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Design and pricing of maintenance service contract based on Nash non-cooperative game approach
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作者 SU Chun HUANG Kui 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2024年第1期118-129,共12页
Nowadays manufacturers are facing fierce challenge.Apart from the products,providing customers with multiple maintenance options in the service contract becomes more popular,since it can help to improve customer satis... Nowadays manufacturers are facing fierce challenge.Apart from the products,providing customers with multiple maintenance options in the service contract becomes more popular,since it can help to improve customer satisfaction,and ultimately promote sales and maximize profit for the manufacturer.By considering the combinations of corrective maintenance and preventive maintenance,totally three types of maintenance service contracts are designed.Moreover,attractive incentive and penalty mechanisms are adopted in the contracts.On this basis,Nash non-cooperative game is applied to analyze the revenue for both the manufacturer and customers,and so as to optimize the pricing mechanism of maintenance service contract and achieve a win-win situation.Numerical experiments are conducted.The results show that by taking into account the incentive and penalty mechanisms,the revenue can be improved for both the customers and manufacturer.Moreover,with the increase of repair rate and improvement factor in the preventive maintenance,the revenue will increase gradually for both the parties. 展开更多
关键词 maintenance service contract Nash game incentive and penalty mechanism corrective maintenance preventive maintenance
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Non-Cooperative Game of Coordinated Scheduling of Parallel Machine Production and Transportation in Shared Manufacturing
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作者 Peng Liu Ke Xu Hua Gong 《Computers, Materials & Continua》 SCIE EI 2023年第7期239-258,共20页
Given the challenges of manufacturing resource sharing and competition in the modern manufacturing industry,the coordinated scheduling problem of parallel machine production and transportation is investigated.The prob... Given the challenges of manufacturing resource sharing and competition in the modern manufacturing industry,the coordinated scheduling problem of parallel machine production and transportation is investigated.The problem takes into account the coordination of production and transportation before production as well as the disparities in machine spatial position and performance.A non-cooperative game model is established,considering the competition and self-interest behavior of jobs from different customers for machine resources.The job from different customers is mapped to the players in the game model,the corresponding optional processing machine and location are mapped to the strategy set,and the makespan of the job is mapped to the payoff.Then the solution of the scheduling model is transformed into the Nash equilibrium of the non-cooperative game model.A Nash equilibrium solution algorithm based on the genetic algorithm(NEGA)is designed,and the effective solution of approximate Nash equilibrium for the game model is realized.The fitness function,single-point crossover operator,and mutation operator are derived from the non-cooperative game model’s characteristics and the definition of Nash equilibrium.Rules are also designed to avoid the generation of invalid offspring chromosomes.The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes.Compared with other algorithms such as heuristic algorithms(FCFS,SPT,and LPT),the simulated annealing algorithm(SA),and the particle swarm optimization algorithm(PSO),experimental results show that the proposed NE-GA algorithm has obvious performance advantages. 展开更多
关键词 non-cooperative game shared manufacturing parallel machine coordinated production and transportation genetic algorithm
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Peer-to-Peer Energy Trading Method of Multi-Virtual Power Plants Based on Non-Cooperative Game
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作者 Jingjing Bai Hongyi Zhou +1 位作者 Zheng Xu Yu Zhong 《Energy Engineering》 EI 2023年第5期1163-1183,共21页
The current electricity market fails to consider the energy consumption characteristics of transaction subjects such as virtual power plants.Besides,the game relationship between transaction subjects needs to be furth... The current electricity market fails to consider the energy consumption characteristics of transaction subjects such as virtual power plants.Besides,the game relationship between transaction subjects needs to be further explored.This paper proposes a Peer-to-Peer energy trading method for multi-virtual power plants based on a non-cooperative game.Firstly,a coordinated control model of public buildings is incorporated into the scheduling framework of the virtual power plant,considering the energy consumption characteristics of users.Secondly,the utility functions of multiple virtual power plants are analyzed,and a non-cooperative game model is established to explore the game relationship between electricity sellers in the Peer-to-Peer transaction process.Finally,the influence of user energy consumption characteristics on the virtual power plant operation and the Peer-to-Peer transaction process is analyzed by case studies.Furthermore,the effect of different parameters on the Nash equilibrium point is explored,and the influence factors of Peer-to-Peer transactions between virtual power plants are summarized.According to the obtained results,compared with the central air conditioning set as constant temperature control strategy,the flexible control strategy proposed in this paper improves the market power of each VPP and the overall revenue of the VPPs.In addition,the upper limit of the service quotation of the market operator have a great impact on the transaction mode of VPPs.When the service quotation decreases gradually,the P2P transaction between VPPs is more likely to occur. 展开更多
关键词 Virtual power plant PEER-TO-PEER energy trading public building non-cooperative game
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Coordinated Scheduling of Two-Agent Production and Transportation Based on Non-Cooperative Game
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作者 Ke Xu Peng Liu Hua Gong 《Intelligent Automation & Soft Computing》 SCIE 2023年第6期3279-3294,共16页
A two-agent production and transportation coordinated scheduling problem in a single-machine environment is suggested to compete for one machine from different downstream production links or various consumers.The jobs... A two-agent production and transportation coordinated scheduling problem in a single-machine environment is suggested to compete for one machine from different downstream production links or various consumers.The jobs of two agents compete for the processing position on a machine,and after the pro-cessed,they compete for the transport position on a transport vehicle to be trans-ported to two agents.The two agents have different objective functions.The objective function of the first agent is the sum of the makespan and the total trans-portation time,whereas the objective function of the second agent is the sum of the total completion time and the total transportation time.Given the competition between two agents for machine resources and transportation resources,a non-cooperative game model with agents as game players is established.The job pro-cessing position and transportation position corresponding to the two agents are mapped as strategies,and the corresponding objective function is the utility func-tion.To solve the game model,an approximate Nash equilibrium solution algo-rithm based on an improved genetic algorithm(NE-IGA)is proposed.The genetic operation based on processing sequence and transportation sequence,as well as the fitness function based on Nash equilibrium definition,are designed based on the features of the two-agent production and transportation coordination scheduling problem.The effectiveness of the proposed algorithm is demonstrated through numerical experiments of various sizes.When compared to heuristic rules such as the Longest Processing Time first(LPT)and the Shortest Processing Time first(SPT),the objective function values of the two agents are reduced by 4.3%and 2.6% on average. 展开更多
关键词 Coordinated scheduling two-agent production and transportation non-cooperative game genetic algorithm
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QoS awared power and admission controls based on non-cooperative game theory in wireless networks
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作者 张阳 朱世华 李峰 《Journal of Pharmaceutical Analysis》 SCIE CAS 2008年第3期149-154,共6页
In order to better accommodate heterogeneous quality of service (QoS) in wireless networks, an algorithm called QoS-aware power and admission controls (QAPAC) is proposed. The system is modeled as a non-cooperative ga... In order to better accommodate heterogeneous quality of service (QoS) in wireless networks, an algorithm called QoS-aware power and admission controls (QAPAC) is proposed. The system is modeled as a non-cooperative game where the users adjust their transmit powers to maximize the utility, thus restraining the interferences. By using adaptive utility functions and tunable pricing parameters according to QoS levels, this algorithm can well meet different QoS requirements and improve system capacity compared with those that ignore the QoS differences. 展开更多
关键词 power and admission control non-cooperative game utility function PRICING heterogeneous QoS
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An Optimized Resource Scheduling Strategy for Hadoop Speculative Execution Based on Non-cooperative Game Schemes
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作者 Yinghang Jiang Qi Liu +3 位作者 Williams Dannah Dandan Jin Xiaodong Liu Mingxu Sun 《Computers, Materials & Continua》 SCIE EI 2020年第2期713-729,共17页
Hadoop is a well-known parallel computing system for distributed computing and large-scale data processes.“Straggling”tasks,however,have a serious impact on task allocation and scheduling in a Hadoop system.Speculat... Hadoop is a well-known parallel computing system for distributed computing and large-scale data processes.“Straggling”tasks,however,have a serious impact on task allocation and scheduling in a Hadoop system.Speculative Execution(SE)is an efficient method of processing“Straggling”Tasks by monitoring real-time running status of tasks and then selectively backing up“Stragglers”in another node to increase the chance to complete the entire mission early.Present speculative execution strategies meet challenges on misjudgement of“Straggling”tasks and improper selection of backup nodes,which leads to inefficient implementation of speculative executive processes.This paper has proposed an Optimized Resource Scheduling strategy for Speculative Execution(ORSE)by introducing non-cooperative game schemes.The ORSE transforms the resource scheduling of backup tasks into a multi-party non-cooperative game problem,where the tasks are regarded as game participants,whilst total task execution time of the entire cluster as the utility function.In that case,the most benefit strategy can be implemented in each computing node when the game reaches a Nash equilibrium point,i.e.,the final resource scheduling scheme to be obtained.The strategy has been implemented in Hadoop-2.x.Experimental results depict that the ORSE can maintain the efficiency of speculative executive processes and improve fault-tolerant and computation performance under the circumstances of Normal Load,Busy Load and Busy Load with Skewed Data. 展开更多
关键词 Distributed computing speculative execution resource scheduling non-cooperative game theory
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Non-cooperative game for network access selection in heterogeneous integrated networks
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作者 郭洪尧 Zhang Xin +2 位作者 He Yunlu Jiang Rui Xie Jiangbo 《High Technology Letters》 EI CAS 2014年第3期282-287,共6页
The integration of different heterogeneous access networks is one of the remarkable characteristics of the next generation network,in which users with multi-network interface terminals can independently select access ... The integration of different heterogeneous access networks is one of the remarkable characteristics of the next generation network,in which users with multi-network interface terminals can independently select access network to obtain the most desired service.A kind of unified quantification model of non-monotone quality of service(QoS) and a model of non-cooperative game between users and networks are proposed for heterogeneous network access selection.An optimal network pricing mechanism could be formulated by using a novel strategy which is used in this non-cooperative game model to balance the interests of both the users and the networks.This access network selection mechanism could select the most suitable network for users,and it also could provide the basis when formulating QoS standards in heterogeneous integrated networks.The simulation results show that this network selection decision-making algorithm can meet the users' demand for different levels service in different scenes and it can also avoid network congestion caused by unbalanced load. 展开更多
关键词 heterogeneous network integration access selection non-cooperative game non-monotone quality of service (QoS)
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Excess Benefit Allocation in Shared Savings Based on Non-cooperative Game Theory
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作者 Xiao Xu 《Proceedings of Business and Economic Studies》 2021年第4期36-42,共7页
Energy saving income distribution mode is of great significance to the energy industry.With the continuous application of new technologies,the problem of excess energy saving income distribution has become one of the ... Energy saving income distribution mode is of great significance to the energy industry.With the continuous application of new technologies,the problem of excess energy saving income distribution has become one of the obstacles to the appreciation of energy performance.At present,the distribution of risk and income is mainly based on the contribution of risk and income,which has some limitations.The benefit distribution of energy saving negotiation between energy saving service companies and clients can be regarded as a bargaining process where an effective range satisfying both parties can be obtained.This provides a new perspective in solving the problem of excess energy saving income distribution in energy management contract projects. 展开更多
关键词 Contract energy management Excess energy saving non-cooperative game theory Bargaining model
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Fuzzy Nash equilibrium of fuzzy n-person non-cooperative game 被引量:2
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作者 Xiaohui Yu Qiang Zhang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第1期47-56,共10页
The fuzzy non-cooperative game with fuzzy payoff function is studied. Based on fuzzy set theory with game theory, the fuzzy Nash equilibrium of fuzzy non-cooperative games is proposed. Most of researchers rank fuzzy n... The fuzzy non-cooperative game with fuzzy payoff function is studied. Based on fuzzy set theory with game theory, the fuzzy Nash equilibrium of fuzzy non-cooperative games is proposed. Most of researchers rank fuzzy number by its center of gravity or by the real number with its maximal membership. By reducing fuzzy number into a real number, we lose much fuzzy information that should be kept during the operations between fuzzy numbers. The fuzzy quantities or alternatives are ordered directly by Yuan's binary fuzzy ordering relation. In doing so, the existence of fuzzy Nash equilibrium for fuzzy non-cooperative games is shown based on the utility function and the crisp Nash theorem. Finally, an illustrative example in traffic flow patterns of equilibrium is given in order to show the detailed calculation process of fuzzy Nash equilibrium. 展开更多
关键词 operational research Nash equilibrium preference relations fuzzy game theory.
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Power Control Algorithm of Cognitive Radio Based on Non-Cooperative Game Theory 被引量:4
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作者 赵军辉 杨涛 +2 位作者 贡毅 王娇 付雷 《China Communications》 SCIE CSCD 2013年第11期143-154,共12页
This paper addresses the power con- trol problems of Cognitive Radio (CR) trader transmission power and interference tempera- ture constraints. First, we propose the interfer- ence constraint which ensures that the ... This paper addresses the power con- trol problems of Cognitive Radio (CR) trader transmission power and interference tempera- ture constraints. First, we propose the interfer- ence constraint which ensures that the Quality of Service (QoS) standards for primary users is considered and a non-cooperative game power control model. Based on the proposed model, we developed a logical utility function based on the Signal-to-Interference-Noise Ratio (S/NR) and a novel algorithm network power control. that is suitable for CR Then, the existence and uniqueness of the Nash Equilibrium (NE) in our utility function are proved by the principle of game theory and the corresponding optimi- zations. Compared to traditional algorithms, the proposed one could converge to an NE in 3-5 iterative operations by setting an appropriate pricing factor. Finally, simulation results ver- ified the stability and superiority of the novel algorithm in flat-fading channel environments. 展开更多
关键词 cognitive radio non-cooperativepower control game theory utility function Na-sh equilibrium target power
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MADRL-based UAV swarm non-cooperative game under incomplete information
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作者 Ershen WANG Fan LIU +4 位作者 Chen HONG Jing GUO Lin ZHAO Jian XUE Ning HE 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2024年第6期293-306,共14页
Unmanned Aerial Vehicles(UAVs)play increasing important role in modern battlefield.In this paper,considering the incomplete observation information of individual UAV in complex combat environment,we put forward an UAV... Unmanned Aerial Vehicles(UAVs)play increasing important role in modern battlefield.In this paper,considering the incomplete observation information of individual UAV in complex combat environment,we put forward an UAV swarm non-cooperative game model based on Multi-Agent Deep Reinforcement Learning(MADRL),where the state space and action space are constructed to adapt the real features of UAV swarm air-to-air combat.The multi-agent particle environment is employed to generate an UAV combat scene with continuous observation space.Some recently popular MADRL methods are compared extensively in the UAV swarm noncooperative game model,the results indicate that the performance of Multi-Agent Soft Actor-Critic(MASAC)is better than that of other MADRL methods by a large margin.UAV swarm employing MASAC can learn more effective policies,and obtain much higher hit rate and win rate.Simulations under different swarm sizes and UAV physical parameters are also performed,which implies that MASAC owns a well generalization effect.Furthermore,the practicability and convergence of MASAC are addressed by investigating the loss value of Q-value networks with respect to individual UAV,the results demonstrate that MASAC is of good practicability and the Nash equilibrium of the UAV swarm non-cooperative game under incomplete information can be reached. 展开更多
关键词 UAV swarm Reinforcement learning Deep learning MULTI-AGENT non-cooperative game Nash equilibrium
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Non-cooperative Game Based Optimal Dispatch Model for Integrated Energy Systems
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作者 Jiandong Duan Qian Sun +2 位作者 Chen Wu Yao Yang Siyu Tu 《CSEE Journal of Power and Energy Systems》 SCIE EI CSCD 2024年第3期1195-1207,共13页
In order to improve the efficiency of energy utilization,the integrated energy system(IES)has emerged.The IES typically acts as a whole system during operations,the subsystems are separated,and the interests of each s... In order to improve the efficiency of energy utilization,the integrated energy system(IES)has emerged.The IES typically acts as a whole system during operations,the subsystems are separated,and the interests of each system are independent.In this paper,considering the relationship between the various energy systems,non-cooperative game theory is used to establish the optimal dispatch model.The proposed model mainly relies on the relationship between the cooperation and competition among various subsystems to obtain the maximum benefit they can accept.Furthermore,the basic definition is combined with the particle swarm optimization algorithm to solve the problem.The results show that the optimization strategy proposed in this paper can operate safely and reliably,and effectively distribute the benefits of each energy system. 展开更多
关键词 Integrated energy system multi-energy complimentarily non-cooperative game theory
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Coverage and capacity optimization in LTE network based on non-cooperative games 被引量:1
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作者 XU Sen HOU Meng +2 位作者 NIU Kai HE Zhi-qiang WU Wei-ling 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2012年第4期14-21,42,共9页
expenditures and operational expenditures (OPEX) (CAPEX) for operator, the coverage and capacity optimization (CCO) is one of the key use cases in long term evolution (LTE) self-organization network (SON). I... expenditures and operational expenditures (OPEX) (CAPEX) for operator, the coverage and capacity optimization (CCO) is one of the key use cases in long term evolution (LTE) self-organization network (SON). In LTE system, some factors (e.g. load, traffic type, user distribution, uplink power setting, inter-cell interference, etc.) limit the coverage and capacity performance. From the view of single cell, it always pursuits maximize performance of coverage and capacity by optimizing the uplink power setting and intra-cell resource allocation, but it may result in decreasing the performance of its neighbor cells. Therefore, the benefit of every cell conflicts each other. In order to tradeoff the benefit of every cell and maximize the performance of the whole network, this paper proposes a multi-cell uplink power allocation scheme based on non-cooperative games. The scheme aims to make the performance of coverage and capacity balanced by the negotiation of the uplink power parameters among multi-cells. So the performance of every cell can reach the Nash equilibrium, making it feasible to reduce the inter-cell interference by setting an appropriate uplink power parameter. Finally, the simulation result shows the proposed algorithm can effectively enhance the performance of coverage and capacity in LTE network. 展开更多
关键词 coverage and capacity power control non-cooperative game Nash equilibrium
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A non-cooperative game-based distributed optimization method for chiller plant control
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作者 Shiyao Li Yiqun Pan +1 位作者 Qiujian Wang Zhizhong Huang 《Building Simulation》 SCIE EI CSCD 2022年第6期1015-1034,共20页
The heating,ventilation,and air-conditioning(HVAC)systems account for about half of the building energy consumption.The optimization methodology access to optimal control strategies of chiller plant has always been of... The heating,ventilation,and air-conditioning(HVAC)systems account for about half of the building energy consumption.The optimization methodology access to optimal control strategies of chiller plant has always been of great concern as it significantly contributes to the energy use of the whole HVAC system.Given that conventional centralized optimization methods relying on a central operator may suffer from dimensionality and a tremendous calculation burden,and show poorer flexibility when solving complex optimization issues,in this paper,a novel distributed optimization approach is presented for chiller plant control.In the proposed distributed control scheme,both trade-offs of coupled subsystems and optimal allocation among devices of the same subsystem are considered by developing a double-layer optimization structure.Non-cooperative game is used to mathematically formulate the interaction between controlled components as well as to divide the initial system-scale nonlinear optimization problem into local-scale ones.To solve these tasks,strategy updating mechanisms(PSO and IPM)are utilized.In this way,the approximate global optimal controlled variables of devices in the chiller plant can be obtained in a distributed and local-knowledge-enabled way without neither global information nor the central workstation.Furthermore,the existence and effectiveness of the proposed distributed scheme were verified by simulation case studies.Simulation results indicate that,by using the proposed distributed optimization scheme,a significant energy saving on a typical summer day can be obtained(1809.47 kW·h).The deviation from the central optimal solution is 3.83%. 展开更多
关键词 chiller plant operation optimization distributed optimization non-cooperative game double-layer optimization graph theory
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Distributed interference suppression scheme for multi-cell uplink OFDMA system based on non-cooperative game
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作者 CHANG Ling-jun TANG Bi-hua +2 位作者 XIE Gang ZENG Ling-kang LIU Kai-ming 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2011年第2期65-71,共7页
In this paper,a distributed interference suppression scheme is proposed for multi-cell uplink orthogonal frequency division multiple access(OFDMA) system.Firstly,we model resource allocation process as a non-coopera... In this paper,a distributed interference suppression scheme is proposed for multi-cell uplink orthogonal frequency division multiple access(OFDMA) system.Firstly,we model resource allocation process as a non-cooperative game.Then we show the concept of Nash equilibrium(NE) and investigate its existence and uniqueness in detail.To enhance the performance of multi-cell OFDMA system,the further improvement process based on NE is given.Several adjustable parameters are set to make the system achieve different tradeoffs between the total capacity and complexity.Simulation results show that the proposed scheme can greatly improve the system performance comparing with conventional scheme. 展开更多
关键词 MULTI-CELL non-cooperative game OFDMA uplink ICI
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Sequential quadratic programming-based non-cooperative target distributed hybrid processing optimization method 被引量:2
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作者 SONG Xiaocheng WANG Jiangtao +3 位作者 WANG Jun SUN Liang FENG Yanghe LI Zhi 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2023年第1期129-140,共12页
The distributed hybrid processing optimization problem of non-cooperative targets is an important research direction for future networked air-defense and anti-missile firepower systems. In this paper, the air-defense ... The distributed hybrid processing optimization problem of non-cooperative targets is an important research direction for future networked air-defense and anti-missile firepower systems. In this paper, the air-defense anti-missile targets defense problem is abstracted as a nonconvex constrained combinatorial optimization problem with the optimization objective of maximizing the degree of contribution of the processing scheme to non-cooperative targets, and the constraints mainly consider geographical conditions and anti-missile equipment resources. The grid discretization concept is used to partition the defense area into network nodes, and the overall defense strategy scheme is described as a nonlinear programming problem to solve the minimum defense cost within the maximum defense capability of the defense system network. In the solution of the minimum defense cost problem, the processing scheme, equipment coverage capability, constraints and node cost requirements are characterized, then a nonlinear mathematical model of the non-cooperative target distributed hybrid processing optimization problem is established, and a local optimal solution based on the sequential quadratic programming algorithm is constructed, and the optimal firepower processing scheme is given by using the sequential quadratic programming method containing non-convex quadratic equations and inequality constraints. Finally, the effectiveness of the proposed method is verified by simulation examples. 展开更多
关键词 non-cooperative target distributed hybrid processing multiple constraint minimum defense cost sequential quadratic programming
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Non-Cooperative Differential Game Based Energy Consumption Control for Dynamic Demand Response in Smart Grid 被引量:5
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作者 Manxi Wang Haitao Xu +3 位作者 Shengsong Yang Lifeng Yang Ruifeng Duan Xianwei Zhou 《China Communications》 SCIE CSCD 2019年第8期107-114,共8页
In this paper, we conduct research on the dynamic demand response problem in smart grid to control the energy consumption. The objective of the energy consumption control is constructed based on differential game, as ... In this paper, we conduct research on the dynamic demand response problem in smart grid to control the energy consumption. The objective of the energy consumption control is constructed based on differential game, as the dynamic of each users’ energy state in smart gird can be described based on a differential equation. Concept of electricity sharing is introduced to achieve load shift of main users from the high price hours to the low price hours. Nash equilibrium is given based on the Hamilton equation and the effectiveness of the proposed model is verified based on the numerical simulation results. 展开更多
关键词 energy CONSUMPTION DYNAMIC DEMAND response smart grid differential game NASH EQUILIBRIUM
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Resource Allocation for Network Security Risk Assessment:A Non-Cooperative Differential Game Based Approach 被引量:1
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作者 XU Haitao LIN Ruijie 《China Communications》 SCIE CSCD 2016年第4期131-135,共5页
In this paper, we propose a non-cooperative differential game theory based resource allocation approach for the network security risk assessment. For the risk assessment, the resource will be used for risk assess, inc... In this paper, we propose a non-cooperative differential game theory based resource allocation approach for the network security risk assessment. For the risk assessment, the resource will be used for risk assess, including response cost and response negative cost. The whole assessment process is considered as a differential game for optimal resource control. The proposed scheme can be obtained through the Nash Equilibrium. It is proved that the game theory based algorithm is applicable and the optimal resource level can be achieved based on the proposed algorithm. 展开更多
关键词 resource allocation security risk assessment differential game non-cooperative Nash Equilibrium
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Equilibrium Strategy of the Pursuit-Evasion Game in Three-Dimensional Space 被引量:1
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作者 Nuo Chen Linjing Li Wenji Mao 《IEEE/CAA Journal of Automatica Sinica》 SCIE EI CSCD 2024年第2期446-458,共13页
The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainl... The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper,we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer's three-degree-of-freedom control and the evader's relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs(HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer's speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium. 展开更多
关键词 Differential game equilibrium strategy pursuit-evasion game threedegree-of-freedom control
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A Non-Cooperative Differential Game-Based Security Model in Fog Computing 被引量:4
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作者 Zhi Li Xianwei Zhou +2 位作者 Yanzhu Liu Haitao Xu Li Miao 《China Communications》 SCIE CSCD 2017年第1期180-189,共10页
Fog computing is a new paradigm providing network services such as computing, storage between the end users and cloud. The distributed and open structure are the characteristics of fog computing, which make it vulnera... Fog computing is a new paradigm providing network services such as computing, storage between the end users and cloud. The distributed and open structure are the characteristics of fog computing, which make it vulnerable and very weak to security threats. In this article, the interaction between vulnerable nodes and malicious nodes in the fog computing is investigated as a non-cooperative differential game. The complex decision making process is reviewed and analyzed. To solve the game, a fictitious play-based algorithm is which the vulnerable node and the malicious nodes reach a feedback Nash equilibrium. We attain optimal strategy of energy consumption with Qo S guarantee for the system, which are conveniently operated and suitable for fog nodes. The system simulation identifies the propagation of malicious nodes. We also determine the effects of various parameters on the optimal strategy. The simulation results support a theoretical foundation to limit malicious nodes in fog computing, which can help fog service providers make the optimal dynamic strategies when different types of nodes dynamically change their strategies. 展开更多
关键词 fog computing differential game fog security feedback nash equilibrium
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