Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate...Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate this impulse game problem with the modified objective function including interaction costs among the players in a discontinuous fashion,and subsequently,to derive a verification theorem for identifying the feedback Nash equilibrium strategy.展开更多
This paper designs distributed Nash equilibrium seeking strategies for heterogeneous dynamic cyber-physical systems.In particular, we are concerned with parametric uncertainties in the control channel of the players. ...This paper designs distributed Nash equilibrium seeking strategies for heterogeneous dynamic cyber-physical systems.In particular, we are concerned with parametric uncertainties in the control channel of the players. Moreover, the weights on communication links can be compromised by time-varying uncertainties, which can result from possibly malicious attacks,faults and disturbances. To deal with the unavailability of measurement of optimization errors, an output observer is constructed,based on which adaptive laws are designed to compensate for physical uncertainties. With adaptive laws, a new distributed Nash equilibrium seeking strategy is designed by further integrating consensus protocols and gradient search algorithms.Moreover, to further accommodate compromised communication weights resulting from cyber-uncertainties, the coupling strengths of the consensus module are designed to be adaptive. As a byproduct, the coupling strengths are independent of any global information. With theoretical investigations, it is proven that the proposed strategies are resilient to these uncertainties and players' actions are convergent to the Nash equilibrium. Simulation examples are given to numerically validate the effectiveness of the proposed strategies.展开更多
为了优化区域交通信号配时方案,提升区域通行效率,文章提出一种基于改进多智能体Nash Q Learning的区域交通信号协调控制方法。首先,采用离散化编码方法,通过划分单元格将连续状态信息转化为离散形式。其次,在算法中融入长短时记忆网络(...为了优化区域交通信号配时方案,提升区域通行效率,文章提出一种基于改进多智能体Nash Q Learning的区域交通信号协调控制方法。首先,采用离散化编码方法,通过划分单元格将连续状态信息转化为离散形式。其次,在算法中融入长短时记忆网络(Long Short Term Memory,LSTM)模块,用于从状态数据中挖掘更多的隐藏信息,丰富Q值表中的状态数据。最后,基于微观交通仿真软件SUMO(Simulation of Urban Mobility)的仿真测试结果表明,相较于原始Nash Q Learning交通信号控制方法,所提方法在低、中、高流量下车辆的平均等待时间分别减少了11.5%、16.2%和10.0%,平均排队长度分别减少了9.1%、8.2%和7.6%,平均停车次数分别减少了18.3%、16.1%和10.0%。结果证明了该算法具有更好的控制效果。展开更多
This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achi...This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization o players' objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized informa tion flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respec tively. Through Lyapunov stability analysis, it is shown that play ers' actions can be steered to a neighborhood of the Nash equilib rium with logarithmic and uniform quantizers, and the quanti fied convergence error depends on the parameter of the quan tizer for both undirected and directed cases. A numerical exam ple is given to verify the theoretical results.展开更多
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
基金supported in part by the National Natural Science Foundation of China(62173051)the Fundamental Research Funds for the Central Universities(2024CDJCGJ012,2023CDJXY-010)+1 种基金the Chongqing Technology Innovation and Application Development Special Key Project(CSTB2022TIADCUX0015,CSTB2022TIAD-KPX0162)the China Postdoctoral Science Foundation(2024M763865)
文摘Dear Editor,This letter addresses the impulse game problem for a general scope of deterministic,multi-player,nonzero-sum differential games wherein all participants adopt impulse controls.Our objective is to formulate this impulse game problem with the modified objective function including interaction costs among the players in a discontinuous fashion,and subsequently,to derive a verification theorem for identifying the feedback Nash equilibrium strategy.
基金supported by the National Key R&D Program of China(2022ZD0119604)the National Natural Science Foundation of China(NSFC)(62173181,62222308,62221004)the Natural Science Foundation of Jiangsu Province(BK20220139)
文摘This paper designs distributed Nash equilibrium seeking strategies for heterogeneous dynamic cyber-physical systems.In particular, we are concerned with parametric uncertainties in the control channel of the players. Moreover, the weights on communication links can be compromised by time-varying uncertainties, which can result from possibly malicious attacks,faults and disturbances. To deal with the unavailability of measurement of optimization errors, an output observer is constructed,based on which adaptive laws are designed to compensate for physical uncertainties. With adaptive laws, a new distributed Nash equilibrium seeking strategy is designed by further integrating consensus protocols and gradient search algorithms.Moreover, to further accommodate compromised communication weights resulting from cyber-uncertainties, the coupling strengths of the consensus module are designed to be adaptive. As a byproduct, the coupling strengths are independent of any global information. With theoretical investigations, it is proven that the proposed strategies are resilient to these uncertainties and players' actions are convergent to the Nash equilibrium. Simulation examples are given to numerically validate the effectiveness of the proposed strategies.
文摘为了优化区域交通信号配时方案,提升区域通行效率,文章提出一种基于改进多智能体Nash Q Learning的区域交通信号协调控制方法。首先,采用离散化编码方法,通过划分单元格将连续状态信息转化为离散形式。其次,在算法中融入长短时记忆网络(Long Short Term Memory,LSTM)模块,用于从状态数据中挖掘更多的隐藏信息,丰富Q值表中的状态数据。最后,基于微观交通仿真软件SUMO(Simulation of Urban Mobility)的仿真测试结果表明,相较于原始Nash Q Learning交通信号控制方法,所提方法在低、中、高流量下车辆的平均等待时间分别减少了11.5%、16.2%和10.0%,平均排队长度分别减少了9.1%、8.2%和7.6%,平均停车次数分别减少了18.3%、16.1%和10.0%。结果证明了该算法具有更好的控制效果。
基金supported by the National Natural Science Foundation of China (NSFC)(62222308, 62173181, 62073171, 62221004)the Natural Science Foundation of Jiangsu Province (BK20200744, BK20220139)+3 种基金Jiangsu Specially-Appointed Professor (RK043STP19001)the Young Elite Scientists Sponsorship Program by CAST (2021QNRC001)1311 Talent Plan of Nanjing University of Posts and Telecommunicationsthe Fundamental Research Funds for the Central Universities (30920032203)。
文摘This paper is concerned with distributed Nash equi librium seeking strategies under quantized communication. In the proposed seeking strategy, a projection operator is synthesized with a gradient search method to achieve the optimization o players' objective functions while restricting their actions within required non-empty, convex and compact domains. In addition, a leader-following consensus protocol, in which quantized informa tion flows are utilized, is employed for information sharing among players. More specifically, logarithmic quantizers and uniform quantizers are investigated under both undirected and connected communication graphs and strongly connected digraphs, respec tively. Through Lyapunov stability analysis, it is shown that play ers' actions can be steered to a neighborhood of the Nash equilib rium with logarithmic and uniform quantizers, and the quanti fied convergence error depends on the parameter of the quan tizer for both undirected and directed cases. A numerical exam ple is given to verify the theoretical results.
基金supported by the National Natural Science Foundation of China(71671035)。
文摘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.
