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 ...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.展开更多
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 origin...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.展开更多
In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on pe...In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.展开更多
How to analyze flocking behaviors of a multi-agent system with local interaction functions is a challenging problem in theory.Motsch and Tadmor in 2011 also stressed the significance to assume that the interaction fun...How to analyze flocking behaviors of a multi-agent system with local interaction functions is a challenging problem in theory.Motsch and Tadmor in 2011 also stressed the significance to assume that the interaction function is rapidly decaying or cut-off at a finite distance(cf.Motsch and Tadmor in J.Stat.Phys.2011).In this paper,we study the flocking behavior of a Cucker–Smale type model with compactly supported interaction functions.Using properties of a connected stochastic matrix,together with an elaborate analysis on perturbations of a linearized system,we obtain a sufficient condition imposed only on model parameters and initial data to guarantee flocking.Moreover,it is shown that the system achieves flocking at an exponential rate.展开更多
基金the National Natural Science Foundation of China (Grant Nos.60221301 and 60334040)
文摘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.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 60821091, 60804043, 60574068)the Knowledge Innovation Project of Chinese Academy of Sciences (Grant No. KJCX3-SYW-S01)
文摘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.
文摘核数据不确定性是造成反应堆物理计算结果不确定性的重要因素之一。基于所需抽样核数据的协方差矩阵开发了随机抽样模块(Stochastic Sampling,SAMP),在此基础上利用SCALE(Standardized Computer Analyses for Licensing Evaluation)软件包实现了混合法和随机抽样法两种不确定性分析方法,以研究多群核数据不确定性对堆芯物理计算的影响。以3×3假想堆芯为对象,对两种方法进行了验证,然后应用于国际原子能机构(International Atomic Energy Agency,IAEA)燃料管理基准题中的Almaraz核电厂首循环堆芯。分析结果表明,两种方法结果符合良好,Almaraz核电厂堆芯keff不确定性约为0.5%,堆芯径向和轴向功率的最大不确定性分别为1.9%和0.45%。
文摘In this paper, we study the flocking behavior of a thermodynamic Cucker–Smale model with local velocity interactions. Using the spectral gap of a connected stochastic matrix, together with an elaborate estimate on perturbations of a linearized system, we provide a sufficient framework in terms of initial data and model parameters to guarantee flocking. Moreover, it is shown that the system achieves a consensus at an exponential rate.
基金The first author is supported by NSFC(Grant No.12001530)。
文摘How to analyze flocking behaviors of a multi-agent system with local interaction functions is a challenging problem in theory.Motsch and Tadmor in 2011 also stressed the significance to assume that the interaction function is rapidly decaying or cut-off at a finite distance(cf.Motsch and Tadmor in J.Stat.Phys.2011).In this paper,we study the flocking behavior of a Cucker–Smale type model with compactly supported interaction functions.Using properties of a connected stochastic matrix,together with an elaborate analysis on perturbations of a linearized system,we obtain a sufficient condition imposed only on model parameters and initial data to guarantee flocking.Moreover,it is shown that the system achieves flocking at an exponential rate.
