Finite-time consensus for a stochastic multi-species system

2015 ◽  
Vol 08 (02) ◽  
pp. 1550025
Author(s):  
Li Wang ◽  
Qimin Zhang ◽  
Yu Zhao
Keyword(s):  
Probability Theory ◽  
Brownian Motion ◽  
Finite Time ◽  
Function Method ◽  
Consensus Problem ◽  
Consensus Protocol ◽  
Lyapunov Function Method ◽  
Definition Of ◽  
Theoretical Results ◽  
Stochastic Lyapunov Function

This paper considers the finite-time consensus problem for a stochastic multi-species system. First, we give out a nonlinear consensus protocol for the multi-species system with Brownian motion, and propose the definition of finite-time consensus in probability. Second, we prove that the multi-species system can achieve finite-time consensus in probability with different proper protocols by use of graph theory, stochastic Lyapunov function method and probability theory. Finally, some simulations are provided to illustrate the effectiveness of the theoretical results.

Fast Finite-Time Consensus Tracking of First-Order Multi-Agent Systems with a Virtual Leader

2014 ◽  
Vol 596 ◽  
pp. 552-559 ◽  
Author(s):  
Qiu Yun Xiao ◽  
Zhi Hai Wu ◽  
Li Peng
Keyword(s):  
Graph Theory ◽  
Finite Time ◽  
Function Method ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
First Order ◽  
Consensus Tracking ◽  
Lyapunov Function Method ◽  
Multi Agent ◽  
Virtual Leader

This paper proposes a novel finite-time consensus tracking protocol for guaranteeing first-order multi-agent systems with a virtual leader to achieve the fast finite-time consensus tracking. The Lyapunov function method, algebra graph theory, homogeneity with dilation and some other techniques are employed to prove that first-order multi-agent systems with a virtual leader applying the proposed protocol can reach the finite-time consensus tracking. Furthermore, theoretical analysis and numerical simulations show that compared with the traditional finite-time consensus tracking protocols, the proposed protocol can accelerate the convergence speed of achieving the finite-time consensus tracking.

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 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.

FINITE-TIME SYNCHRONIZATION OF DYNAMICAL NETWORKS COUPLED WITH COMPLEX-VARIABLE CHAOTIC SYSTEMS

2013 ◽  
Vol 24 (09) ◽  
pp. 1350058 ◽  
Author(s):  
ZHAOYAN WU ◽  
QINGLING YE ◽  
DANFENG LIU
Keyword(s):  
Complex Variable ◽  
Finite Time ◽  
Function Method ◽  
Chaotic Systems ◽  
Time Synchronization ◽  
Sufficient Conditions ◽  
Time Stability ◽  
Dynamical Networks ◽  
Finite Time Stability ◽  
Lyapunov Function Method

In this paper, finite-time synchronization of dynamical networks coupled with complex-variable chaotic systems is investigated. According to Lyapunov function method and finite-time stability theory, both the dynamical networks without and with coupling delay are considered through designing proper finite-time controllers. Several sufficient conditions for finite-time synchronization are derived and verified to be effective by some numerical examples.

Fast Finite-Time Consensus Tracking of Heterogeneous Multi-Agent Systems with a Virtual Leader

2014 ◽  
Vol 687-691 ◽  
pp. 580-586 ◽  
Author(s):  
Qiu Yun Xiao ◽  
Zhi Hai Wu ◽  
Li Peng
Keyword(s):  
Graph Theory ◽  
Lyapunov Function ◽  
Finite Time ◽  
Function Method ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Consensus Tracking ◽  
Lyapunov Function Method ◽  
Multi Agent ◽  
Virtual Leader

This paper proposes a novel finite-time consensus tracking protocol for guaranteeing heterogeneous multi-agent systems with a virtual leader to achieve the fast finite-time consensus tracking. The Lyapunov function method, algebra graph theory, homogeneity with dilation and some other techniques are employed to prove that heterogeneous multi-agent systems with a virtual leader applying the proposed protocol can reach the finite-time consensus tracking. Numerical simulations indicate that compared with traditional finite-time consensus tracking protocols, the proposed protocol can accelerate the convergence speed of the finite-time consensus tracking.

scholarly journals Hub-Induced Synchronization in Scale-Free Networks with Cluster Structure

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Jianbao Zhang ◽  
Zhongjun Ma ◽  
Jinde Cao
Keyword(s):  
Lyapunov Function ◽  
Function Method ◽  
Cluster Structure ◽  
Sufficient Conditions ◽  
Cluster Synchronization ◽  
Numerical Examples ◽  
Scale Free ◽  
Lyapunov Function Method ◽  
Scale Free Networks ◽  
Theoretical Results

A recent research indicated that the corticocortical connectivity network of the cat possesses cluster structure and that each cluster in the network is scale-free and has a most connected hub. Motivated by that research, we slightly modify the network model and derive sufficient conditions for cluster synchronization of the modified network based on Lyapunov function method. The obtained results indicate that cluster synchronization can be induced by the hubs of the scale-free networks. In our opinion, the concept of hub-induced synchronization provides a better understanding of cluster synchronization in scale-free networks. Numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Distributed consensus of multi-agent systems with increased convergence rate

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ke-cai Cao ◽  
Yun Chai ◽  
Chenglin Liu
Keyword(s):  
Convergence Rate ◽  
Finite Time ◽  
Nearest Neighbor ◽  
Laplacian Matrix ◽  
Consensus Problem ◽  
Multi Agent System ◽  
Multi Agent Systems ◽  
Consensus Protocol ◽  
Agent Systems ◽  
Multi Agent

AbstractConsensus problem with faster convergence rate of consensus problem has been considered in this paper. Adding more edges such as that connecting each agent and its second-nearest neighbor or changing the consensus protocol such as mixing asymptotic terms and terms of finite-time has been proved to be possible ways in increasing the convergence rate of multi-agent system in this paper. Based on analysis of Laplacian matrix, increasing of the convergence rate has been proved using the second-smallest eigenvalue for the first method. Concerning the second method, advantages of asymptotic consensus protocol and finite-time consensus protocol have been mixed together with the help of homogeneity function and theory of Lyapunov. Simulation results using matlab are also presented to illustrate the newly designed consensus protocols in increasing the convergence rate.

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