The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Th...The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.展开更多
This paper studies the existence and uniqueness of solutions of fully coupled forward-backward stochastic differential equations with Brownian motion and random jumps.The result is applied to solve a linear-quadratic ...This paper studies the existence and uniqueness of solutions of fully coupled forward-backward stochastic differential equations with Brownian motion and random jumps.The result is applied to solve a linear-quadratic optimal control and a nonzero-sum differential game of backward stochastic differential equations.The optimal control and Nash equilibrium point are explicitly derived. Also the solvability of a kind Riccati equations is discussed.All these results develop those of Lim, Zhou(2001) and Yu,Ji(2008).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 two-player nonzero-sum linear-exponential-quadratic stochastic differential game is studied.The game takes into account the players'attitudes to risk.The nonlinear transformations and change of probability mea...The two-player nonzero-sum linear-exponential-quadratic stochastic differential game is studied.The game takes into account the players'attitudes to risk.The nonlinear transformations and change of probability measure techniques are used to study the existence of both open-loop and closed-loop Nash equilibria for the game.Some examples are constructed to illustrate their differences.Furthermore,theoretical results are applied to solve the risk-sensitive portfolio game problem in the financial market and show the effects of risk attitudes and economic performance on equilibria.展开更多
This study introduces a novel bargaining solution termed the"'min-distance bargaining solution"and applies it to a differential games model.A comprehensive algorithm for implementing this new solution is...This study introduces a novel bargaining solution termed the"'min-distance bargaining solution"and applies it to a differential games model.A comprehensive algorithm for implementing this new solution is presented,considering its time consistency within the differential games framework.Realistic scenarios are carefully analyzed to derive insightful findings regarding the mindistance solution,which are further validated through simulations using the resource extraction differential games model.Specifically,we examine scenarios such as managing a finite resource stock in the resource extraction game.Furthermore,a comparative analysis is conducted,pitting the mindistance bargaining solution against well-established alternatives such as Nash bargaining,Kalai-Smorodinsky,and Egalitarian solutions.By subjecting these solutions to numerical evaluations,the study offers valuable insights into decision-making processes.The findings not only contribute to negotiation theory by providing theoretical support but also have practical implications for decision-makers seeking effective strategies.This research significantly advances the field of negotiation theory,particularly in the context of differential games.The proposed min-distance bargaining solution demonstrates its applicability to real-world scenarios and enhances our understanding of strategic decision-making.展开更多
In this paper,a distributed adaptive dynamic programming(ADP)framework based on value iteration is proposed for multi-player differential games.In the game setting,players have no access to the information of others&#...In this paper,a distributed adaptive dynamic programming(ADP)framework based on value iteration is proposed for multi-player differential games.In the game setting,players have no access to the information of others'system parameters or control laws.Each player adopts an on-policy value iteration algorithm as the basic learning framework.To deal with the incomplete information structure,players collect a period of system trajectory data to compensate for the lack of information.The policy updating step is implemented by a nonlinear optimization problem aiming to search for the proximal admissible policy.Theoretical analysis shows that by adopting proximal policy searching rules,the approximated policies can converge to a neighborhood of equilibrium policies.The efficacy of our method is illustrated by three examples,which also demonstrate that the proposed method can accelerate the learning process compared with the centralized learning framework.展开更多
The existence and uniqueness of the solutions for one kind of forward- backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. ...The existence and uniqueness of the solutions for one kind of forward- backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.展开更多
This paper studies a class of continuous-time two person zero-sum stochastic differential games characterized by linear It?’s differential equation with state-dependent noise and Markovian parameter jumps. Under the ...This paper studies a class of continuous-time two person zero-sum stochastic differential games characterized by linear It?’s differential equation with state-dependent noise and Markovian parameter jumps. Under the assumption of stochastic stabilizability, necessary and sufficient condition for the existence of the optimal control strategies is presented by means of a system of coupled algebraic Riccati equations via using the stochastic optimal control theory. Furthermore, the stochastic H∞ control problem for stochastic systems with Markovian jumps is discussed as an immediate application, and meanwhile, an illustrative example is presented.展开更多
The problem of in-orbit cooperative target enclosing involving N thrust-limited satellites under collision avoidance and maneuver amplitude constraints is studied. In order to find global optimal trajectories for targ...The problem of in-orbit cooperative target enclosing involving N thrust-limited satellites under collision avoidance and maneuver amplitude constraints is studied. In order to find global optimal trajectories for target enclosing task with all constraints above, by integrating the collision threat and maneuver boundaries into a novel nonlinear cost functional, the studied target enclosing problem is described as a nonlinear nonzero-sum differential game. Further, to avoid iterative calculations caused by traditional nonlinear-game-solving methods, an approximate solution which can be constructed directly is designed. Then the approximate Nash equilibrium strategies can be educed by the constructive approximate solution for the proposed nonzero-sum game. Analysis shows that the proposed control strategies can asymptotically approach the exact one and can ensure a zero-error tracking of the enclosing configuration.Simulation results illustrate lower time costs and better enclosing accuracy while the collision avoidance and maneuver amplitude constraints are satisfied simultaneously.展开更多
For the high altitude cruising flight phase of a hypersonic cruise missile （HCM）, a relative motion mod- el between the missile and the target is established by defining virtual target and combining the theory of th...For the high altitude cruising flight phase of a hypersonic cruise missile （HCM）, a relative motion mod- el between the missile and the target is established by defining virtual target and combining the theory of the dif- ferential geometry with missile motion equations. Based on the model, the motion between the missile and the tar- get is considered as a single target differential game problem, and a new open-loop differential game midcourse guidance law （DGMGL） is deduced by solving the corresponding Hamiltonian Function. Meanwhile, a new struc- ture of a closed-loop DGMGL is presented and the training data for back propagation neural network （BPNN） are designed. By combining the theory of BPNN with the open-loop DGMGL obtained above, the law intelligence is realized. Finally, simulation is carried out and the validity of the law is testified.展开更多
This paper studies the proximate satellite interception guidance strategies where both the interceptor and target can perform orbital maneuvers with magnitude limited thrusts. This problem is regarded as a pursuit-eva...This paper studies the proximate satellite interception guidance strategies where both the interceptor and target can perform orbital maneuvers with magnitude limited thrusts. This problem is regarded as a pursuit-evasion game since satellites in both sides will try their best to capture or escape. In this game, the distance of these two players is small enough so that the highly nonlinear earth-centered gravitational dynamics can be reduced to the linear Clohessy-Wiltshire（CW） equations. The system is then simplified by introducing the zero effort miss variables. Saddle solution is formulated for the pursuit-evasion game and time-to-go is estimated similarly as that for the exoatmospheric interception. Then a vector guidance is derived to ensure that the interception can be achieved in the optimal time. The proposed guidance law is validated by numerical simulations.展开更多
For intercepting modern high maneuverable targets, a novel adaptive weighted differential game guidance law based on the game theory of mixed strategy is proposed, combining two guidance laws which are derived from th...For intercepting modern high maneuverable targets, a novel adaptive weighted differential game guidance law based on the game theory of mixed strategy is proposed, combining two guidance laws which are derived from the perfect and imperfect in- formation pattern, respectively. The weights vary according to the estimated error of the target＇s acceleration, the guidance law is generated by directly using the estimation of target＇s acceleration when the estimated error is small, and a differential game guidance law with adaptive penalty coefficient is implemented when the estimated error is large. The adaptive penalty coeffi- cients are not constants and they can be adjusted with current target maneuverability. The superior homing performance of the new guidance law is verified by computer simulations.展开更多
A conflict of three players, including an attacker, a defender, and a target with bounded control is discussed based on the differential game theories in which the target and the defender use an optimal pursuit strate...A conflict of three players, including an attacker, a defender, and a target with bounded control is discussed based on the differential game theories in which the target and the defender use an optimal pursuit strategy. The current approach chooses the miss distance as the outcome of the conflict. Different optimal guidance laws are investigated, and feasible conditions are analyzed for the attacker to accomplish an attacking task. For some given conditions, the attacker cannot intercept the target by only using a one-to-one optimal pursuit guidance law; thus, a guidance law for the attacker to reach a critical safe value is investigated.Specifically, the guidance law is divided into two parts. Before the engagement time between the defender and the attacker, the attacker uses this derived guidance law to guarantee that the evasion distance from the defender is safe, and that the zero-effort-miss(ZEM) distance between the attacker and the target is the smallest.After that engagement time, the attacker uses the optimal one-toone guidance law to accomplish the pursuit task. The advantages and limited conditions of these derived guidance laws are also investigated by using nonlinear simulations.展开更多
The optimal guidance problem for an interceptor against a ballistic missile with active defense is investigated in this paper.A class of optimal guidance schemes are proposed based on linear quadratic differential gam...The optimal guidance problem for an interceptor against a ballistic missile with active defense is investigated in this paper.A class of optimal guidance schemes are proposed based on linear quadratic differential game method and numerical solution of Riccati differential equation.By choosing proper parameters, the proposed guidance schemes are able to drive the interceptor to the target and away from the defender simultaneously.Additionally, fuel cost, control saturation,chattering phenomenon and parameters selection were taken into account.Satisfaction of the proposed guidance schemes of the saddle point condition is proven theoretically.Finally, nonlinear numerical examples are included to demonstrate the effectiveness and performance of the developed guidance approaches.Comparison of control performance between different guidance schemes are presented and analysis.展开更多
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
This paper is concerned with a scenario of multiple attackers trying to intercept a target with active defense.Three types of agents are considered in the guidance:The multiple attackers,the target and the defender,wh...This paper is concerned with a scenario of multiple attackers trying to intercept a target with active defense.Three types of agents are considered in the guidance:The multiple attackers,the target and the defender,where the attackers aim to pursuit the target from different directions and evade from the defender simultaneously.The guidance engagement is formulated in the framework of a zero-sum two-person differential game between the two opposing teams,such that the measurements on the maneuver of the target or estimations on the defending strategy of the defender can be absent.Cooperation of the attackers resides in two aspects:redundant interception under the threat of the defender and the relative intercept geometry with the target.The miss distances,the relative intercept angle errors and the costs of the agents are combined into a single performance index of the game.Such formulation enables a unitary approach to the design of guidance laws for the agents.To minimize the control efforts and miss distances for the attackers,an optimization method is proposed to find the best anticipated miss distances to the defender under the constraint that the defender is endowed with a capture radius.Numerical simulations with two cases are conducted to illustrate the effectiveness of the proposed cooperative guidance law.展开更多
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
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 order to intercept the future targets that are characterized by high maneuverability, multiple interceptors may be launched and aimed at single target. The scenario of two missiles P and Q intercepting a single tar...In order to intercept the future targets that are characterized by high maneuverability, multiple interceptors may be launched and aimed at single target. The scenario of two missiles P and Q intercepting a single target is modeled as a two-pursuit single-evader non-zero-sum linear quadratic differential game. The intercept space is decomposed into three subspaces which are mutually disjoint and their union covers the entire intercept space. The effect of adding the second interceptor arises in the intercept space of both P and Q （PQ-intercept space）. A guidance law is derived from the Nash equilibrium strategy set （NESS） of the game. Simulation studies are focused on the PQ-intercept space. It is indicated that 1） increasing the target＇s maneuverability will enlarge PQ-intercept space; 2） the handover conditions will be released if the initial zero-effort-miss （ZEM） of both interceptors has opposite sign; 3） overvaluation of the target＇s maneuverability by choosing a small weight coefficient will generate robust performance with respect to the target maneuvering command switch time and decrease the fuel requirement; and 4） cooperation between interceptors increases the interception probability.展开更多
In this paper, a Stackelberg differential game based approach is proposed to solve the bandwidth allocation problems in satellite communication network. All the satellites are divided into two groups, one has high dow...In this paper, a Stackelberg differential game based approach is proposed to solve the bandwidth allocation problems in satellite communication network. All the satellites are divided into two groups, one has high download requirements, and the other one has low download requirements. Each satellites group has its own controller for bandwidth allocation, and can get payments from the satellites for the allocated resources. The relationships between the controllers and satellites are formed as a Stackelberg game. In our model, differential equation is introduced to describe the bandwidth dynamics for the whole satellite communication network. Combine the differential equation and Stackelberg game together, we can formulate the bandwidth allocation problems in satellite communication network as a Stackelber differential game. The solutions to the proposed game is solved based the Bellman dynamic equations. Numerical simulations are given to prove the effeteness and correctness of the proposed approach.展开更多
基金Project supported by the National Natural Science Foundation of China (No.10371067) thePlanned Item for the Outstanding Young Teachers of Ministry of Education of China (No.2057) the Special Fund for Ph.D. Program of Ministry of Education of China ( No.20020422020) and the Fok Ying Tung Education Foundation for Young College Teachers(No.91064)
文摘The existence and uniqueness of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions.Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.
基金supported by National Natural Science Foundation of China(10671112)National Basic Research Program of China(973 Program)(2007CB814904)the Natural Science Foundation of Shandong Province(Z2006A01)
文摘This paper studies the existence and uniqueness of solutions of fully coupled forward-backward stochastic differential equations with Brownian motion and random jumps.The result is applied to solve a linear-quadratic optimal control and a nonzero-sum differential game of backward stochastic differential equations.The optimal control and Nash equilibrium point are explicitly derived. Also the solvability of a kind Riccati equations is discussed.All these results develop those of Lim, Zhou(2001) and Yu,Ji(2008).
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.
文摘The two-player nonzero-sum linear-exponential-quadratic stochastic differential game is studied.The game takes into account the players'attitudes to risk.The nonlinear transformations and change of probability measure techniques are used to study the existence of both open-loop and closed-loop Nash equilibria for the game.Some examples are constructed to illustrate their differences.Furthermore,theoretical results are applied to solve the risk-sensitive portfolio game problem in the financial market and show the effects of risk attitudes and economic performance on equilibria.
文摘This study introduces a novel bargaining solution termed the"'min-distance bargaining solution"and applies it to a differential games model.A comprehensive algorithm for implementing this new solution is presented,considering its time consistency within the differential games framework.Realistic scenarios are carefully analyzed to derive insightful findings regarding the mindistance solution,which are further validated through simulations using the resource extraction differential games model.Specifically,we examine scenarios such as managing a finite resource stock in the resource extraction game.Furthermore,a comparative analysis is conducted,pitting the mindistance bargaining solution against well-established alternatives such as Nash bargaining,Kalai-Smorodinsky,and Egalitarian solutions.By subjecting these solutions to numerical evaluations,the study offers valuable insights into decision-making processes.The findings not only contribute to negotiation theory by providing theoretical support but also have practical implications for decision-makers seeking effective strategies.This research significantly advances the field of negotiation theory,particularly in the context of differential games.The proposed min-distance bargaining solution demonstrates its applicability to real-world scenarios and enhances our understanding of strategic decision-making.
基金supported by the Aeronautical Science Foundation of China(20220001057001)an Open Project of the National Key Laboratory of Air-based Information Perception and Fusion(202437)
文摘In this paper,a distributed adaptive dynamic programming(ADP)framework based on value iteration is proposed for multi-player differential games.In the game setting,players have no access to the information of others'system parameters or control laws.Each player adopts an on-policy value iteration algorithm as the basic learning framework.To deal with the incomplete information structure,players collect a period of system trajectory data to compensate for the lack of information.The policy updating step is implemented by a nonlinear optimization problem aiming to search for the proximal admissible policy.Theoretical analysis shows that by adopting proximal policy searching rules,the approximated policies can converge to a neighborhood of equilibrium policies.The efficacy of our method is illustrated by three examples,which also demonstrate that the proposed method can accelerate the learning process compared with the centralized learning framework.
基金国家自然科学基金，Outstanding Young Teachers of Ministry of Education of China，Special Fund for Ph.D.Program of Ministry of Education of China，Fok Ying Tung Education Foundation
文摘The existence and uniqueness of the solutions for one kind of forward- backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. Then these results were applied to nonzero-sum differential games with random jumps to get the explicit form of the open-loop Nash equilibrium point by the solution of the forward-backward stochastic differential equations.
文摘This paper studies a class of continuous-time two person zero-sum stochastic differential games characterized by linear It?’s differential equation with state-dependent noise and Markovian parameter jumps. Under the assumption of stochastic stabilizability, necessary and sufficient condition for the existence of the optimal control strategies is presented by means of a system of coupled algebraic Riccati equations via using the stochastic optimal control theory. Furthermore, the stochastic H∞ control problem for stochastic systems with Markovian jumps is discussed as an immediate application, and meanwhile, an illustrative example is presented.
基金supported in part by the National Natural Science Foundation of China(Grant Nos. 12172288 and 12472046)the National Key Research and Development Program of China (Grant No. 2021YFC2202600)
文摘The problem of in-orbit cooperative target enclosing involving N thrust-limited satellites under collision avoidance and maneuver amplitude constraints is studied. In order to find global optimal trajectories for target enclosing task with all constraints above, by integrating the collision threat and maneuver boundaries into a novel nonlinear cost functional, the studied target enclosing problem is described as a nonlinear nonzero-sum differential game. Further, to avoid iterative calculations caused by traditional nonlinear-game-solving methods, an approximate solution which can be constructed directly is designed. Then the approximate Nash equilibrium strategies can be educed by the constructive approximate solution for the proposed nonzero-sum game. Analysis shows that the proposed control strategies can asymptotically approach the exact one and can ensure a zero-error tracking of the enclosing configuration.Simulation results illustrate lower time costs and better enclosing accuracy while the collision avoidance and maneuver amplitude constraints are satisfied simultaneously.
文摘For the high altitude cruising flight phase of a hypersonic cruise missile （HCM）, a relative motion mod- el between the missile and the target is established by defining virtual target and combining the theory of the dif- ferential geometry with missile motion equations. Based on the model, the motion between the missile and the tar- get is considered as a single target differential game problem, and a new open-loop differential game midcourse guidance law （DGMGL） is deduced by solving the corresponding Hamiltonian Function. Meanwhile, a new struc- ture of a closed-loop DGMGL is presented and the training data for back propagation neural network （BPNN） are designed. By combining the theory of BPNN with the open-loop DGMGL obtained above, the law intelligence is realized. Finally, simulation is carried out and the validity of the law is testified.
基金co-supported by the National Natural Science Foundation of China (Nos.61603115,91438202 and91638301)China Postdoctoral Science Foundation (No.2015M81455)+1 种基金the Open Fund of National Defense Key Discipline Laboratory of Micro-Spacecraft Technology of China (No.HIT.KLOF.MST.201601)the Heilongjiang Postdoctoral Fund of China (No.LBH-Z15085)
文摘This paper studies the proximate satellite interception guidance strategies where both the interceptor and target can perform orbital maneuvers with magnitude limited thrusts. This problem is regarded as a pursuit-evasion game since satellites in both sides will try their best to capture or escape. In this game, the distance of these two players is small enough so that the highly nonlinear earth-centered gravitational dynamics can be reduced to the linear Clohessy-Wiltshire（CW） equations. The system is then simplified by introducing the zero effort miss variables. Saddle solution is formulated for the pursuit-evasion game and time-to-go is estimated similarly as that for the exoatmospheric interception. Then a vector guidance is derived to ensure that the interception can be achieved in the optimal time. The proposed guidance law is validated by numerical simulations.
基金National Natural Science Foundation of China (60874040)
文摘For intercepting modern high maneuverable targets, a novel adaptive weighted differential game guidance law based on the game theory of mixed strategy is proposed, combining two guidance laws which are derived from the perfect and imperfect in- formation pattern, respectively. The weights vary according to the estimated error of the target＇s acceleration, the guidance law is generated by directly using the estimation of target＇s acceleration when the estimated error is small, and a differential game guidance law with adaptive penalty coefficient is implemented when the estimated error is large. The adaptive penalty coeffi- cients are not constants and they can be adjusted with current target maneuverability. The superior homing performance of the new guidance law is verified by computer simulations.
基金supported by the National Natural Science Foundation of China(11672093)
文摘A conflict of three players, including an attacker, a defender, and a target with bounded control is discussed based on the differential game theories in which the target and the defender use an optimal pursuit strategy. The current approach chooses the miss distance as the outcome of the conflict. Different optimal guidance laws are investigated, and feasible conditions are analyzed for the attacker to accomplish an attacking task. For some given conditions, the attacker cannot intercept the target by only using a one-to-one optimal pursuit guidance law; thus, a guidance law for the attacker to reach a critical safe value is investigated.Specifically, the guidance law is divided into two parts. Before the engagement time between the defender and the attacker, the attacker uses this derived guidance law to guarantee that the evasion distance from the defender is safe, and that the zero-effort-miss(ZEM) distance between the attacker and the target is the smallest.After that engagement time, the attacker uses the optimal one-toone guidance law to accomplish the pursuit task. The advantages and limited conditions of these derived guidance laws are also investigated by using nonlinear simulations.
文摘The optimal guidance problem for an interceptor against a ballistic missile with active defense is investigated in this paper.A class of optimal guidance schemes are proposed based on linear quadratic differential game method and numerical solution of Riccati differential equation.By choosing proper parameters, the proposed guidance schemes are able to drive the interceptor to the target and away from the defender simultaneously.Additionally, fuel cost, control saturation,chattering phenomenon and parameters selection were taken into account.Satisfaction of the proposed guidance schemes of the saddle point condition is proven theoretically.Finally, nonlinear numerical examples are included to demonstrate the effectiveness and performance of the developed guidance approaches.Comparison of control performance between different guidance schemes are presented and analysis.
基金supported by National Key R&D Program of China, No.2018YFB1003905the Fundamental Research Funds for the Central Universities, No.FRF-TP-18-008A3
文摘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.
基金supported by the Science and Technology Innovation 2030-Key Project of “New Generation Artificial Intelligence”,China(No.2020AAA0108200)the National Natural Science Foundation of China(Nos.61873011,61922008,61973013 and 61803014)+3 种基金the Defense Industrial Technology Development Program,China(No.JCKY2019601C106)the Innovation Zone Project,China(No.18-163-00-TS-001-00134)the Foundation Strengthening Program Technology Field Fund,China(No.2019-JCJQ-JJ-243)the Fund from Key Laboratory of Dependable Service Computing in Cyber Physical Society,China(No.CPSDSC202001)。
文摘This paper is concerned with a scenario of multiple attackers trying to intercept a target with active defense.Three types of agents are considered in the guidance:The multiple attackers,the target and the defender,where the attackers aim to pursuit the target from different directions and evade from the defender simultaneously.The guidance engagement is formulated in the framework of a zero-sum two-person differential game between the two opposing teams,such that the measurements on the maneuver of the target or estimations on the defending strategy of the defender can be absent.Cooperation of the attackers resides in two aspects:redundant interception under the threat of the defender and the relative intercept geometry with the target.The miss distances,the relative intercept angle errors and the costs of the agents are combined into a single performance index of the game.Such formulation enables a unitary approach to the design of guidance laws for the agents.To minimize the control efforts and miss distances for the attackers,an optimization method is proposed to find the best anticipated miss distances to the defender under the constraint that the defender is endowed with a capture radius.Numerical simulations with two cases are conducted to illustrate the effectiveness of the proposed cooperative guidance law.
基金supported by the National Science Foundation Project of P. R. China (No. 61501026,61572072)Fundamental Research Funds for the Central Universities (No. FRF-TP-15-032A1)
文摘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.
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.
文摘In order to intercept the future targets that are characterized by high maneuverability, multiple interceptors may be launched and aimed at single target. The scenario of two missiles P and Q intercepting a single target is modeled as a two-pursuit single-evader non-zero-sum linear quadratic differential game. The intercept space is decomposed into three subspaces which are mutually disjoint and their union covers the entire intercept space. The effect of adding the second interceptor arises in the intercept space of both P and Q （PQ-intercept space）. A guidance law is derived from the Nash equilibrium strategy set （NESS） of the game. Simulation studies are focused on the PQ-intercept space. It is indicated that 1） increasing the target＇s maneuverability will enlarge PQ-intercept space; 2） the handover conditions will be released if the initial zero-effort-miss （ZEM） of both interceptors has opposite sign; 3） overvaluation of the target＇s maneuverability by choosing a small weight coefficient will generate robust performance with respect to the target maneuvering command switch time and decrease the fuel requirement; and 4） cooperation between interceptors increases the interception probability.
基金supported by National Science Foundation Project of P. R. China (No. 61501026, U1603116)
文摘In this paper, a Stackelberg differential game based approach is proposed to solve the bandwidth allocation problems in satellite communication network. All the satellites are divided into two groups, one has high download requirements, and the other one has low download requirements. Each satellites group has its own controller for bandwidth allocation, and can get payments from the satellites for the allocated resources. The relationships between the controllers and satellites are formed as a Stackelberg game. In our model, differential equation is introduced to describe the bandwidth dynamics for the whole satellite communication network. Combine the differential equation and Stackelberg game together, we can formulate the bandwidth allocation problems in satellite communication network as a Stackelber differential game. The solutions to the proposed game is solved based the Bellman dynamic equations. Numerical simulations are given to prove the effeteness and correctness of the proposed approach.
