scholarly journals On the General Consensus Protocol in Multiagent Networks with Double-Integrator Dynamics and Coupling Time Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Tao Dong ◽  
Xiaofeng Liao
Keyword(s):  
Time Delay ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Consensus Algorithm ◽  
Directed Network ◽  
Consensus Protocol ◽  
Special Cases ◽  
Coupling Time ◽  
Almost All ◽  
Double Integrator

This paper considers the problem of the convergence of the consensus algorithm for multiple agents in a directed network where each agent is governed by double-integrator dynamics and coupling time delay. The advantage of this protocol is that almost all the existing linear local interaction consensus protocols can be considered as special cases of the present paper. By combining algebraic graph theory and matrix theory and studying the distribution of the eigenvalues of the associated characteristic equation, some necessary and sufficient conditions are derived for reaching the second-order consensus. Finally, an illustrative example is also given to support the theoretical results.

scholarly journals Exponential Stability of Stochastic Nonlinear Dynamical Price System with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Wenli Zhu ◽  
Xinfeng Ruan ◽  
Ye Qin ◽  
Jie Zhuang
Keyword(s):  
Time Delay ◽  
Exponential Stability ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Price System ◽  
Nonlinear Dynamical ◽  
System With Delay ◽  
Exponentially Stable ◽  
Theoretical Results

Based on Lyapunov stability theory, Itô formula, stochastic analysis, and matrix theory, we study the exponential stability of the stochastic nonlinear dynamical price system. Using Taylor's theorem, the stochastic nonlinear system with delay is reduced to ann-dimensional semilinear stochastic differential equation with delay. Some sufficient conditions of exponential stability and corollaries for such price system are established by virtue of Lyapunov function. The time delay upper limit is solved by using our theoretical results when the system is exponentially stable. Our theoretical results show that if the classical price Rayleigh equation is exponentially stable, so is its perturbed system with delay provided that both the time delay and the intensity of perturbations are small enough. Two examples are presented to illustrate our 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 Second-Order Consensus for Multiagent Systems under Directed and Switching Topologies

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Lixin Gao ◽  
Jingjing Zhang ◽  
Wenhai Chen
Keyword(s):  
Function Method ◽  
Sufficient Conditions ◽  
Common Lyapunov Function ◽  
Special Cases ◽  
Lyapunov Function Method ◽  
Leader Following ◽  
The Common ◽  
Feedback Laws ◽  
Integrator Model ◽  
Double Integrator

We consider multiagent consensus problems in a decentralized fashion. The interconnection topology among the agents is switching and directed. The agent dynamics is expressed in the form of a double-integrator model. Two different cases are considered: one is the leader-following case and the other is the leaderless case. Based on graph theory and the common Lyapunov function method, some sufficient conditions are established for the consensus stability of the considered systems with the neighbor-based feedback laws in both leader-following case and leaderless case, respectively. As special cases, the consensus conditions for balanced and undirected interconnection topology cases can be established directly. Finally, two numerical examples are given to illustrate the obtained results.

scholarly journals Leader-Follower Consensus of Second-Order Multiagent Systems with Absent Velocity Measurement and Time Delay

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Panpan Yang ◽  
Ye Tang ◽  
Maode Yan ◽  
Lei Zuo
Keyword(s):  
Time Delay ◽  
Multiagent Systems ◽  
Velocity Measurement ◽  
Sufficient Conditions ◽  
Constant Time Delay ◽  
Constant Time ◽  
Time Varying ◽  
Consensus Protocol ◽  
Time Varying Delay ◽  
Varying Delay

The leader-follower consensus problem of second-order multiagent systems with both absent velocity measurement and time delay is considered. First of all, the consensus protocol is designed by introducing an auxiliary system to compensate for the unavailability of the velocity information. Then, time delay is incorporated into the consensus protocol and two cases with, respectively, constant time delay and time-varying delay are investigated. For the case of constant time delay, Lyapunov-Razumikhin theorem is deployed to obtain the sufficient conditions that guarantee the stability of the consensus algorithm. For the case of time-varying delay, the sufficient conditions are also derived by resorting to the Lyapunov-Razumkhin theorem and linear matrix inequalities (LMIs). Various numerical simulations demonstrate the correctness of the theoretical results.

STABILITY ANALYSIS OF A CLASS OF GENERAL PERIODIC NEURAL NETWORKS WITH DELAYS AND IMPULSES

2009 ◽  
Vol 19 (05) ◽  
pp. 375-386 ◽  
Author(s):  
YONG ZHAO ◽  
YONGHUI XIA ◽  
QISHAO LU
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Periodic Solution ◽  
Stability Analysis ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Real Life ◽  
Network Systems ◽  
Globally Exponential Stability ◽  
Special Cases

Based on the inequality analysis, matrix theory and spectral theory, a class of general periodic neural networks with delays and impulses is studied. Some sufficient conditions are established for the existence and globally exponential stability of a unique periodic solution. Furthermore, the results are applied to some typical impulsive neural network systems as special cases, with a real-life example to show feasibility of our results.

Consensus of fractional-order multi-agent systems with input time delay

2017 ◽  
Vol 20 (1) ◽  
Author(s):  
Wei Zhu ◽  
Bo Chen ◽  
Jie Yang
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Matrix Theory ◽  
Sufficient Conditions ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Input Time ◽  
Bounded Input ◽  
Function Matrix

AbstractMany phenomena in inter-disciplinary fields can be explained naturally by coordinated behavior of agents with fractional-order dynamics. Under the assumption that the interconnection topology of all agents has a spanning tree, the consensuses of linear and nonlinear fractional-order multi-agent systems with input time delay are studied, respectively. Based on the properties of Mittag-Leffler function, matrix theory, stability theory of fractional-order differential equations, some sufficient conditions on consensus are derived by using the technique of inequality, which shows that the consensus can be achieved for any bounded input time delay. Finally, two numerical examples are given to illustrate the effectiveness of the theoretical results.

scholarly journals Containment Control of Heterogeneous Discrete-Time Multiagent Systems with Time Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Jiawei Wu ◽  
Yongguang Yu ◽  
Guojian Ren
Keyword(s):  
Time Delay ◽  
Convex Hull ◽  
Multiagent Systems ◽  
Control Strategy ◽  
Topological Structure ◽  
Sufficient Conditions ◽  
Final Position ◽  
Containment Control ◽  
Reduced Order ◽  
Double Integrator

In this paper, the containment control of heterogeneous MASs with multi-interactional leaders is addressed. The objective of the containment control is of two layers. The leaders converge to an expected form; subsequently, the followers enter the convex hull spanned by the leader’s final position. To achieve the goal, the dynamics of the leaders and the followers are modeled by a single integrator and a double integrator, respectively. A reduced-order transformation is employed to obtain the sufficient conditions for realizing the follower agents’ control. In this manner, the maximum allowed time delay is given. Moreover, based on the topological structure and matrix, it confirms that the followers are able to enter the expected convex hull. Finally, the numerical simulation reveals the effectiveness of the control strategy.

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.

Mean Square Consensus Control for Second Order Multi-Agent Systems under Fixed Topologies and Measurement Noises

2011 ◽  
Vol 403-408 ◽  
pp. 4036-4043 ◽  
Author(s):  
Xue Liang Liu ◽  
Bu Gong Xu ◽  
Li Hua Xie
Keyword(s):  
Matrix Theory ◽  
Sufficient Conditions ◽  
Second Order ◽  
Mean Square ◽  
Multi Agent Systems ◽  
Consensus Protocol ◽  
Agent Systems ◽  
Multi Agent ◽  
Measurement Noises ◽  
Mean Square Consensus

This paper considers the mean square consensus problems for second order multi-agent systems with fixed topologies and measurement noises. Two cases were analyzed: 1) undirected networks with fixed topologies; 2) undirected networks with fixed topologies and measurement noises. In order to attenuate the measurement noises, a time-varying consensus gain was introduced in the consensus protocol. Sufficient conditions were derived for all agents to reach consensus in mean square via algebraic graph theory, matrix theory and stochastic analysis approach, by constructing an appropriate Lyapunov function. A numerical example was given to verify our theoretical analysis.

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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