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

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…     

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.     

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.     

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.     

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。     

Consensus of multi-agent linear dynamic systems via impulsive control protocols

In this article, we introduce impulsive control protocols for multi-agent linear dynamic systems. First, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the consensus of the multi-agent linear dynamic systems by the theory of impulsive systems. Furthermore, how to select the discrete instants and impulsive matrices is discussed. The case that the topologies of networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.     

Finite-time consensus for stochastic multi-agent systems

In this article, we study the finite-time consensus in probability for stochastic multi-agent systems. First, we give the nonlinear consensus protocol for multi-agent systems with Gaussian white noise, and define the concept of finite-time consensus in probability. Second, we prove that multi-agent systems can achieve the finite-time consensus in probability under five different kinds of communication topologies by using graph theory, stochastic Lyapunov theory and probability theory. Finally, some simulation examples are provided to illustrate the effectiveness of the theoretical results.     

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.     

Leader-following consensus of high-order multi-agent linear systems with bounded transmission channels

The leader-following consensus of high-order multi-agent linear systems with bounded transmission channels is considered. Agents modelled as LTI dynamics exchange information according to a network which can be described as a graph with agents as its vertices and information transmission channels as its edges. The transmission channels are bounded. The objective is leader-following in the sense that the state of all agents should converge to that of the leader vehicle. Detailed analysis of the leader-following consensus under bounded transmission channels is investigated for both fixed and switching network topologies.     

Distributed leader-following consensus for second-order multi-agent systems with nonlinear inherent dynamics

In this paper, the leader-following consensus problem for second-order multi-agent systems with nonlinear inherent dynamics is investigated. Two distributed control protocols are proposed under fixed undirected communication topology and fixed directed communication topology. Some sufficient conditions are obtained for the states of followers converging to the state of virtual leader globally exponentially. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Simulations are also given to verify the effectiveness of the theoretical results.     

Distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies

In this article, we study distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies. The analysis is based on graph theory and nonnegative matrix theory. We propose two kinds of consensus protocols based on the consensus protocol of first-order and second-order multi-agent systems. Some necessary and sufficient conditions that the heterogeneous multi-agent system solves the consensus problems under different consensus protocols are presented with fixed topology. We also give some sufficient conditions for consensus of the heterogeneous multi-agent system with switching topology. Simulation examples are provided to demonstrate the effectiveness of the theoretical results.     

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.