This paper presents a mode-switching collaborative defense strategy for spacecraft pursuit-evasiondefense scenarios.In these scenarios,the pursuer tries to avoid the defender while capturing the evader,while the evade...This paper presents a mode-switching collaborative defense strategy for spacecraft pursuit-evasiondefense scenarios.In these scenarios,the pursuer tries to avoid the defender while capturing the evader,while the evader and defender form an alliance to prevent the pursuer from achieving its goal.First,the behavioral modes of the pursuer,including attack and avoidance modes,were established using differential game theory.These modes are then recognized by an interactive multiple model-matching algorithm(IMM),that uses several smooth variable structure filters to match the modes of the pursuer and update their probabilities in real time.Based on the linear-quadratic optimization theory,combined with the results of strategy identification,a two-way cooperative optimal strategy for the defender and evader is proposed,where the evader aids the defender to intercept the pursuer by performing luring maneuvers.Simulation results show that the interactive multi-model algorithm based on several smooth variable structure filters perform well in the strategy identification of the pursuer,and the cooperative defense strategy based on strategy identification has good interception performance when facing pursuers,who are able to flexibly adjust their game objectives.展开更多
When the maneuverability of a pursuer is not significantly higher than that of an evader,it will be difficult to intercept the evader with only one pursuer.Therefore,this article adopts a two-to-one differential game ...When the maneuverability of a pursuer is not significantly higher than that of an evader,it will be difficult to intercept the evader with only one pursuer.Therefore,this article adopts a two-to-one differential game strategy,the game of kind is generally considered to be angle-optimized,which allows unlimited turns,but these practices do not take into account the effect of acceleration,which does not correspond to the actual situation,thus,based on the angle-optimized,the acceleration optimization and the acceleration upper bound constraint are added into the game for consideration.A two-to-one differential game problem is proposed in the three-dimensional space,and an improved multi-objective grey wolf optimization(IMOGWO)algorithm is proposed to solve the optimal game point of this problem.With the equations that describe the relative motions between the pursuers and the evader in the three-dimensional space,a multi-objective function with constraints is given as the performance index to design an optimal strategy for the differential game.Then the optimal game point is solved by using the IMOGWO algorithm.It is proved based on Markov chains that with the IMOGWO,the Pareto solution set is the solution of the differential game.Finally,it is verified through simulations that the pursuers can capture the escapee,and via comparative experiments,it is shown that the IMOGWO algorithm performs well in terms of running time and memory usage.展开更多
The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding sto...The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding stochastic and impulse. For the stochastic model without impulses, the existence and uniqueness of solution, and the existence of positive periodic solutions are proved, and a sufficient condition for strategy extinction is given. For the stochastic model with impulses, the existence of positive periodic solutions is proved. Numerical results show that noise and impulses directly affect the model, but the periodicity of the model does not change.展开更多
As a crucial process in the coordinated strikes of unmanned aerial vehicles(UAVs), weapon-target assignment is vital for optimizing the allocation of available weapons and effectively exploiting the capabilities of UA...As a crucial process in the coordinated strikes of unmanned aerial vehicles(UAVs), weapon-target assignment is vital for optimizing the allocation of available weapons and effectively exploiting the capabilities of UAVs. Existing weapon-target assignment methods primarily focus on macro cluster constraints while neglecting individual strategy updates. This paper proposes a novel weapon-target assignment method for UAVs based on the multi-strategy threshold public goods game(PGG). By analyzing the concept mapping between weapon-target assignment for UAVs and multi-strategy threshold PGG, a weapon-target assignment model for UAVs based on the multi-strategy threshold PGG is established, which is adaptively complemented by the diverse cooperation-defection strategy library and the utility function based on the threshold mechanism. Additionally, a multi-chain Markov is formulated to quantitatively describe the stochastic evolutionary dynamics, whose evolutionary stable distribution is theoretically derived through the development of a strategy update rule based on preference-based aspiration dynamic. Numerical simulation results validate the feasibility and effectiveness of the proposed method, and the impacts of selection intensity, preference degree and threshold on the evolutionary stable distribution are analyzed. Comparative simulations show that the proposed method outperforms GWO, DE, and NSGA-II, achieving 17.18% higher expected utility than NSGA-II and reducing evolutionary stable times by 25% in large-scale scenario.展开更多
In the realm of aerial warfare,the protection of Unmanned Aerial Vehicles(UAVs) against adversarial threats is crucial.In order to balance the impact of response delays and the demand for onboard applications,this pap...In the realm of aerial warfare,the protection of Unmanned Aerial Vehicles(UAVs) against adversarial threats is crucial.In order to balance the impact of response delays and the demand for onboard applications,this paper derives three analytical game strategies for the active defense of UAVs from differential game theory,accommodating the first-order dynamic delays.The targeted UAV executes evasive maneuvers and launches a defending missile to intercept the attacking missile,which constitutes a UAVMissile-Defender(UMD) three-body game problem.We explore two distinct operational paradigms:the first involves the UAV and the defender working collaboratively to intercept the incoming threat,while the second prioritizes UAV self-preservation,with independent maneuvering away from potentially sacrificial engagements.Starting with model linearization and order reduction,the Collaborative Interception Strategy(CIS) is first derived via a linear quadratic differential game formulation.Building upon CIS,we further explore two distinct strategies:the Informed Defender Interception Strategy(IDIS),which utilizes UAV maneuvering information,and the Unassisted Defender Interception Strategy(UDIS),which does not rely on UAV maneuvering information.Additionally,we investigate the conditions for the existence of saddle point solutions and their relationship with vehicle maneuverability and response agility.The simulations demonstrate the effectiveness and advantages of the proposed strategies.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
A differential game guidance scheme with obstacle avoidance,based on the formulation of a combined linear quadratic and norm-bounded differential game,is designed for a three-player engagement scenario,which includes ...A differential game guidance scheme with obstacle avoidance,based on the formulation of a combined linear quadratic and norm-bounded differential game,is designed for a three-player engagement scenario,which includes a pursuer,an interceptor,and an evader.The confrontation between the players is divided into four phases(P1-P4)by introducing the switching time,and proposing different guidance strategies according to the phase where the static obstacle is located:the linear quadratic game method is employed to devise the guidance scheme for the energy optimization when the obstacle is located in the P1 and P3 stages;the norm-bounded differential game guidance strategy is presented to satisfy the acceleration constraint under the circumstance that the obstacle is located in the P2 and P4 phases.Furthermore,the radii of the static obstacle and the interceptor are taken as the design parameters to derive the combined guidance strategy through the dead-zone function,which guarantees that the pursuer avoids the static obstacle,and the interceptor,and attacks the evader.Finally,the nonlinear numerical simulations verify the performance of the game guidance strategy.展开更多
Game theory can be applied to the air combat decision-making problem of multiple unmanned combat air vehicles(UCAVs).However,it is difficult to have satisfactory decision-making results completely relying on air comba...Game theory can be applied to the air combat decision-making problem of multiple unmanned combat air vehicles(UCAVs).However,it is difficult to have satisfactory decision-making results completely relying on air combat situation information,because there is a lot of time-sensitive information in a complex air combat environment.In this paper,a constraint strategy game approach is developed to generate intelligent decision-making for multiple UCAVs in complex air combat environment with air combat situation information and time-sensitive information.Initially,a constraint strategy game is employed to model attack-defense decision-making problem in complex air combat environment.Then,an algorithm is proposed for solving the constraint strategy game based on linear programming and linear inequality(CSG-LL).Finally,an example is given to illustrate the effectiveness of the proposed approach.展开更多
The research of cluster supply chains is a new direction and a hotspot of the industrial cluster theory. On the condition of the coordination game, the enterprises may be stuck on the non-efficient equilibrium status,...The research of cluster supply chains is a new direction and a hotspot of the industrial cluster theory. On the condition of the coordination game, the enterprises may be stuck on the non-efficient equilibrium status, which becomes an important problem that must be considered on cluster supply chains. A symmetrical coordination game model is constituted to describe the competition and cooperation relationship of the same-quality manufacturers on cluster supply chains. The methods of the non-cooperation game theory and the evolutionary game theory are respectively used to analyze the model, whose parameters＇ influences under each method are then compared. It can be concluded that the analysis of the evolutionary game theory is more realistic and practical. Finally, three approaches are considered to break away from being path-dependence locked-in non-efficient status during this coordination game evolutionary process, which provide the development of cluster supply chains with an effective forecasting and Pareto optimizing method.展开更多
The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if so...The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.展开更多
In non-dedicated cooperative relay networks, each node is autonomous and selfish in nature, and thus spontaneous cooperation among nodes is challenged. To stimulate the selfish node to participate in cooperation, a pr...In non-dedicated cooperative relay networks, each node is autonomous and selfish in nature, and thus spontaneous cooperation among nodes is challenged. To stimulate the selfish node to participate in cooperation, a pricing-based cooperation engine using game theory was designed. Firstly, the feasible regions of the charge price and reimbursement price were deduced. Then, the non-cooperative and cooperative games were adopted to analyze the amount of bandwidth that initiating cooperation node(ICN) forwards data through participating cooperation node(PCN) and the amount of bandwidth that PCN helps ICN to relay data. Meanwhile, the Nash equilibrium solutions of cooperation bandwidth allocations(CBAs) were obtained through geometrical interpretation. Secondly, a pricing-based cooperation engine was proposed and a cooperative communication system model with cooperation engines was depicted. Finally, an algorithm based on game theory was proposed to realize the cooperation engine. The simulation results demonstrate that, compared with the system without pricing-based incentive, the proposed system can significantly improve the ICN's metric measured by bit-per-Joule and increase the PCN's revenue.展开更多
基金the Science and Technology Department,Heilongjiang Province under Grant Agreement No JJ2022LH0315。
文摘This paper presents a mode-switching collaborative defense strategy for spacecraft pursuit-evasiondefense scenarios.In these scenarios,the pursuer tries to avoid the defender while capturing the evader,while the evader and defender form an alliance to prevent the pursuer from achieving its goal.First,the behavioral modes of the pursuer,including attack and avoidance modes,were established using differential game theory.These modes are then recognized by an interactive multiple model-matching algorithm(IMM),that uses several smooth variable structure filters to match the modes of the pursuer and update their probabilities in real time.Based on the linear-quadratic optimization theory,combined with the results of strategy identification,a two-way cooperative optimal strategy for the defender and evader is proposed,where the evader aids the defender to intercept the pursuer by performing luring maneuvers.Simulation results show that the interactive multi-model algorithm based on several smooth variable structure filters perform well in the strategy identification of the pursuer,and the cooperative defense strategy based on strategy identification has good interception performance when facing pursuers,who are able to flexibly adjust their game objectives.
基金National Natural Science Foundation of China(NSFC61773142,NSFC62303136)。
文摘When the maneuverability of a pursuer is not significantly higher than that of an evader,it will be difficult to intercept the evader with only one pursuer.Therefore,this article adopts a two-to-one differential game strategy,the game of kind is generally considered to be angle-optimized,which allows unlimited turns,but these practices do not take into account the effect of acceleration,which does not correspond to the actual situation,thus,based on the angle-optimized,the acceleration optimization and the acceleration upper bound constraint are added into the game for consideration.A two-to-one differential game problem is proposed in the three-dimensional space,and an improved multi-objective grey wolf optimization(IMOGWO)algorithm is proposed to solve the optimal game point of this problem.With the equations that describe the relative motions between the pursuers and the evader in the three-dimensional space,a multi-objective function with constraints is given as the performance index to design an optimal strategy for the differential game.Then the optimal game point is solved by using the IMOGWO algorithm.It is proved based on Markov chains that with the IMOGWO,the Pareto solution set is the solution of the differential game.Finally,it is verified through simulations that the pursuers can capture the escapee,and via comparative experiments,it is shown that the IMOGWO algorithm performs well in terms of running time and memory usage.
基金Supported by the National Natural Science Foundation of China(10671182)。
文摘The article studies the evolutionary dynamics of two-population two-strategy game models with and without impulses. First, the payment matrix is given and two evolutionary dynamics models are established by adding stochastic and impulse. For the stochastic model without impulses, the existence and uniqueness of solution, and the existence of positive periodic solutions are proved, and a sufficient condition for strategy extinction is given. For the stochastic model with impulses, the existence of positive periodic solutions is proved. Numerical results show that noise and impulses directly affect the model, but the periodicity of the model does not change.
基金supported by the National Natural Science Foundation of China (No. 62073267)。
文摘As a crucial process in the coordinated strikes of unmanned aerial vehicles(UAVs), weapon-target assignment is vital for optimizing the allocation of available weapons and effectively exploiting the capabilities of UAVs. Existing weapon-target assignment methods primarily focus on macro cluster constraints while neglecting individual strategy updates. This paper proposes a novel weapon-target assignment method for UAVs based on the multi-strategy threshold public goods game(PGG). By analyzing the concept mapping between weapon-target assignment for UAVs and multi-strategy threshold PGG, a weapon-target assignment model for UAVs based on the multi-strategy threshold PGG is established, which is adaptively complemented by the diverse cooperation-defection strategy library and the utility function based on the threshold mechanism. Additionally, a multi-chain Markov is formulated to quantitatively describe the stochastic evolutionary dynamics, whose evolutionary stable distribution is theoretically derived through the development of a strategy update rule based on preference-based aspiration dynamic. Numerical simulation results validate the feasibility and effectiveness of the proposed method, and the impacts of selection intensity, preference degree and threshold on the evolutionary stable distribution are analyzed. Comparative simulations show that the proposed method outperforms GWO, DE, and NSGA-II, achieving 17.18% higher expected utility than NSGA-II and reducing evolutionary stable times by 25% in large-scale scenario.
基金supported by the China Postdoctoral Science Foundation (Grant No.2021M700321)the Fundamental Research Funds for the Central Universities (Grant No.YWF-23-Q1041)。
文摘In the realm of aerial warfare,the protection of Unmanned Aerial Vehicles(UAVs) against adversarial threats is crucial.In order to balance the impact of response delays and the demand for onboard applications,this paper derives three analytical game strategies for the active defense of UAVs from differential game theory,accommodating the first-order dynamic delays.The targeted UAV executes evasive maneuvers and launches a defending missile to intercept the attacking missile,which constitutes a UAVMissile-Defender(UMD) three-body game problem.We explore two distinct operational paradigms:the first involves the UAV and the defender working collaboratively to intercept the incoming threat,while the second prioritizes UAV self-preservation,with independent maneuvering away from potentially sacrificial engagements.Starting with model linearization and order reduction,the Collaborative Interception Strategy(CIS) is first derived via a linear quadratic differential game formulation.Building upon CIS,we further explore two distinct strategies:the Informed Defender Interception Strategy(IDIS),which utilizes UAV maneuvering information,and the Unassisted Defender Interception Strategy(UDIS),which does not rely on UAV maneuvering information.Additionally,we investigate the conditions for the existence of saddle point solutions and their relationship with vehicle maneuverability and response agility.The simulations demonstrate the effectiveness and advantages of the proposed strategies.
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.
基金supported by National Natural Science Foundation(NNSF)of China under(Grant No.62273119)。
文摘A differential game guidance scheme with obstacle avoidance,based on the formulation of a combined linear quadratic and norm-bounded differential game,is designed for a three-player engagement scenario,which includes a pursuer,an interceptor,and an evader.The confrontation between the players is divided into four phases(P1-P4)by introducing the switching time,and proposing different guidance strategies according to the phase where the static obstacle is located:the linear quadratic game method is employed to devise the guidance scheme for the energy optimization when the obstacle is located in the P1 and P3 stages;the norm-bounded differential game guidance strategy is presented to satisfy the acceleration constraint under the circumstance that the obstacle is located in the P2 and P4 phases.Furthermore,the radii of the static obstacle and the interceptor are taken as the design parameters to derive the combined guidance strategy through the dead-zone function,which guarantees that the pursuer avoids the static obstacle,and the interceptor,and attacks the evader.Finally,the nonlinear numerical simulations verify the performance of the game guidance strategy.
基金supported by Major Projects for Science and Technology Innovation 2030(Grant No.2018AA0100800)Equipment Pre-research Foundation of Laboratory(Grant No.61425040104)in part by Jiangsu Province“333”project under Grant BRA2019051.
文摘Game theory can be applied to the air combat decision-making problem of multiple unmanned combat air vehicles(UCAVs).However,it is difficult to have satisfactory decision-making results completely relying on air combat situation information,because there is a lot of time-sensitive information in a complex air combat environment.In this paper,a constraint strategy game approach is developed to generate intelligent decision-making for multiple UCAVs in complex air combat environment with air combat situation information and time-sensitive information.Initially,a constraint strategy game is employed to model attack-defense decision-making problem in complex air combat environment.Then,an algorithm is proposed for solving the constraint strategy game based on linear programming and linear inequality(CSG-LL).Finally,an example is given to illustrate the effectiveness of the proposed approach.
基金the National Natural Science Foundation of China (60374023)the Natural ScienceFoundation of Guangdong Province (011629).
文摘The research of cluster supply chains is a new direction and a hotspot of the industrial cluster theory. On the condition of the coordination game, the enterprises may be stuck on the non-efficient equilibrium status, which becomes an important problem that must be considered on cluster supply chains. A symmetrical coordination game model is constituted to describe the competition and cooperation relationship of the same-quality manufacturers on cluster supply chains. The methods of the non-cooperation game theory and the evolutionary game theory are respectively used to analyze the model, whose parameters＇ influences under each method are then compared. It can be concluded that the analysis of the evolutionary game theory is more realistic and practical. Finally, three approaches are considered to break away from being path-dependence locked-in non-efficient status during this coordination game evolutionary process, which provide the development of cluster supply chains with an effective forecasting and Pareto optimizing method.
文摘The solvability of the coupled Riccati differential equations appearing in the differential game approach to the formation control problem is vital to the finite horizon Nash equilibrium solution.These equations(if solvable)can be solved numerically by using the terminal value and the backward iteration.To investigate the solvability and solution of these equations the formation control problem as the differential game is replaced by a discrete-time dynamic game.The main contributions of this paper are as follows.First,the existence of Nash equilibrium controls for the discretetime formation control problem is shown.Second,a backward iteration approximate solution to the coupled Riccati differential equations in the continuous-time differential game is developed.An illustrative example is given to justify the models and solution.
基金Project(61201143)supported by the National Natural Science Foundation of China
文摘In non-dedicated cooperative relay networks, each node is autonomous and selfish in nature, and thus spontaneous cooperation among nodes is challenged. To stimulate the selfish node to participate in cooperation, a pricing-based cooperation engine using game theory was designed. Firstly, the feasible regions of the charge price and reimbursement price were deduced. Then, the non-cooperative and cooperative games were adopted to analyze the amount of bandwidth that initiating cooperation node(ICN) forwards data through participating cooperation node(PCN) and the amount of bandwidth that PCN helps ICN to relay data. Meanwhile, the Nash equilibrium solutions of cooperation bandwidth allocations(CBAs) were obtained through geometrical interpretation. Secondly, a pricing-based cooperation engine was proposed and a cooperative communication system model with cooperation engines was depicted. Finally, an algorithm based on game theory was proposed to realize the cooperation engine. The simulation results demonstrate that, compared with the system without pricing-based incentive, the proposed system can significantly improve the ICN's metric measured by bit-per-Joule and increase the PCN's revenue.
