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A Survey of Distributed Algorithms for Aggregative Games
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作者 Huaqing Li Jun Li +2 位作者 Liang Ran Lifeng Zheng Tingwen Huang 《IEEE/CAA Journal of Automatica Sinica》 2025年第5期859-871,共13页
Game theory-based models and design tools have gained substantial prominence for controlling and optimizing behavior within distributed engineering systems due to the inherent distribution of decisions among individua... Game theory-based models and design tools have gained substantial prominence for controlling and optimizing behavior within distributed engineering systems due to the inherent distribution of decisions among individuals.In non-cooperative settings,aggregative games serve as a mathematical framework model for the interdependent optimal decision-making problem among a group of non-cooperative players.In such scenarios,each player's decision is influenced by an aggregation of all players'decisions.Nash equilibrium(NE)seeking in aggregative games has emerged as a vibrant topic driven by applications that harness the aggregation property.This paper presents a comprehensive overview of the current research on aggregative games with a focus on communication topology.A systematic classification is conducted on distributed algorithm research based on communication topologies such as undirected networks,directed networks,and time-varying networks.Furthermore,it sorts out the challenges and compares the algorithms'convergence performance.It also delves into real-world applications of distributed optimization techniques grounded in aggregative games.Finally,it proposes several challenges that can guide future research directions. 展开更多
关键词 Aggregative game distributed algorithm Nash equilibrium(NE) networked control
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Spatial Grasp Model for Distributed Management and Its Comparison With Traditional Algorithms 被引量:1
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作者 Peter Simon Sapaty 《International Relations and Diplomacy》 2025年第3期164-179,共16页
The word“spatial”fundamentally relates to human existence,evolution,and activity in terrestrial and even celestial spaces.After reviewing the spatial features of many areas,the paper describes basics of high level m... The word“spatial”fundamentally relates to human existence,evolution,and activity in terrestrial and even celestial spaces.After reviewing the spatial features of many areas,the paper describes basics of high level model and technology called Spatial Grasp for dealing with large distributed systems,which can provide spatial vision,awareness,management,control,and even consciousness.The technology description includes its key Spatial Grasp Language(SGL),self-evolution of recursive SGL scenarios,and implementation of SGL interpreter converting distributed networked systems into powerful spatial engines.Examples of typical spatial scenarios in SGL include finding shortest path tree and shortest path between network nodes,collecting proper information throughout the whole world,elimination of multiple targets by intelligent teams of chasers,and withstanding cyber attacks in distributed networked systems.Also this paper compares Spatial Grasp model with traditional algorithms,confirming universality of the former for any spatial systems,while the latter just tools for concrete applications. 展开更多
关键词 spatial awareness spatial control spatial consciousness Spatial Grasp Technology Spatial Grasp Language spatial scenarios cyber attacks distributed algorithms mobile agents
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Stability analysis of distributed Kalman filtering algorithm for stochastic regression model
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作者 Siyu Xie Die Gan Zhixin Liu 《Control Theory and Technology》 2025年第2期161-175,共15页
The work proposes a distributed Kalman filtering(KF)algorithm to track a time-varying unknown signal process for a stochastic regression model over network systems in a cooperative way.We provide the stability analysi... The work proposes a distributed Kalman filtering(KF)algorithm to track a time-varying unknown signal process for a stochastic regression model over network systems in a cooperative way.We provide the stability analysis of the proposed distributed KF algorithm without independent and stationary signal assumptions,which implies that the theoretical results are able to be applied to stochastic feedback systems.Note that the main difficulty of stability analysis lies in analyzing the properties of the product of non-independent and non-stationary random matrices involved in the error equation.We employ analysis techniques such as stochastic Lyapunov function,stability theory of stochastic systems,and algebraic graph theory to deal with the above issue.The stochastic spatio-temporal cooperative information condition shows the cooperative property of multiple sensors that even though any local sensor cannot track the time-varying unknown signal,the distributed KF algorithm can be utilized to finish the filtering task in a cooperative way.At last,we illustrate the property of the proposed distributed KF algorithm by a simulation example. 展开更多
关键词 distributed Kalman filtering algorithm Stochastic cooperative information condition Sensor networks (L_(p))-exponential stability Stochastic regression model
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Obstacle avoidance for multi-missile network via distributed coordination algorithm 被引量:14
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作者 Zhao Jiang Zhou Rui 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2016年第2期441-447,共7页
A distributed coordination algorithm is proposed to enhance the engagement of the multi-missile network in consideration of obstacle avoidance. To achieve a cooperative interception, the guidance law is developed in a... A distributed coordination algorithm is proposed to enhance the engagement of the multi-missile network in consideration of obstacle avoidance. To achieve a cooperative interception, the guidance law is developed in a simple form that consists of three individual components for tar- get capture, time coordination and obstacle avoidance. The distributed coordination algorithm enables a group of interceptor missiles to reach the target simultaneously, even if some member in the multi-missile network can only collect the information from nearest neighbors. The simula- tion results show that the guidance strategy provides a feasible tool to implement obstacle avoid- ance for the multi-missile network with satisfactory accuracy of target capture. The effects of the gain parameters are also discussed to evaluate the proposed approach. 展开更多
关键词 Cooperative guidance distributed algorithms Impact time Missile guidance Multiple missiles Obstacle avoidance Proportional navigation
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A Fully Distributed Approach to Optimal Energy Scheduling of Users and Generators Considering a Novel Combined Neurodynamic Algorithm in Smart Grid 被引量:6
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作者 Chentao Xu Xing He 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2021年第7期1325-1335,共11页
A fully distributed microgrid system model is presented in this paper.In the user side,two types of load and plug-in electric vehicles are considered to schedule energy for more benefits.The charging and discharging s... A fully distributed microgrid system model is presented in this paper.In the user side,two types of load and plug-in electric vehicles are considered to schedule energy for more benefits.The charging and discharging states of the electric vehicles are represented by the zero-one variables with more flexibility.To solve the nonconvex optimization problem of the users,a novel neurodynamic algorithm which combines the neural network algorithm with the differential evolution algorithm is designed and its convergence speed is faster.A distributed algorithm with a new approach to deal with the inequality constraints is used to solve the convex optimization problem of the generators which can protect their privacy.Simulation results and comparative experiments show that the model and algorithms are effective. 展开更多
关键词 Differential evolution algorithm distributed algorithm electric vehicle neural network zero-one variable.
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Energy Economic Dispatch for Photovoltaic-Storage via Distributed Event-Triggered Surplus Algorithm 被引量:2
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作者 Kaicheng Liu Chen Liang +2 位作者 Naiyue Wu Xiaoyang Dong Hui Yu 《Energy Engineering》 EI 2024年第9期2621-2637,共17页
This paper presents a novel approach to economic dispatch in smart grids equipped with diverse energy devices.This method integrates features including photovoltaic(PV)systems,energy storage coupling,varied energy rol... This paper presents a novel approach to economic dispatch in smart grids equipped with diverse energy devices.This method integrates features including photovoltaic(PV)systems,energy storage coupling,varied energy roles,and energy supply and demand dynamics.The systemmodel is developed by considering energy devices as versatile units capable of fulfilling various functionalities and playing multiple roles simultaneously.To strike a balance between optimality and feasibility,renewable energy resources are modeled with considerations for forecasting errors,Gaussian distribution,and penalty factors.Furthermore,this study introduces a distributed event-triggered surplus algorithm designed to address the economic dispatch problem by minimizing production costs.Rooted in surplus theory and finite time projection,the algorithm effectively rectifies network imbalances caused by directed graphs and addresses local inequality constraints.The algorithm greatly reduces the communication burden through event triggering mechanism.Finally,both theoretical proofs and numerical simulations verify the convergence and event-triggered nature of the algorithm. 展开更多
关键词 Fully distributed algorithm economic dispatch directed graph renewable energy resource
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Distributed Algorithms for Event Reporting in Mobile-Sink WSNs for Internet of Things 被引量:5
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作者 Catalina Aranzazu-Suescun Mihaela Cardei 《Tsinghua Science and Technology》 SCIE EI CAS CSCD 2017年第4期413-426,共14页
Wireless Sensor Networks(WSNs) have many applications, such as climate monitoring systems, fire detection, smart homes, and smart cities. It is expected that WSNs will be integrated into the Internet of Things(IoT... Wireless Sensor Networks(WSNs) have many applications, such as climate monitoring systems, fire detection, smart homes, and smart cities. It is expected that WSNs will be integrated into the Internet of Things(IoT)and participate in various tasks. WSNs play an important role monitoring and reporting environment information and collecting surrounding context. In this paper we consider a WSN deployed for an application such as environment monitoring, and a mobile sink which acts as the gateway between the Internet and the WSN. Data gathering is a challenging problem in WSNs and in the IoT because the information has to be available quickly and effectively without delays and redundancies. In this paper we propose several distributed algorithms for composite event detection and reporting to a mobile sink. Once data is collected by the sink, it can be shared using the IoT infrastructure. We analyze the performance of our algorithms using WSNet simulator, which is specially designed for event-based WSNs. We measure various metrics such as average residual energy, percentage of composite events processed successfully at the sink, and the average number of hops to reach the sink. 展开更多
关键词 composite events distributed algorithm energy efficiency event-based clustering Internet of Things mobile sink wireless sensor networks
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A Distributed Algorithm for Determining Minimal Covers of Acyclic Database Schemes
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作者 叶新铭 《Journal of Computer Science & Technology》 SCIE EI CSCD 1994年第3期204-214,共11页
Acyclic databases possess several desirable properties for their design and use. Adistributed algorithm is proposed for determining a minimal cover of an alpha-, beta-,gamma-, or Berge-acyclic database scheme over a s... Acyclic databases possess several desirable properties for their design and use. Adistributed algorithm is proposed for determining a minimal cover of an alpha-, beta-,gamma-, or Berge-acyclic database scheme over a set of attributes in a distributedenvironment. 展开更多
关键词 Alpha- beta- gamma- Berge-acyclic depth-first-search tree distributed algorithm minimal cover HYPERGRAPH
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A Distributed Algorithm for Multi-Region Problemin BEM
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作者 胡庆生 汪晓岩 庄镇泉 《Journal of Computer Science & Technology》 SCIE EI CSCD 1999年第6期558-564,共7页
The situation of multi-region problem may often appear when boundary element method (BEM) is applied in practical problems especially in VLSI-CAD.It is difficult to deal with this problem if traditional methods are us... The situation of multi-region problem may often appear when boundary element method (BEM) is applied in practical problems especially in VLSI-CAD.It is difficult to deal with this problem if traditional methods are used. Particularly,when the problem to be solved contains a lot of materials, the advantages of usingBEM such as simplicity) convenience and rapidity will be weakened due to the complexity of solving complex boundary element equation. In this paper a distributedalgorithm for multi-region problem in BEM is presented. This algorithm has beenimplemented in a distributed system consisting of 3 workstations to extract VLSIlayout parameters. The results show that the calculation time of this distributedalgorithm is less than that of the traditional methods. The results also demonstratethat this algorithm can speed up the computation and has the features of parallelismand high efficiency. 展开更多
关键词 boundary element method (BEM) distributed algorithm VLSICAD
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Distributed multicast routing algorithm with dynamic performance in multimedia networks
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作者 Zhu Baoping Zhang Kun 《Engineering Sciences》 EI 2009年第3期28-34,共7页
The delay and DVBMT problem is known to be NP-complete. In this paper,an efficient distributed dynamic multicast routing algorithm was proposed to produce routing trees with delay and delay variation constraints. The ... The delay and DVBMT problem is known to be NP-complete. In this paper,an efficient distributed dynamic multicast routing algorithm was proposed to produce routing trees with delay and delay variation constraints. The proposed algorithm is fully distributed,and supports the dynamic reorganizing of the multicast tree in response to changes for the destination. Simulations demonstrate that our algorithm is better in terms of tree delay and routing success ratio as compared with other existing algorithms,and performs excellently in delay variation performance under lower time complexity,which ensures it to support the requirements of real-time multimedia communications more effectively. 展开更多
关键词 multicast routing distributed algorithm dynamic performance delay and delay variation-bounded multimedia networks
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Distributed consensus algorithm for networked Euler-Lagrange systems with self-delays and uncertainties 被引量:3
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作者 Xu Zhu dianguo Yan Yaohong Qu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2012年第6期898-905,共8页
A distributed coordinated consensus problem for multiple networked Euler-Lagrange systems is studied.The communication between agents is subject to time delays,unknown parameters and nonlinear inputs,but only with the... A distributed coordinated consensus problem for multiple networked Euler-Lagrange systems is studied.The communication between agents is subject to time delays,unknown parameters and nonlinear inputs,but only with their states available for measurement.When the communication topology of the system is connected,an adaptive control algorithm with selfdelays and uncertainties is suggested to guarantee global full-state synchro-nization that the difference between the agent's positions and ve-locities asymptotically converges to zero.Moreover,the distributed sliding-mode law is given for chaotic systems with nonlinear inputs to compensate for the effects of nonlinearity.Finally,simulation results show the effectiveness of the proposed control algorithm. 展开更多
关键词 networked multi-agent system Euler-Lagrange(EL)system distributed consensus algorithm Lyapunov stability self-delay uncertainty.
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Distributed genetic algorithm for optimal planar arrays of aperture synthesis telescope
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作者 贺小箭 唐新怀 +1 位作者 尤晋元 文建国 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2004年第3期419-425,共7页
Sparse arrays of telescopes have a limited (u, v)-plane coverage. In this paper, an optimization method for designing planar arrays of an aperture synthesis telescope is proposed that is based on distributed genetic a... Sparse arrays of telescopes have a limited (u, v)-plane coverage. In this paper, an optimization method for designing planar arrays of an aperture synthesis telescope is proposed that is based on distributed genetic algorithm. This distributed genetic algorithm is implemented on a network of workstations using community communication model. Such an aperture synthesis system performs with imperfection of (u, v) components caused by deviations and(or) some missing baselines. With the maximum (u, v)-plane coverage of this rotation-optimized array, the image of the source reconstructed by inverse Fourier transform is satisfactory. 展开更多
关键词 distributed genetic algorithm optical aperture synthesis optimum planar array (u v) -spectrum sampling.
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Study on the Distributed Routing Algorithm and Its Security for Peer-to-Peer Computing
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作者 ZHOUShi-jie 《Journal of Electronic Science and Technology of China》 2005年第2期187-188,共2页
关键词 peer-to-peer computing P2P distributed computing information security distributed routing algorithm bidding-electing algorithm one-way accumulator
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Topological optimization of metamaterial absorber based on improved estimation of distribution algorithm
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作者 TAO Shifei LIU Beichen +2 位作者 LIU Sixing WU Fan WANG Hao 《Journal of Systems Engineering and Electronics》 2025年第3期634-641,共8页
An improved estimation of distribution algorithm(IEDA)is proposed in this paper for efficient design of metamaterial absorbers.This algorithm establishes a probability model through the selected dominant groups and sa... An improved estimation of distribution algorithm(IEDA)is proposed in this paper for efficient design of metamaterial absorbers.This algorithm establishes a probability model through the selected dominant groups and samples from the model to obtain the next generation,avoiding the problem of building-blocks destruction caused by crossover and mutation.Neighboring search from artificial bee colony algorithm(ABCA)is introduced to enhance the local optimization ability and improved to raise the speed of convergence.The probability model is modified by boundary correction and loss correction to enhance the robustness of the algorithm.The proposed IEDA is compared with other intelligent algorithms in relevant references.The results show that the proposed IEDA has faster convergence speed and stronger optimization ability,proving the feasibility and effectiveness of the algorithm. 展开更多
关键词 METAMATERIAL topological optimization estimation of distribution algorithm
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Design and Application of a New Distributed Dynamic Spatio-Temporal Privacy Preserving Mechanisms
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作者 Jiacheng Xiong Xingshu Chen +1 位作者 Xiao Lan Liangguo Chen 《Computers, Materials & Continua》 2025年第8期2273-2303,共31页
In the era of big data,the growing number of real-time data streams often contains a lot of sensitive privacy information.Releasing or sharing this data directly without processing will lead to serious privacy informa... In the era of big data,the growing number of real-time data streams often contains a lot of sensitive privacy information.Releasing or sharing this data directly without processing will lead to serious privacy information leakage.This poses a great challenge to conventional privacy protection mechanisms(CPPM).The existing data partitioning methods ignore the number of data replications and information exchanges,resulting in complex distance calculations and inefficient indexing for high-dimensional data.Therefore,CPPM often fails to meet the stringent requirements of efficiency and reliability,especially in dynamic spatiotemporal environments.Addressing this concern,we proposed the Principal Component Enhanced Vantage-point tree(PEV-Tree),which is an enhanced data structure based on the idea of dimension reduction,and constructed a Distributed Spatio-Temporal Privacy Preservation Mechanism(DST-PPM)on it.In this work,principal component analysis and the vantage tree are used to establish the PEV-Tree.In addition,we designed three distributed anonymization algorithms for data streams.These algorithms are named CK-AA,CL-DA,and CT-CA,fulfill the anonymization rules of K-Anonymity,L-Diversity,and T-Closeness,respectively,which have different computational complexities and reliabilities.The higher the complexity,the lower the risk of privacy leakage.DST-PPM can reduce the dimension of high-dimensional information while preserving data characteristics and dividing the data space into vantage points based on distance.It effectively enhances the data processing workflow and increases algorithmefficiency.To verify the validity of the method in this paper,we conducted empirical tests of CK-AA,CL-DA,and CT-CA on conventional datasets and the PEV-Tree,respectively.Based on the big data background of the Internet of Vehicles,we conducted experiments using artificial simulated on-board network data.The results demonstrated that the operational efficiency of the CK-AA,CL-DA,and CT-CA is enhanced by 15.12%,24.55%,and 52.74%,respectively,when deployed on the PEV-Tree.Simultaneously,during homogeneity attacks,the probabilities of information leakage were reduced by 2.31%,1.76%,and 0.19%,respectively.Furthermore,these algorithms showcased superior utility(scalability)when executed across PEV-Trees of varying scales in comparison to their performance on conventional data structures.It indicates that DST-PPM offers marked advantages over CPPM in terms of efficiency,reliability,and scalability. 展开更多
关键词 Privacy preserving distributed anonymization algorithm VP-Tree data stream internet of vehicles
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Distributed three-dimensional cooperative guidance via receding horizon control 被引量:11
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作者 Zhao Jiang Zhou Rui 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2016年第4期972-983,共12页
The paper presents a new three-dimensional (3D) cooperative guidance approach by the receding horizon control (RHC) technique. The objective is to coordinate the impact time of a group of interceptor missiles against ... The paper presents a new three-dimensional (3D) cooperative guidance approach by the receding horizon control (RHC) technique. The objective is to coordinate the impact time of a group of interceptor missiles against the stationary target. The framework of a distributed RHC scheme is developed, in which each interceptor missile is assigned its own finite-horizon optimal control problem (FHOCP) and only shares the information with its neighbors. The solution of the local FHOCP is obtained by the constrained particle swarm optimization (PSO) method that is integrated into the distributed RHC framework with enhanced equality and inequality constraints. The numerical simulations show that the proposed guidance approach is feasible to implement the cooperative engagement with satisfied accuracy of target capture. Finally, the computation efficiency of the distributed RHC scheme is discussed in consideration of the PSO parameters, control update period and prediction horizon. (C) 2016 Chinese Society of Aeronautics and Astronautics. Production and hosting by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license. 展开更多
关键词 distributed algorithms Impact time Missile guidance Multiple missiles Particle swarm optimization (PSO) Receding horizon control (RHC) Three-dimensional (3D)
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Novel operating theatre scheduling method based on estimation of distribution algorithm 被引量:3
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作者 周炳海 殷萌 《Journal of Southeast University(English Edition)》 EI CAS 2016年第1期112-118,共7页
In order to improve the efficiency of operating rooms,reduce the costs for hospitals and improve the level of service qualities, a scheduling method was developed based on an estimation of distribution algorithm( EDA... In order to improve the efficiency of operating rooms,reduce the costs for hospitals and improve the level of service qualities, a scheduling method was developed based on an estimation of distribution algorithm( EDA). First, a scheduling problem domain is described. Based on assignment constraints and resource capacity constraints, the mathematical programming models are set up with an objective function to minimize the system makespan. On the basis of the descriptions mentioned above, a solution policy of generating feasible scheduling solutions is established. Combined with the specific constraints of operating theatres, the EDA-based algorithm is put forward to solve scheduling problems. Finally, simulation experiments are designed to evaluate the scheduling method. The orthogonal table is chosen to determine the parameters in the proposed method. Then the genetic algorithm and the particle swarm optimization algorithm are chosen for comparison with the EDA-based algorithm, and the results indicate that the proposed method can decrease the makespan of the surgical system regardless of the size of operations. Moreover, the computation time of the EDA-based algorithm is only approximately 5 s when solving the large scale problems, which means that the proposed algorithm is suitable for carrying out an on-line scheduling optimization of the patients. 展开更多
关键词 operating theatre scheduling estimation of distribution algorithm MAKESPAN
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Distributed localization for anchor-free sensor networks 被引量:9
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作者 Cui Xunxue Shan Zhiguan Liu Jianjun 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2008年第3期405-418,共14页
Geographic location of nodes is very useful in a sensor network. Previous localization algorithms assume that there exist some anchor nodes in this kind of network, and then other nodes are estimated to create their c... Geographic location of nodes is very useful in a sensor network. Previous localization algorithms assume that there exist some anchor nodes in this kind of network, and then other nodes are estimated to create their coordinates. Once there are not anchors to be deployed, those localization algorithms will be invalidated. Many papers in this field focus on anchor-based solutions. The use of anchors introduces many limitations, since anchors require external equipments such as global position system, cause additional power consumption. A novel positioning algorithm is proposed to use a virtual coordinate system based on a new concept--virtual anchor. It is executed in a distributed fashion according to the connectivity of a node and the measured distances to its neighbors. Both the adjacent member information and the ranging distance result are combined to generate the estimated position of a network, one of which is independently adopted for localization previously. At the position refinement stage the intermediate estimation of a node begins to be evaluated on its reliability for position mutation; thus the positioning optimization process of the whole network is avoided falling into a local optimal solution. Simulation results prove that the algorithm can resolve the distributed localization problem for anchor-free sensor networks, and is superior to previous methods in terms of its positioning capability under a variety of circumstances. 展开更多
关键词 anchor-free localization distributed algorithm position estimation sensor networks.
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Robust Airfoil Optimization with Multi-objective Estimation of Distribution Algorithm 被引量:7
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作者 钟小平 《Chinese Journal of Aeronautics》 SCIE EI CSCD 2008年第4期289-295,共7页
A transonic airfoil designed by means of classical point-optimization may result in its dramatically inferior performance under off-design conditions. To overcome this shortcoming, robust design is proposed to find ou... A transonic airfoil designed by means of classical point-optimization may result in its dramatically inferior performance under off-design conditions. To overcome this shortcoming, robust design is proposed to find out the optimal profile of an airfoil to maintain its performance in an uncertain environment. The robust airfoil optimization is aimed to minimize mean values and variances of drag coefficients while satisfying the lift and thickness constraints over a range of Mach numbers. A multi-objective estimation of distribution algorithm is applied to the robust airfoil optimization on the base of the RAE2822 benchmark airfoil. The shape of the airfoil is obtained through superposing ten Hick-Henne shape functions upon the benchmark airfoil. A set of design points is selected according to a uniform design table for aerodynamic evaluation. A Kriging model of drag coefficient is constructed with those points to reduce computing costs. Over the Mach range from 0.7 to 0.8, the airfoil generated by the robust optimization has a configuration characterized by supercritical airfoil with low drag coefficients. The small fluctuation in its drag coefficients means that the performance of the robust airfoil is insensitive to variation of Mach number. 展开更多
关键词 airfoil robust design multi-objective estimation of distribution algorithm uncertain environment drag FLUCTUATION
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Distributed best response dynamics for Nash equilibrium seeking in potential games 被引量:2
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作者 Shijie HUANG Peng YI 《Control Theory and Technology》 EI CSCD 2020年第3期324-332,共9页
In this paper,we consider distributed Nash equilibrium(NE)seeking in potential games over a multi-agent network,where each agent can not observe the actions of all its rivals.Based on the best response dynamics,we des... In this paper,we consider distributed Nash equilibrium(NE)seeking in potential games over a multi-agent network,where each agent can not observe the actions of all its rivals.Based on the best response dynamics,we design a distributed NE seeking algorithm by incorporating the non-smooth finite-time average tracking dynamics,where each agent only needs to know its own action and exchange information with its neighbours through a communication graph.We give a sufficient condition for the Lipschitz continuity of the best response mapping for potential games,and then prove the convergence of the proposed algorithm based on the Lyapunov theory.Numerical simulations are given to verify the resultandillustrate the effectiveness of the algorithm. 展开更多
关键词 distributed algorithms Nash equilibrium seeking best response dynamics non-smooth finite-time tracking dynamics potential games
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