New conditions for synchronization in dynamical communication networks

This paper investigates synchronization in a typical multi-agent system in which the communication network changes according to the system state. Through building new relationships between a matrix and its associated graph and estimating the diameter of the communication network, we prove that synchronization can be achieved if the speed of agents is bounded by O(n^−β), where n is the number of agents and β is bounded by a constant independent of n, which is much better than the existing bound O(n⁻ⁿ). Some simulations are provided to illustrate the theoretical results.     

Synchronization of multi-agent systems with delayed control input information from neighbors

In this paper, we consider the synchronization of continuous multi-agent systems with integrator node dynamics. We comparatively study two control protocols, a standard local voting protocol, and a protocol that includes information about the control inputs of neighbors. It is shown that using control input information from neighbors improves performance in two aspects. First, the performance is improved with respect to a certain quadratic performance index defined herein and second, speed of convergence can be selected arbitrarily, independently of the graph topology. Realistically, control input information from neighbors can only be received after a time delay. It is therefore shown that the second protocol using time-delayed control input information from neighbors guarantees the synchronization of the multi-agent system for any nonnegative delay. Furthermore, it is shown that the convergence rate using time-delayed control inputs can still be selected with considerable freedom, and remains superior to the performance of the standard local voting protocol which depends on the graph topology. Some numerical examples and experiments are given to demonstrate the effectiveness of the new protocols.     

Robust consensus of multi-agent systems with noise

The consensus problem of multi-agent systems has attracted wide attention from researchers in recent years, following the initial work of Jadbabaie et al. on the analysis of a simplified Vicsek model. While the original Vicsek model contains noise effects, almost all the existing theoretical results on consensus problem, however, do not take the noise effects into account. The purpose of this paper is to initiate a study of the consensus problems under noise disturbances. First, the class of multi-agent systems under study is transformed into a general time-varying system with noise. Then, for such a system, the equivalent relationships are established among (i) robust consensus, (ii) the positivity of the second smallest eigenvalue of a weighted Laplacian matrix, and (iii) the joint connectivity of the associated dynamical neighbor graphs. Finally, this basic equivalence result is shown to be applicable to several classes of concrete multi-agent models with noise. Supported by the National Natural Science Foundation of China (Grant Nos. 60821091, 60804043, 60574068), and the Knowledge Innovation Project of Chinese Academy of Sciences (Grant No. KJCX3-SYW-S01)     

Robust consensus of multi-agent systems with time-varying delays in noisy environment

Over the last ten years, the consensus of multi-agent systems (MAS) has received increasing attention from mechanics, mathematics, physics, engineering sciences, social sciences, and so on. It is well known that the robustness of consensus of MAS is usually determined by several key factors, including noise, time-delays, and packet drop. In this paper, we introduce a general time-delayed MAS model with noise and also further investigate its robust consensus. In particular, we prove that the proposed algorit...     

A note on connectivity of multi-agent systems with proximity graphs and linear feedback protocol

In this note, we investigate the possibility of simplifying the connectivity verification for multi-agent systems with proximity graphs and the linear feedback protocol. A Lyapunov-like approach is developed for analyzing the monotonicity of the largest edge length in the network. Based on this approach, we provide an initial-connectivity-based sufficient condition for dynamic connectivity. In particular, when each initial node degree is not less than three fourth of the graph order, initial network connectivity implies dynamic connectivity.     

Synchronization of general discrete Lur＇e systems

This paper studies a master-slave type of synchronization systems for a general form of two discrete Lur＇e systems. Some simple necessary and/or sufficient conditions for synchronization are derived. They are basically algebraic conditions, and are convement to be applied in engineering applications.     

Synchronization of general discrete Lur'e systems

This paper studies a master_slave type of synchronization systems for a general form of two discrete Lur'e systems. Some simple necessary and/or sufficient conditions for synchronization are derived. They are basically algebraic conditions, and are convenient to be applied in engineering applications.     

A novel group consensus protocol for heterogeneous multi-agent systems

In this paper, we consider the group consensus problem of heterogeneous multi-agent systems. Based on the feature of heterogeneous agents, a novel protocol is proposed for heterogeneous multi-agent systems. First, the state transformation method is used and an equivalent system is obtained. Then, the group consensus problem is analysed and some sufficient and/or necessary conditions are given for heterogenous multi-agent systems under undirected and directed networks, respectively. Finally, simulation examples are presented to demonstrate the effectiveness of the theoretical results.     

Synchronization of general discrete Lur''''e systems

1IntroductionChaos synchronization[1,2]has beeninvestigatedfor adecade,for which many effective methods have beenpresented[2,3~9,10~18].The aimof this paper is tofurther develop some simple criteria for the synchronizationoftwo coupled general discrete systems inthe Lur’e form,which has not beenfully addressedinthe literature.The paper is organized as follows.In Section2,theproblemunder consideration is formulated.In Section3,the main results of this paper are presented with proofs.There ar…     

Consensus of a group of mobile agents in three dimensions

This paper investigates the consensus problem of a three dimensional (3D) version of the widely studied Vicsek model, where each member moves in 3D Euclidean space with a constant speed with headings updated according to the average direction of neighbors. In comparison with the original Vicsek model, each agent’s heading is determined by two angle sequences interacting with each other, one of which evolves according to a “linear” non-homogeneous equation, which makes the theoretical analysis quite complicated. By analyzing the underlying structure of the system and relying on estimation of some characteristics concerning the initial states, we will establish consensus results for 3D Vicsek model under random framework without resorting to any a priori connectivity assumption.     

多智能体网络系统的能控性代数条件

能控性是多智能体系统研究的核心问题,主要包括结构可控性和精准可控性。对多智能体系统的模型和能控性代数条件进行了总结。在相对协议和绝对协议条件下,运用图论和矩阵论的知识系统分析了多智能体系统能控性的代数条件。按照同质多智能体到异质多智能体的顺序,对现有的多智能体系统模型和代数条件进行了梳理,并在已有结论的基础上对多智能体系统能控性的代数条件进行了改善,进一步提出了新的代数条件。多智能体能控性代数条件的改进大大简化了能控性的计算量。     

Second-order consensus in multi-agent dynamical systems with sampled position data

This paper studies second-order consensus in multi-agent dynamical systems with sampled position data. A distributed linear consensus protocol with second-order dynamics is designed, where both the current and some sampled past position data are utilized. It is found that second-order consensus in such a multi-agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period. A necessary and sufficient condition for reaching consensus of the system in this setting is established, based on which consensus regions are then characterized. It is shown that if all the eigenvalues of the Laplacian matrix are real, then second-order consensus in the multi-agent system can be reached for any sampling period except at some critical points depending on the spectrum of the Laplacian matrix. However, if there exists at least one eigenvalue of the Laplacian matrix with a nonzero imaginary part, second-order consensus cannot be reached for sufficiently small or sufficiently large sampling periods. In such cases, one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods. Finally, simulation examples are given to verify and illustrate the theoretical analysis.     

Necessary and sufficient conditions of stationary average consensus for second-order multi-agent systems

This paper investigates the stationary average consensus problem for second-order discrete-time multi-agent systems (SDMAS). A stationary consensus problem is to find a control algorithm that brings the state of a group of agents to a common constant value which is called the collective decision. We introduce the concept of stationary average consensus of SDMAS and propose a consensus algorithm. Based on the polynomial stability and the graph theory, we obtain two necessary and sufficient conditions of stationary average consensus of SDMAS. The last theorem provides an algebraic criterion of stationary average consensus, and can help us to determine the parameters in the consensus algorithm. Furthermore, in this consensus algorithm, only the states of the agents are transferred among the agents. Therefore, this algorithm can not only solve the stationary average consensus problem but also reduce the amount of transferred data. A numerical example is provided to illustrate the efficiency of our results.     

Synchronization in networks of identical linear systems

The paper investigates the synchronization of a network of identical linear state-space models under a possibly time-varying and directed interconnection structure. The main result is the construction of a dynamic output feedback coupling that achieves synchronization if the decoupled systems have no exponentially unstable mode and if the communication graph is uniformly connected. The result can be interpreted as a generalization of classical consensus algorithms. Stronger conditions are shown to be sufficient–but to some extent, also necessary–to ensure synchronization with the diffusive static output coupling often considered in the literature.     

Combining graph connectivity &; dominant set clustering for video summarization

The paper presents an automatic video summarization technique based on graph theory methodology and the dominant sets clustering algorithm. The large size of the video data set is handled by exploiting the connectivity information of prototype frames that are extracted from a down-sampled version of the original video sequence. The connectivity information for the prototypes which is obtained from the whole set of data improves video representation and reveals its structure. Automatic selection of the optimal number of clusters and hereafter keyframes is accomplished at a next step through the dominant set clustering algorithm. The method is free of user-specified modeling parameters and is evaluated in terms of several metrics that quantify its content representational ability. Comparison of the proposed summarization technique to the Open Video storyboard, the Adaptive clustering algorithm and the Delaunay clustering approach, is provided.

基于相关性的同步优化算法

给出了一种基于数据相关图的同步优化算法，作为自动并行化编译器中的一个独立遍，利用并行化编译器对程序的相关性分析结果来实现编译时barrier同步优化。     

Distributed finite-time consensus tracking for nonlinear multi-agent systems with a time-varying reference state

This paper investigates the consensus tracking problem for nonlinear multi-agent systems with a time-varying reference state. The consensus reference is taken as a virtual leader, whose output is only its position information that is available to only a subset of a group of followers. The dynamics of each follower consists of two terms: nonlinear inherent dynamics and a simple communication protocol relying only on the position of its neighbours. In this paper, the consensus tracking problem is respectively considered under fixed and switching communication topologies. Some corresponding sufficient conditions are obtained to guarantee the states of followers can converge to the state of the virtual leader in finite time. Rigorous proofs are given by using graph theory, matrix theory, and Lyapunov theory. Simulations are presented to illustrate the theoretical analysis.     

Group consensus control for heterogeneous multi-agent systems with fixed and switching topologies

In this paper, the group consensus problems of heterogeneous multi-agent systems with fixed and switching topologies are investigated. First, a class of distributed group consensus protocol is proposed for achieving the group consensus of heterogeneous multi-agent systems by using the neighbours’ information. Then, some corresponding sufficient conditions are obtained to guarantee the achievement of group consensus. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Finally, numerical simulations are also given to verify the theoretical analysis.     

Connectivity and synchronization of Vicsek model

The collective behavior of multi-agent systems is an important studying point for the investigation of complex systems, and a basic model of multi-agent systems is the so called Vicsek model, which possesses some key features of complex systems, such as dynamic behavior, local interaction, changing neighborhood, etc. This model looks simple, but the nonlinearly coupled relationship makes the theoretical analysis quite complicated. Jadbabaie et al. analyzed the linearized heading equations in this model and showed that all agents will synchronize eventually, provided that the neighbor graphs associated with the agents＇ positions satisfy a certain connectivity condition. Much subsequent research effort has been devoted to the analysis of the Vicsek model since the publication of Jadbabaie＇s work. However, an unresolved key problem is when such a connectivity is satisfied. This paper given a sufficient condition to guarantee the synchronization of the Vicsek model, which is imposed on the model parameters only. Moreover, some counterexamples are given to show that the connectivity of the neighbor graphs is not sufficient for synchronization of the Vicsek model if the initial headings are allowed to be in [0,2π）, which reveals some fundamental differences between the Vicsek model and its linearized version.