relax the in-degree balance condition. By using graph theory, general Nyquist criterion and Gerschgorin disc theorem, the time delay upper limit that the system may allow is obtained. The conclusions indicate that there is no relationship between weighted couple-group consensus and communication time delay. When the agents input time delay, the coupling weight between the agents, and the systems control parameters are satisfied, the multiagent system can converge to any given weighted coupling group consistent state. The experimental simulation results verify the correctness of the conclusion.

Sign in / Sign up

Export Citation Format

Share Document