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Spontaneous Recovery in Directed Dynamical Networks
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作者 Xueming Liu Xian Yan H.Eugene Stanley 《Engineering》 SCIE EI CAS CSCD 2024年第6期208-214,共7页
Complex networked systems,which range from biological systems in the natural world to infrastructure systems in the human-made world,can exhibit spontaneous recovery after a failure;for example,a brain may spontaneous... Complex networked systems,which range from biological systems in the natural world to infrastructure systems in the human-made world,can exhibit spontaneous recovery after a failure;for example,a brain may spontaneously return to normal after a seizure,and traffic flow can become smooth again after a jam.Previous studies on the spontaneous recovery of dynamical networks have been limited to undirected networks.However,most real-world networks are directed.To fill this gap,we build a model in which nodes may alternately fail and recover,and we develop a theoretical tool to analyze the recovery properties of directed dynamical networks.We find that the tool can accurately predict the final fraction of active nodes,and the prediction accuracy decreases as the fraction of bidirectional links in the network increases,which emphasizes the importance of directionality in network dynamics.Due to different initial states,directed dynamical networks may show alternative stable states under the same control parameter,exhibiting hysteresis behavior.In addition,for networks with finite sizes,the fraction of active nodes may jump back and forth between high and low states,mimicking repetitive failure-recovery processes.These findings could help clarify the system recovery mechanism and enable better design of networked systems with high resilience. 展开更多
关键词 network resilience Directed dynamical networks Spontaneous recovery
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Percolation transitions in edge-coupled interdependent networks with directed dependency links
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作者 高彦丽 于海波 +2 位作者 周杰 周银座 陈世明 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第9期586-595,共10页
We propose a model of edge-coupled interdependent networks with directed dependency links(EINDDLs)and develop the theoretical analysis framework of this model based on the self-consistent probabilities method.The phas... We propose a model of edge-coupled interdependent networks with directed dependency links(EINDDLs)and develop the theoretical analysis framework of this model based on the self-consistent probabilities method.The phase transition behaviors and parameter thresholds of this model under random attacks are analyzed theoretically on both random regular(RR)networks and Erd¨os-Renyi(ER)networks,and computer simulations are performed to verify the results.In this EINDDL model,a fractionβof connectivity links within network B depends on network A and a fraction(1-β)of connectivity links within network A depends on network B.It is found that randomly removing a fraction(1-p)of connectivity links in network A at the initial state,network A exhibits different types of phase transitions(first order,second order and hybrid).Network B is rarely affected by cascading failure whenβis small,and network B will gradually converge from the first-order to the second-order phase transition asβincreases.We present the critical values ofβfor the phase change process of networks A and B,and give the critical values of p andβfor network B at the critical point of collapse.Furthermore,a cascading prevention strategy is proposed.The findings are of great significance for understanding the robustness of EINDDLs. 展开更多
关键词 edge-coupled interdependent networks with directed dependency links percolation transitions cascading failures robustness analysis
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Circular Formation Flight Control for Unmanned Aerial Vehicles With Directed Network and External Disturbance 被引量:11
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作者 Yangyang Chen Rui Yu +1 位作者 Ya Zhang Chenglin Liu 《IEEE/CAA Journal of Automatica Sinica》 EI CSCD 2020年第2期505-516,共12页
This paper proposes a new distributed formation flight protocol for unmanned aerial vehicles(UAVs)to perform coordinated circular tracking around a set of circles on a target sphere.Different from the previous results... This paper proposes a new distributed formation flight protocol for unmanned aerial vehicles(UAVs)to perform coordinated circular tracking around a set of circles on a target sphere.Different from the previous results limited in bidirectional networks and disturbance-free motions,this paper handles the circular formation flight control problem with both directed network and spatiotemporal disturbance with the knowledge of its upper bound.Distinguishing from the design of a common Lyapunov fiunction for bidirectional cases,we separately design the control for the circular tracking subsystem and the formation keeping subsystem with the circular tracking error as input.Then the whole control system is regarded as a cascade connection of these two subsystems,which is proved to be stable by input-tostate stability(ISS)theory.For the purpose of encountering the external disturbance,the backstepping technology is introduced to design the control inputs of each UAV pointing to North and Down along the special sphere(say,the circular tracking control algorithm)with the help of the switching function.Meanwhile,the distributed linear consensus protocol integrated with anther switching anti-interference item is developed to construct the control input of each UAV pointing to east along the special sphere(say,the formation keeping control law)for formation keeping.The validity of the proposed control law is proved both in the rigorous theory and through numerical simulations. 展开更多
关键词 Directed network external disturbance flight control unmanned aerial vehicles(UAVs)
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Distributed Fault-Tolerant Containment Control for Nonlinear Multi-Agent Systems Under Directed Network Topology via Hierarchical Approach 被引量:3
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作者 Shuyi Xiao Jiuxiang Dong 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2021年第4期806-816,共11页
This paper investigates the distributed fault-tolerant containment control(FTCC)problem of nonlinear multi-agent systems(MASs)under a directed network topology.The proposed control framework which is independent on th... This paper investigates the distributed fault-tolerant containment control(FTCC)problem of nonlinear multi-agent systems(MASs)under a directed network topology.The proposed control framework which is independent on the global information about the communication topology consists of two layers.Different from most existing distributed fault-tolerant control(FTC)protocols where the fault in one agent may propagate over network,the developed control method can eliminate the phenomenon of fault propagation.Based on the hierarchical control strategy,the FTCC problem with a directed graph can be simplified to the distributed containment control of the upper layer and the fault-tolerant tracking control of the lower layer.Finally,simulation results are given to demonstrate the effectiveness of the proposed control protocol. 展开更多
关键词 Adaptive fault-tolerant control directed network topology distributed control hierarchical control multi-agent systems(MASs)
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Distributed Containment Control of Networked Nonlinear Second-order Systems With Unknown Parameters 被引量:3
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作者 Long Ma Haibo Min +2 位作者 Shicheng Wang Yuan Liu Zhiguo Liu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2018年第1期232-239,共8页
In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the le... In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders(regulation case) and dynamic leaders(dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders,while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders.Finally, all the theoretical results are illustrated by numerical simulations. 展开更多
关键词 Containment control directed network topology multi-agent systems nonlinear second-order systems
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DIRECT DISPLACEMENT OF PARALLEL MECHANISM WITH WAVELET NETWORK 被引量:1
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作者 CHEN Weishan CHEN Hua LIU Junkao 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2007年第2期69-72,共4页
A new method solution for the direct displacement of parallel mechanism, wavelet network method, is proposed. Comparing with the classical analytical and numerical methods, this method can be extended to any parallel ... A new method solution for the direct displacement of parallel mechanism, wavelet network method, is proposed. Comparing with the classical analytical and numerical methods, this method can be extended to any parallel mechanism with any selected degree of freedom and configuration. A wavelet network suiting to approach multi-input and multi-output system is constructed. The network is optimized by analyzing the sparseness of input data and selecting the fitting wavelets by orthogonalization method according to the output data. Then it is applied to solve the direct displace- ment of a general six-degree-of-freedom parallel mechanism as a numerical example. For comparison purposes, a BP neural network is also used for this problem. Simulation results show that the wavelet network performs better than BP neural network. In addition, the wavelet network learns much faster than BP network. 展开更多
关键词 Direct displacement Parallel mechanism Wavelet network
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Bounded consensus tracking of second-order multi-agent systems with sampling delay under directed networks
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作者 李丽 方华京 《Chinese Physics B》 SCIE EI CAS CSCD 2013年第11期253-261,共9页
The bounded consensus tracking problems of second-order multi-agent systems under directed networks with sam- pling delay are addressed in this paper. When the sampling delay is more than a sampling period, new protoc... The bounded consensus tracking problems of second-order multi-agent systems under directed networks with sam- pling delay are addressed in this paper. When the sampling delay is more than a sampling period, new protocols based on sampled-data control are proposed so that each agent can track the time-varying reference state of the virtual leader. By using the delay decomposition approach, the augmented matrix method, and the frequency domain analysis, necessary and sufficient conditions are obtained, which guarantee that the bounded consensus tracking is realized. Furthermore, some numerical simulations are presented to demonstrate the effectiveness of the theoretical results. 展开更多
关键词 second-order multi-agent systems bounded consensus tracking sampling delay directed networks
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Global Synchronization of Directed Networks with Fast Switching Topologies
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作者 LU Xin-Biao QIN Bu-Zhi LU Xin-Yu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第12期1019-1024,共6页
Global synchronization of a class of directed dynamical networks with switching topologies is investigated.It is found that if there is a directed spanning tree in the fixed time-average of network topology and the ti... Global synchronization of a class of directed dynamical networks with switching topologies is investigated.It is found that if there is a directed spanning tree in the fixed time-average of network topology and the time-averageis achieved sufficiently fast,then the network will reach global synchronization for sufficiently large coupling strength. 展开更多
关键词 global synchronization directed network fast switch
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Empirical investigation of topological and weighted properties of a bus transport network from China
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作者 冯树民 胡宝雨 +2 位作者 聂涔 申翔浩 慈玉生 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第3期111-117,共7页
Many bus transport networks (BTNs) have evolved into directed networks. A new representation model for BTNs is proposed, called directed-space P. The bus transport network of Harbin (BTN-H) is described as a direc... Many bus transport networks (BTNs) have evolved into directed networks. A new representation model for BTNs is proposed, called directed-space P. The bus transport network of Harbin (BTN-H) is described as a directed and weighted complex network by the proposed representation model and by giving each node weights. The topological and weighted properties are revealed in detail. In-degree and out-degree distributions, in-weight and out-weight distributions are presented as an exponential law, respectively. There is a strong relation between in-weight and in-degree (also between out-weight and out-degree), which can be fitted by a power function. Degree-degree and weight-weight correlations are investigated to reveal that BTN-H has a disassortative behavior as the nodes have relatively high degree (or weight). The disparity distributions of out-degree and in-degree follow an approximate power-law. Besides, the node degree shows a near linear increase with the number of routes that connect to the corresponding station. These properties revealed in this paper can help public transport planners to analyze the status quo of the BTN in nature. 展开更多
关键词 bus transport network directed and weighted network empirical distributions CORRELATIONS
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Structural Reliability Analysis Based on Support Vector Machine and Dual Neural Network Direct Integration Method
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作者 NIE Xiaobo LI Haibin 《Journal of Donghua University(English Edition)》 CAS 2021年第1期51-56,共6页
Aiming at the reliability analysis of small sample data or implicit structural function,a novel structural reliability analysis model based on support vector machine(SVM)and neural network direct integration method(DN... Aiming at the reliability analysis of small sample data or implicit structural function,a novel structural reliability analysis model based on support vector machine(SVM)and neural network direct integration method(DNN)is proposed.Firstly,SVM with good small sample learning ability is used to train small sample data,fit structural performance functions and establish regular integration regions.Secondly,DNN is approximated the integral function to achieve multiple integration in the integration region.Finally,structural reliability was obtained by DNN.Numerical examples are investigated to demonstrate the effectiveness of the present method,which provides a feasible way for the structural reliability analysis. 展开更多
关键词 support vector machine(SVM) neural network direct integration method structural reliability small sample data performance function
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Preparation technologies for polymer composites with high-directional thermal conductivity:A review
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作者 Yanshuai Duan Huitao Yu +2 位作者 Fei Zhang Mengmeng Qin Wei Feng 《Nano Research》 SCIE EI CSCD 2024年第11期9796-9814,共19页
With the rapid development of science and technology,electronic devices are moving towards miniaturization and integration,which brings high heat dissipation requirements.During the heat dissipation process of a heati... With the rapid development of science and technology,electronic devices are moving towards miniaturization and integration,which brings high heat dissipation requirements.During the heat dissipation process of a heating element,heat may spread to adjacent components,causing a decrease in the performance of the element.To avoid this situation,the ability to directionally transfer heat energy is urgently needed.Therefore,thermal interface materials(TIMs)with directional high thermal conductivity are more critical in thermal management system of electronic devices.For decades,many efforts have been devoted to the design and fabrication of TIMs with high-directional thermal conductivity.Benefiting from the advantage in feasibility,low-cost and scalability,compositing with thermal conductive fillers has been proved to be promising strategy for fabricating the high-directional thermal conductive TIMs.This review summarizes the present preparation technologies of polymer composites with high-directional thermal conductivity based on structural engineering of thermal conductive fillers,focusing on the manufacturing process,mechanisms,achievements,advantages and disadvantages of different technologies.Finally,we summarize the existing problems and potential challenges in the field of directional high thermal conductivity composites. 展开更多
关键词 preparation technologies directional networks polymer composites high-directional thermal conductivity
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Fully Distributed Nash Equilibrium Seeking for High-Order Players With Actuator Limitations 被引量:4
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作者 Maojiao Ye Qing-Long Han +1 位作者 Lei Ding Shengyuan Xu 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2023年第6期1434-1444,共11页
This paper explores the problem of distributed Nash equilibrium seeking in games, where players have limited knowledge on other players' actions. In particular, the involved players are considered to be high-order... This paper explores the problem of distributed Nash equilibrium seeking in games, where players have limited knowledge on other players' actions. In particular, the involved players are considered to be high-order integrators with their control inputs constrained within a pre-specified region. A linear transformation for players' dynamics is firstly utilized to facilitate the design of bounded control inputs incorporating multiple saturation functions. By introducing consensus protocols with adaptive and time-varying gains, the unknown actions for players are distributively estimated. Then, a fully distributed Nash equilibrium seeking strategy is exploited, showcasing its remarkable properties: (1) ensuring the boundedness of control inputs;(2) avoiding any global information/parameters;and (3) allowing the graph to be directed. Based on Lyapunov stability analysis, it is theoretically proved that the proposed distributed control strategy can lead all the players' actions to the Nash equilibrium. Finally, an illustrative example is given to validate effectiveness of the proposed method. 展开更多
关键词 Actuator limitation directed networks GAMES Nash equilibrium
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MLDA:a multi-level k-degree anonymity scheme on directed social network graphs
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作者 Yuanjing HAO Long LI +1 位作者 Liang CHANG Tianlong GU 《Frontiers of Computer Science》 SCIE EI CSCD 2024年第2期199-215,共17页
With the emergence of network-centric data,social network graph publishing is conducive to data analysts to mine the value of social networks,analyze the social behavior of individuals or groups,implement personalized... With the emergence of network-centric data,social network graph publishing is conducive to data analysts to mine the value of social networks,analyze the social behavior of individuals or groups,implement personalized recommendations,and so on.However,published social network graphs are often subject to re-identification attacks from adversaries,which results in the leakage of users’privacy.The-anonymity technology is widely used in the field of graph publishing,which is quite effective to resist re-identification attacks.However,the current researches still exist some issues to be solved:the protection of directed graphs is less concerned than that of undirected graphs;the protection of graph structure is often ignored while achieving the protection of nodes’identities;the same protection is performed for different users,which doesn’t meet the different privacy requirements of users.Therefore,to address the above issues,a multi-level-degree anonymity(MLDA)scheme on directed social network graphs is proposed in this paper.First,node sets with different importance are divided by the firefly algorithm and constrained connectedness upper approximation,and they are performed different-degree anonymity protection to meet the different privacy requirements of users.Second,a new graph anonymity method is proposed,which achieves the addition and removal of edges with the help of fake nodes.In addition,to improve the utility of the anonymized graph,a new edge cost criterion is proposed,which is used to select the most appropriate edge to be removed.Third,to protect the community structure of the original graph as much as possible,fake nodes contained in a same community are merged prior to fake nodes contained in different communities.Experimental results on real datasets show that the newly proposed MLDA scheme is effective to balance the privacy and utility of the anonymized graph. 展开更多
关键词 directed social network graph graph publishing k-degree anonymity community structure graph utility
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Theory and Experiments on Enclosing Control of Multi-Agent Systems 被引量:4
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作者 Yihui Wang Yanfei Liu Zhong Wang 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2021年第10期1677-1685,共9页
This paper proposes a control strategy called enclosing control.This strategy can be described as follows:the followers design their control inputs based on the state information of neighbor agents and move to specifi... This paper proposes a control strategy called enclosing control.This strategy can be described as follows:the followers design their control inputs based on the state information of neighbor agents and move to specified positions.The convex hull formed by these followers contains the leaders.We use the single-integrator model to describe the dynamics of the agents and proposes a continuous-time control protocol and a sampled-data based protocol for multi-agent systems with stationary leaders with fixed network topology.Then the state differential equations are analyzed to obtain the parameter requirements for the system to achieve convergence.Moreover,the conditions achieving enclosing control are established for both protocols.A special enclosing control with no leader located on the convex hull boundary under the protocols is studied,which can effectively prevent enclosing control failures caused by errors in the system.Moreover,several simulations are proposed to validate theoretical results and compare the differences between the three control protocols.Finally,experimental results on the multi-robot platform are provided to verify the feasibility of the protocol in the physical system. 展开更多
关键词 Cooperative control directed network topology enclosing control leader-following multi-agent systems
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Surface Coverage Algorithm in Directional Sensor Networks for Three-Dimensional Complex Terrains 被引量:5
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作者 Fu Xiao Xiekun Yang +3 位作者 Meng Yang Lijuan Sun Ruchuan Wang Panlong Yang 《Tsinghua Science and Technology》 SCIE EI CAS CSCD 2016年第4期397-406,共10页
Coverage is an important issue in the area of wireless sensor networks, which reflects the monitoring quality of the sensor networks in scenes. Most sensor coverage research focuses on the ideal two-dimensional (2-D... Coverage is an important issue in the area of wireless sensor networks, which reflects the monitoring quality of the sensor networks in scenes. Most sensor coverage research focuses on the ideal two-dimensional (2-D) plane and full three-dimensional (3-D) space. However, in many real-world applications, the target field is a 3-D complex surface, which makes conventional methods unsuitable. In this paper, we study the coverage problem in directional sensor networks for complex 3-D terrains, and design a new surface coverage algorithm. Based on a 3-D directional sensing model of nodes, this algorithm employs grid division, simulated annealing, and local optimum ideas to improve the area coverage ratio by optimizing the position coordinates and the deviation angles of the nodes, which results in coverage enhancement for complex 3-D terrains. We also conduct extensive simulations to evaluate the performance of our algorithms. 展开更多
关键词 directional sensor networks surface coverage simulated annealing complex terrains
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Deploy Efficiency Driven k-Barrier Construction Scheme Based on Target Circle in Directional Sensor Network 被引量:2
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作者 Xing-Gang Fan Zhi-Cong Che +3 位作者 Feng-Dan Hu Tao Liu Jin-Shan Xu Xiao-Long Zhou 《Journal of Computer Science & Technology》 SCIE EI CSCD 2020年第3期647-664,共18页
With the increasing demand for security,building strong barrier coverage in directional sensor networks is important for effectively detecting un-authorized intrusions.In this paper,we propose an efficient scheme to f... With the increasing demand for security,building strong barrier coverage in directional sensor networks is important for effectively detecting un-authorized intrusions.In this paper,we propose an efficient scheme to form the strong barrier coverage by adding the mobile nodes one by one into the barrier.We first present the concept of target circle which determines the appropriate residence region and working direction of any candidate node to be added.Then we select the optimal relay sensor to be added into the current barrier based on its input-output ratio(barrier weight)which reflects the extension of barrier coverage.This strategy looses the demand of minimal required sensor nodes(maximal gain of each sensor)or maximal lifetime of one single barrier,leading to an augmentation of sensors to be used.Numerical simulation results show that,compared with the available schemes,the proposed method significantly reduces the minimal deploy density required to establish k-barrier,and increases the total service lifetime with a high deploy efficiency. 展开更多
关键词 directional sensor network barrier coverage target circle deploy efficiency
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Linear and nonlinear generalized consensuses of multi-agent systems 被引量:1
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作者 过榴晓 胡满峰 +1 位作者 胡爱花 徐振源 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第5期167-171,共5页
Consensus in directed networks of multiple agents, as an important topic, has become an active research subject. Over the past several years, some types of consensus problems have been studied. In this paper, we propo... Consensus in directed networks of multiple agents, as an important topic, has become an active research subject. Over the past several years, some types of consensus problems have been studied. In this paper, we propose a novel type of consensus, the generalized consensus (GC), which includes the traditional consensus, the anti-consensus, and the cluster consensus as its special cases. Based on the Lyapunov's direct method and the graph theory, a simple control algorithm is designed to achieve the generalized consensus in a network of agents. Numerical simulations of linear and nonlinear GC are used to verify the effectiveness of the theoretical analysis. 展开更多
关键词 generalized consensus multi-agent system directed network connection topology
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Flocking of multi-robot systems with connectivity maintenance on directed graphs
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作者 Yutian Mao Lihua Dou +1 位作者 Hao Fang Jie Chen 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第3期470-482,共13页
Analysis and design techniques for cooperative flocking of nonholonomic multi-robot systems with connectivity maintenance on directed graphs are presented. First, a set of bounded and smoothly distributed control prot... Analysis and design techniques for cooperative flocking of nonholonomic multi-robot systems with connectivity maintenance on directed graphs are presented. First, a set of bounded and smoothly distributed control protocols are devised via carefully designing a class of bounded artificial potential fields (APF) which could guarantee the connectivity maintenance, col ision avoidance and distance stabilization simultaneously during the system evolution. The connectivity of the underlying network can be preserved, and the desired stable flocking behavior can be achieved provided that the initial communication topology is strongly connected rather than undirected or balanced, which relaxes the constraints for group topology and extends the previous work to more generalized directed graphs. Furthermore, the proposed control algorithm is extended to solve the flocking problem with a virtual leader. In this case, it is shown that al robots can asymptotically move with the desired velocity and orientation even if there is only one informed robot in the team. Finally, nontrivial simulations and experiments are conducted to verify the effectiveness of the proposed algorithm. 展开更多
关键词 multi-robot system nonholonomic kinematics FLOCKING directed network connectivity maintenance bounded artificial potential field (APF).
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Event-Triggered Zero-Gradient-Sum Distributed Algorithm for Convex Optimization with Time-Varying Communication Delays and Switching Directed Topologies
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作者 Lei Ye 《Journal of Applied Mathematics and Physics》 2022年第4期1247-1265,共19页
Nowadays, distributed optimization algorithms are widely used in various complex networks. In order to expand the theory of distributed optimization algorithms in the direction of directed graph, the distributed conve... Nowadays, distributed optimization algorithms are widely used in various complex networks. In order to expand the theory of distributed optimization algorithms in the direction of directed graph, the distributed convex optimization problem with time-varying delays and switching topologies in the case of directed graph topology is studied. The event-triggered communication mechanism is adopted, that is, the communication between agents is determined by the trigger conditions, and the information exchange is carried out only when the conditions are met. Compared with continuous communication, this greatly saves network resources and reduces communication cost. Using Lyapunov-Krasovskii function method and inequality analysis, a new sufficient condition is proposed to ensure that the agent state finally reaches the optimal state. The upper bound of the maximum allowable delay is given. In addition, Zeno behavior will be proved not to exist during the operation of the algorithm. Finally, a simulation example is given to illustrate the correctness of the results in this paper. 展开更多
关键词 Distributed Convex Optimisation Zero-Gradient-Sum Algorithm Event-Triggered Time-Varying Delays Switching network Multi-Agent System Directed network
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Two-dimensional gain cross-grating based on spatial modulation of active Raman gain
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作者 王丽 周凤雪 +2 位作者 郭洪菊 钮月萍 龚尚庆 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第11期265-269,共5页
Based on the spatial modulation of active Raman gain,a two-dimensional gain cross-grating is theoretically proposed.As the probe field propagates along the z direction and passes through the intersectant region of the... Based on the spatial modulation of active Raman gain,a two-dimensional gain cross-grating is theoretically proposed.As the probe field propagates along the z direction and passes through the intersectant region of the two orthogonal standingwave fields in the x-y plane,it can be effectively diffracted into the high-order directions,and the zero-order diffraction intensity is amplified at the same time.In comparison with the two-dimensional electromagnetically induced cross-grating based on electromagnetically induced transparency,the two-dimensional gain cross-grating has much higher diffraction intensities in the first-order and the high-order directions.Hence,it is more suitable to be utilized as all-optical switching and routing in optical networking and communication. 展开更多
关键词 grating routing networking utilized directions transparency switching normalized resonant created
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