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 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 Formation-Containment Control of Second-Order Multiagent Systems via Intermittent Communication

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Mao-Dong Xia ◽  
Cheng-Lin Liu ◽  
Fei Liu
Keyword(s):  
Multiagent Systems ◽  
Lyapunov Functions ◽  
Second Order ◽  
Control Algorithms ◽  
Distributed Coordination ◽  
Time Intervals ◽  
Containment Control ◽  
Convergence Conditions ◽  
Intermittent Communication ◽  
Theoretical Results

This paper investigates the formation-containment control of second-order multiagent systems with intermittent communication. Distributed coordination control algorithms are proposed under aperiodic intermittent communication, where each agent only communicates with its neighboring agents on some disconnected time intervals. By means of constructing Lyapunov functions, sufficient convergence conditions are obtained for the leaders reaching a prescribed formation asymptotically and the followers converging into the convex hull formed by leaders asymptotically, respectively. Besides, sufficient convergence conditions are also provided for second-order multiagent systems converging to the desired formation-containment under time-varying communication delay and intermittent communication. Finally, the validity of theoretical results is illustrated by numerical simulations.

Multiconsensus of first-order multiagent systems with directed topologies

2020 ◽  
Vol 34 (23) ◽  
pp. 2050240
Author(s):  
Xiao-Wen Zhao ◽  
Guangsong Han ◽  
Qiang Lai ◽  
Dandan Yue
Keyword(s):  
Multiagent Systems ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Consensus Problem ◽  
Multiple Agents ◽  
First Order ◽  
The Matrix ◽  
Directed Topologies ◽  
Necessary And Sufficient ◽  
Theoretical Results

The multiconsensus problem of first-order multiagent systems with directed topologies is studied. A novel consensus problem is introduced in multiagent systems — multiconsensus. The states of multiple agents in each subnetwork asymptotically converge to an individual consistent value in the presence of information exchanges among subnetworks. Linear multiconsensus protocols are proposed to solve the multiconsensus problem, and the matrix corresponding to the protocol is designed. Necessary and sufficient conditions are derived based on matrix theory, under which the stationary multiconsensus and dynamic multiconsensus can be reached. Simulations are provided to demonstrate the effectiveness of 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 Bipartite Consensus of Heterogeneous Multiagent Systems Based on Distributed Event-Triggered Control

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Xiaoyu Wang ◽  
Kaien Liu ◽  
Zhijian Ji ◽  
Shitao Han
Keyword(s):  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Input Delay ◽  
Consensus Problem ◽  
Consensus Protocol ◽  
Control Scheme ◽  
Event Triggering ◽  
Bipartite Consensus ◽  
Theoretical Results ◽  
Event Triggered

In this paper, the bipartite consensus problem of heterogeneous multiagent systems composed of first-order and second-order agents is considered by utilizing the event-triggered control scheme. Under structurally balanced directed topology, event-triggered bipartite consensus protocol is put forward, and event-triggering functions consisting of measurement error and threshold are designed. To exclude Zeno behavior, an exponential function is introduced in the threshold. The bipartite consensus problem is transformed into the corresponding stability problem by means of gauge transformation and model transformation. By virtue of Lyapunov method, sufficient conditions for systems without input delay are obtained to guarantee bipartite consensus. Furthermore, for the case with input delay, sufficient conditions which include an admissible upper bound of the delay are obtained to guarantee bipartite consensus. Finally, numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.

scholarly journals Consensus of Multiagent Systems with Directed Topology and Communication Time Delay Bases on the Laplace Transform

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Bo Liu ◽  
Li Wang ◽  
Dehui Sun ◽  
Xinmao Zhu
Keyword(s):  
Time Delay ◽  
Laplace Transform ◽  
Multiagent Systems ◽  
Consensus Problem ◽  
Directed Topology ◽  
Communication Time ◽  
The Laplace Transform ◽  
Initial States ◽  
Directed Topologies ◽  
Theoretical Results

This paper investigates the consensus problem of multiagent systems with directed topologies. Different from the literatures, a new method, the Laplace transform, to study the consensus of multiagent systems with directed topology and communication time delay is proposed. The accurate state of the consensus center and the upper bound of the communication delay to make the agents reach consensus are given. It is proved that all the agents could aggregate and eventually form a cohesive cluster in finite time under certain conditions, and the consensus center is only determined by the initial states and the communication configuration among the agents. Finally, simulations are given to illustrate the theoretical results.

scholarly journals Distributed Attitude Consensus for Multiple Rigid Spacecraft under Jointly Connected Switching Topologies

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Long Ma ◽  
Shicheng Wang ◽  
Haibo Min ◽  
Shouyi Liao ◽  
Zhiguo Liu
Keyword(s):  
Function Method ◽  
Consensus Problem ◽  
Time Intervals ◽  
Common Lyapunov Function ◽  
Switching Topologies ◽  
First Case ◽  
Lyapunov Function Method ◽  
Communication Topology ◽  
Leader Following ◽  
Rigid Spacecraft

We study the distributed leader-following attitude consensus problem for multiple rigid spacecraft with a single leader under jointly connected switching topologies. Two cases are considered, where the first case is with a static leader and the second case is with a dynamic leader. By constructing an auxiliary vector and a distributed observer for each follower spacecraft, the controllers are designed to drive all the attitudes of the follower spacecraft to the leader’s, respectively, for both of the two cases, though there are some time intervals in which the communication topology is not connected. The whole system is proved to be stable by using common Lyapunov function method. Finally, the theoretical result is illustrated by numerical simulations.

H∞ consensus of multi-agent systems in directed networks with Lipschitz non-linear dynamics

2016 ◽  
Vol 39 (12) ◽  
pp. 1877-1884 ◽  
Author(s):  
Wei Liu ◽  
Shaolei Zhou ◽  
Qingpo Wu ◽  
Gaoyang Yin
Keyword(s):  
Matrix Decomposition ◽  
Consensus Problem ◽  
Multi Agent Systems ◽  
External Disturbances ◽  
Agent Systems ◽  
Directed Spanning Tree ◽  
General Network ◽  
Multi Agent ◽  
Theoretical Results ◽  
Relative States

This paper studies the H∞ consensus problem of multi-agent systems with Lipschitz non-linearities and external disturbances in a general network. The topology is just required to contain a directed spanning tree. Distributed consensus controllers are constructed based on relative states information of neighbour agents. A novel matrix decomposition based approach is introduced to analyse the H∞ consensus problem, in which the H∞ consensus problem is converted into a H∞ control problem of lower dimension system by performing a proper linear variable transformation. Finally, the effectiveness of the theoretical results is illustrated via a numerical simulation.

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.

scholarly journals Consensus of High-Order Linear Multiagent Systems with Multitype Switching Topologies Based on the Dynamic Dwell Time Approach

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Yaxiao Zhang ◽  
Yangzhou Chen ◽  
Xiaojun Qu
Keyword(s):  
Multiagent Systems ◽  
Dwell Time ◽  
High Order ◽  
Sufficient Condition ◽  
Consensus Problem ◽  
Switching Rule ◽  
Switching Topologies ◽  
The Stability ◽  
Necessary And Sufficient ◽  
The Impact

This paper investigates the consensus problem of high-order continuous-time linear multiagent systems (LMASs) with multitype switching topologies which include both consensusable and unconsensusable communication topologies. A linear transformation is introduced, which equivalently transforms the consensus problem into the stability problem of a corresponding switched system, along with a necessary and sufficient condition to analyze the consensus problem. This paper is aimed at studying the impact of a switching rule on communication topologies for consensus of LMASs. Based on the dynamic dwell time method, a sufficient condition is derived for consensus of LMASs. It is shown that, with switching signals that satisfy this switching rule, LMASs can achieve consensus under directed switching communication topologies. A numerical example is provided to illustrate the effectiveness of the theoretical results.

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