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 Robust Leaderless Consensus of Uncertain Multiagent Systems with Fast Switching Topologies

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Wei Liu ◽  
Shaolei Zhou ◽  
Shi Yan ◽  
Gaoyang Yin
Keyword(s):  
Multiagent Systems ◽  
Special Property ◽  
Laplacian Matrix ◽  
Graph Laplacian ◽  
Consensus Problem ◽  
Time Intervals ◽  
Fast Switching ◽  
Switching Topologies ◽  
Directed Spanning Tree ◽  
Theoretical Results

This paper investigates the robust leaderless consensus problem of uncertain multiagent systems with directed fast switching topologies. The topologies are assumed to jointly contain a directed spanning tree. Based on a special property of the graph Laplacian matrix, the consensus problem is converted into a stabilization problem by performing a proper variable transformation. Averaging method is employed for analysis. It is proved that if the topologies switch sufficiently fast and the controllers are properly designed, the robust leaderless consensus can still be achieved even when all the possible topologies are unconnected in the switching time intervals. Finally, a numerical simulation is provided to illustrate the effectiveness of the theoretical results.

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 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 Average Consensus in Networks of Neutral Dynamical Agents with Fixed and Switching Topologies

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Yingying Wu ◽  
Yuangong Sun
Keyword(s):  
Sufficient Conditions ◽  
Laplacian Matrix ◽  
Switching Topology ◽  
Linear Matrix ◽  
Switching Topologies ◽  
Average Consensus ◽  
Eigenvalues Of The Laplacian ◽  
Fixed Topology ◽  
Necessary And Sufficient ◽  
Theoretical Results

This paper addresses the average consensus problem of neutral multiagent systems in undirected networks with fixed and switching topologies. For the case of fixed topology, necessary and sufficient conditions to average consensus are established by decoupling the neutral multiagent system in terms of the eigenvalues of the Laplacian matrix. For the case of switching topology, sufficient conditions to average consensus are given in terms of linear matrix inequalities to determine the allowable upper bound of the time-varying communication delay. Finally, two examples are worked out to explain the effectiveness of the theoretical results.

Schooling for multi-agent systems via impulsive containment control algorithms with quantized information

2018 ◽  
Vol 41 (3) ◽  
pp. 828-841 ◽  
Author(s):  
Hong-Xiao Zhang ◽  
Li Ding ◽  
Zhi-Wei Liu
Keyword(s):  
Sufficient Conditions ◽  
Laplacian Matrix ◽  
Control Algorithms ◽  
Multi Agent Systems ◽  
Containment Control ◽  
Agent Systems ◽  
Eigenvalues Of The Laplacian ◽  
Multi Agent ◽  
Necessary And Sufficient ◽  
Theoretical Results

In the paper, schooling problems based on containment control in multi-agent systems that have static or dynamic leaders under directed and undirected communication topologies are investigated. We propose a periodic impulsive containment control algorithm to realize schooling in multi-agent systems. Both ideal and quantized relative state measurements are considered under this framework. Some necessary and sufficient conditions, which depend on the eigenvalues of the Laplacian matrix that is associated with the communication graph, the impulsive period as well as the gain parameters, are obtained to realize the containment control of schooling. Finally, some numerical simulations are illustrated to verify the theoretical results.

DIMERS AND SPANNING TREES: SOME RECENT RESULTS

2002 ◽  
Vol 16 (14n15) ◽  
pp. 1951-1961 ◽  
Author(s):  
F. Y. WU
Keyword(s):  
Spanning Tree ◽  
Recent Progress ◽  
Spanning Trees ◽  
Central Charge ◽  
Laplacian Matrix ◽  
Spatial Dimension ◽  
Two Dimensions ◽  
Eigenvalues Of The Laplacian ◽  
Text Correction ◽  
Orientable Surfaces

This paper reviews some recent progress on dimer and spanning tree enumerations. We use the Kasteleyn formulation to enumerate close-packed dimers on a simple-quartic net embedded on non-orientable surfaces, and obtain solutions in the form of double products. For spanning trees the enumeration is carried out by evaluating the eigenvalues of the Laplacian matrix associated with the lattice, a procedure which holds in any spatial dimension. In two dimensions a bijection due to Temperley relates spanning tree and dimer configurations on two related lattices. We use this bijection to enumerate dimers on a net with a vacancy on the boundary. It is found that the occurrence of a vacancy induces a [Formula: see text] correction to the enumeration, where N is the linear size of the lattice, and changes the central charge from c = 1 to -2.

scholarly journals Partial Component Consensus of Discrete-Time Multiagent Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Wenjun Hu ◽  
Gang Zhang ◽  
Zhongjun Ma ◽  
Binbin Wu
Keyword(s):  
Multiagent Systems ◽  
Discrete Time ◽  
Matrix Theory ◽  
Pinning Control ◽  
Directed Network ◽  
Strong Function ◽  
Partial Stability ◽  
Partial Component ◽  
The Matrix ◽  
Error System

The multiagent system has the advantages of simple structure, strong function, and cost saving, which has received wide attention from different fields. Consensus is the most basic problem in multiagent systems. In this paper, firstly, the problem of partial component consensus in the first-order linear discrete-time multiagent systems with the directed network topology is discussed. Via designing an appropriate pinning control protocol, the corresponding error system is analyzed by using the matrix theory and the partial stability theory. Secondly, a sufficient condition is given to realize partial component consensus in multiagent systems. Finally, the numerical simulations are given to illustrate the theoretical results.

scholarly journals A Nonlinear Consensus Protocol of Multiagent Systems Considering Measuring Errors

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Xiaochu Wang ◽  
Kaichun Zhao ◽  
Zheng You ◽  
Lungui Zheng
Keyword(s):  
Multiagent Systems ◽  
Energy Cost ◽  
Additional Condition ◽  
Consensus Protocol ◽  
Communication Topology ◽  
Measurement Uncertainties ◽  
Theoretical Analyses ◽  
Theoretical Results

In order to avoid a potential waste of energy during consensus controls in the case where there exist measurement uncertainties, a nonlinear protocol is proposed for multiagent systems under a fixed connected undirected communication topology and extended to both the cases with full and partial access a reference. Distributed estimators are utilized to help all agents agree on the understandings of the reference, even though there may be some agents which cannot access to the reference directly. An additional condition is also considered, where self-known configuration offsets are desired. Theoretical analyses of stability are given. Finally, simulations are performed, and results show that the proposed protocols can lead agents to achieve loose consensus and work effectively with less energy cost to keep the formation, which have illustrated the theoretical results.

scholarly journals On the Group Controllability of Leader-Based Continuous-Time Multiagent Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Bo Liu ◽  
Licheng Wu ◽  
Rong Li ◽  
Housheng Su ◽  
Yue Han
Keyword(s):  
Numerical Simulations ◽  
Multiagent Systems ◽  
Continuous Time ◽  
Entire Group ◽  
Multiple Leaders ◽  
Theoretical Results

The group controllability of continuous-time multiagent systems (MASs) with multiple leaders is considered in this paper, where the entire group is compartmentalized into a few subgroups. The group controllability concept of continuous-time MASs with multiple leaders is put forward, and the group controllability criteria are obtained for switching and fixed topologies, respectively. Finally, the numerical simulations are given to prove the validity of the theoretical results.

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