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 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 Bipartite Consensus of Heterogeneous Multiagent Systems with Diverse Input Delays

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Hongtao Ye ◽  
Zhongqiu Chen ◽  
Wenguang Luo ◽  
Jiayan Wen ◽  
Kene Li
Keyword(s):  
Theoretical Analysis ◽  
Multiagent Systems ◽  
Matrix Theory ◽  
Frequency Domain Analysis ◽  
Upper Bounds ◽  
Consensus Problem ◽  
The Novel ◽  
First Order ◽  
Bipartite Consensus ◽  
Input Delays

This paper investigates the bipartite consensus problem of heterogeneous multiagent systems with diverse input delays. Based on the systems composed of first-order and second-order agents, the novel control protocols are designed. Using frequency-domain analysis and matrix theory, the corresponding upper bounds of the allowable delays are obtained under the undirected topology and directed topology, respectively. Finally, simulation examples are given to verify the theoretical analysis.

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 Collective Coordination of High-Order Dynamic Multiagent Systems Guided by Multiple Leaders

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Xin-Lei Feng ◽  
Ting-Zhu Huang ◽  
Jin-Liang Shao
Keyword(s):  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Second Order ◽  
High Order ◽  
Necessary And Sufficient Conditions ◽  
Numerical Examples ◽  
Necessary And Sufficient ◽  
Multiple Leaders ◽  
Theoretical Results

For second-order and high-order dynamic multiagent systems with multiple leaders, the coordination schemes that all the follower agents flock to the polytope region formed by multiple leaders are considered. Necessary and sufficient conditions which the follower agents can enter the polytope region by the leaders are obtained. Finally, numerical examples are given to illustrate our theoretical results.

scholarly journals Exponential Robust Consensus of Multiagent Systems with Markov Jump Parameters

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
He Zhang ◽  
Huihui Ji ◽  
Zhiyong Ye ◽  
Tan Senping
Keyword(s):  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Stochastic Method ◽  
Matrix Inequality ◽  
Markov Jump ◽  
The Matrix ◽  
Robust Consensus ◽  
Theoretical Results

Exponential robust consensus of stochastic multiagent systems is studied. Coupling structures of multiagent systems are Markov jump switching; that is, multiagent systems contain Markov jump parameters. Sufficient conditions of almost surely exponential robust consensus are derived by utilizing the stochastic method and the approach of the matrix inequality. Finally, two simulations are shown to demonstrate the validity of the achieved theoretical results.

Optimally scalable matrices

1977 ◽  
Vol 287 (1345) ◽  
pp. 307-349 ◽  
Keyword(s):  
Matrix Theory ◽  
Sufficient Conditions ◽  
Spectral Structure ◽  
Combinatorial Matrix Theory ◽  
Sign Distribution ◽  
Special Cases ◽  
The Matrix ◽  
Singular Matrices ◽  
Necessary And Sufficient

The characterization of matrices which can be optimally scaled with respect to various modes of scaling is studied. Particular attention is given to the following two problems: ( a) The characterization of those square matrices for which inf lub (D -1 MD) D is attainable for some non-singular diagonal matrix D . ( b) The characterization of those square non-singular matrices A for which inf cond 12 (D 1 AD 2 ) D 1 , D 2 is attainable for some non-singular diagonal matrices D 1 and D 2 . For norms having certain properties, various necessary and sufficient conditions for optimal scalability are obtained when, in problem ( a ), the matrix A and, in problem ( b ), both A and A -1 have chequerboard sign distribution. The characterizations so established impose various conditions on the combinatorial and spectral structure of the matrices. These are investigated by using results from the Perron-Frobenius theory of non-negative matrices and combinatorial matrix theory. It is shown that the Holder or l p -norms have the required properties, and that, in general, the only norms having all of the properties needed, for both the necessary and the sufficient conditions to be satisfied, are variants of the l p -norms. For the special cases p = 1 and p = oo, the characterizations obtained hold for all matrices, irrespective of sign distribution.

scholarly journals Couple-Group Consensus for Multiagent Systems via Time-Dependent Event-Triggered Control

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Huiyang Liu ◽  
Xiaoshuang Wang
Keyword(s):  
Multiagent Systems ◽  
Matrix Theory ◽  
Time Dependent ◽  
Communication Delays ◽  
Group Consensus ◽  
First Order ◽  
Zeno Behavior ◽  
The Matrix ◽  
Second Order Systems ◽  
Event Triggered

This paper investigates couple-group consensus problems for multiagent first-order and second-order systems. Several consensus protocols are proposed based on the time-dependent distributed event-triggered control. For the case of no communication delays, the time-dependent event-triggered strategies are applied to couple-group consensus problems. Based on the matrix theory, algebraic conditions for couple-group consensus are established. For the system with communication delays, based on event-triggered strategies, a Lyapunov-Krasovskii functional is constructed to prove the input-to-state stability of the systems. Moreover, Zeno behavior is excluded. Finally, numeral examples are given to illustrate the effectiveness of these results.

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.

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