Maneuvering confrontation method and system based on asymmetric information game

Abstract

The invention provides a maneuvering confrontation method and system based on an asymmetric information game. The maneuvering confrontation method comprises the steps that S1, differential equation form mathematical model characterization of the maneuvering game is established; establishing a feasible strategy space of the maneuvering game based on the differential game expression; establishing a representation description of asymmetric observation information of the two parties, and designing a target decision function of information favor of an information dominant party and risk avoidance of an information disadvantaged party; calculating a payment function of the asymmetric information game; and generating a reliable differential game strategy according to the payment function. According to the method, a discrete equation form of a maneuvering game and expression of an information asymmetric structure are provided, an improved payment function of an asymmetric form is given, and an effective method is provided for establishing a maneuvering confrontation model more conforming to information conditions.

Description

Technical Field

[0001] The present invention relates to the field of confrontation technology, and in particular to a mobile confrontation method and system based on asymmetric information game. Background Art

[0002] Maneuver confrontation is a game model involving multiple parties. Each party continuously adjusts its strategy to achieve the optimal maneuver result and position situation. It usually involves position perception, control of maneuver performance and selection of maneuver timing, emphasizing rapid response to the environment and the ability to predict the opponent's strategy.

[0003] Existing maneuver confrontation games mostly use optimization estimation, mathematical game and other related methods, which are divided into two steps. First, vector analysis, matrix game and other methods are used to complete the maneuver modeling analysis, and then nonlinear programming, improved simplex method and other methods are used to complete the strategy solution. These methods often discretize the state space and optional countermeasures of the maneuver countermeasures, which simplifies the feasible range of the strategy on the one hand, and also brings the problem of insufficient continuity of the selected strategy on the other hand.

[0004] Compared with the above methods, the theoretical research on differential game strategies is based on dynamic programming. When multiple parties conduct strategy activities, a group of differential equations is used to describe the game state and rules. It is a method based on differential equations to solve the optimal strategy for dynamic continuous transformation of multiple states. The dynamic continuity and mathematical characteristics of differential strategies make them more suitable for use in confrontation environments. They have the advantages of fast solution speed, clear mapping characteristics, generation of continuous strategies, and easy migration of pure mathematical strategies.

[0005] However, the actual confrontational environment has a strong characteristic of observation uncertainty and incompleteness, and the information structure obtained by both parties will greatly affect the outcome of the decision. The so-called asymmetric information structure means that one party in the game has obtained more information than the other party. In this game confrontation scenario, the party with more information will be more inclined to adopt favorable strategies, using the observation information difference between the environment and the control parameters to induce the other party into an unfavorable position and limit the set of optional countermeasures of the disadvantaged party, thereby causing greater decision-making losses to the opponent. The party with less information is more inclined to adopt a risk-averse strategy, evaluate the current information loss and deviation, and adjust to choose more cautious countermeasures, thereby reducing the decision-making losses caused by insufficient information.

[0006] Patent document CN106953879A discloses a network defense strategy selection method for an optimal response dynamic evolutionary game model, including: based on bounded rationality conditions, using the optimal response dynamic learning mechanism, constructing an attack and defense evolutionary game model based on optimal response dynamics; using the dynamic evolutionary process and defense evolutionary equilibrium point of the defense party strategy selection, the problem of defense strategy selection between different defenders is studied; based on the established optimal response dynamic evolutionary game model, the model is analyzed and solved through specific examples to generalize the evolutionary game model.

[0007] However, the strategies generated by existing mobile confrontation methods often consider the game conditions when both parties have complete and consistent information. In the scenario of incomplete and asymmetric information, the applicability of such strategies is reduced, which will affect the final game confrontation effect. How to use the asymmetric information structure in the confrontation environment to establish a mobile tracking and avoidance strategy that meets the information conditions is of inventive significance. Summary of the invention

[0008] In view of the defects in the prior art, the purpose of the present invention is to provide a mobile confrontation method and system based on asymmetric information game.

[0009] A mobile confrontation method based on asymmetric information game provided by the present invention includes:

[0010] Step S1: Establish a mathematical model representation of the maneuvering game in the form of a differential equation;

[0011] Step S2: establishing a feasible strategy space of the maneuvering game based on the differential game representation;

[0012] Step S3: Establish a characterization description of the observation information asymmetry between the two parties, and design a target decision function for the party with information advantage and the party with information disadvantage to avoid risks;

[0013] Step S4: Calculate the payoff function of the asymmetric information game;

[0014] Step S5: Generate a reliable differential game strategy based on the payment function.

[0015] Preferably, step S1 includes establishing a kinematic differential game expression of both parties in the game, confirming the control input variables, and converting the motion relationship in the fixed coordinate system into a relative motion equation, and the kinematic differential game expression of the two parties in the maneuverable pursuit is as follows:

[0016]

[0017] Among them, x p (t) represents the state vector of the pursuer at time t during the pursuit process, x e(t) represents the state vector of the evading party at time t during the pursuit process, f p With f e They represent the kinematic forms of the two parties respectively, u(t) and v(t) represent the control strategies adopted by the two parties in pursuit and escape respectively;

[0018] Combining each state vector, the relative motion relationship is converted into the following formula:

[0019]

[0020] Among them, x(t) represents the relative distance, and the initial state x(t0) is a fixed x 0 The duration of the game t0 is the initial time of the game, t f The game ends time.

[0021] Preferably, step S2 includes confirming the game maneuverability constraints and motion state conversion equations, including the game start and end time, and the feasible maneuverability variable range.

[0022] Preferably, let and represents the range of feasible maneuverability variables;

[0023] Establish a set of optional maneuver strategies for both parties, expressed in the form of constraints:

[0024] g ρ (x p (t),x w (t),t)≥0

[0025] h ρ (x e (t),x w (t),t)≥0

[0026] Among them, g ρ With h ρ They represent the trajectory constraint equations of the two parties, and ρ represents the information set of the environment and control variables;

[0027] The terminal boundary conditions of the game are:

[0028] Φ(x(t f ),t f )=0 or

[0029] g ρ (x p (t),x w (t),t)<0 or

[0030] h ρ (x e (t),xw (t),t)<0

[0031] Among them, Φ(x(t f ),t f )=0 means the mobile game task is over, g ρ (x p (t),x w (t),t)<0 and h ρ (x e (t),x w (t),t)<0 indicates a violation of the game performance constraint.

[0032] Preferably, step S3 comprises:

[0033] Step S3.1: According to the characteristics of information asymmetry in maneuver confrontation, the advantaged party designs a favorable strategy, and the benefit function is expressed as:

[0034]

[0035] in, It represents the behavioral benefits of the advantaged party making targeted strategies after knowing the true value information of the environment and control variables and the biased information known by the disadvantaged party. It indicates information advantage;

[0036] Step S3.2: Estimate the impact of parameter changes on the game boundary based on the first-order sensitivity function and design the risk avoidance strategy of the tracking party; construct the relative sensitivity function matrix S of the constraint γ :

[0037] S γ (t) = RS g (t)

[0038] Where R is the amplification factor, Reason The diagonal matrix formed by

[0039] The risk measurement function of the disadvantaged party with asymmetric information can be finally expressed as:

[0040]

[0041] Risk aversion benefit function for the disadvantaged party The meaning of represents the risk that the party with information disadvantage assesses itself to leave the feasible strategy space under the condition of unknown environment and control parameters.

[0042] Preferably, the asymmetric observation information between the two parties is manifested in the difference in the understanding of the knowledge of the environment and the control variable parameter ρ between the two parties.

[0043] Preferably, the step S4 comprises:

[0044] The basic payment function of the mobile pursuit confrontation process is:

[0045]

[0046] Where H(·) represents the terminal payment function, G p (·) and G e (·) represents the process payment function of the two parties in pursuit and escape;

[0047] The total payoff function of the game under asymmetric information conditions is:

[0048]

[0049] Considering the information situation where the advantaged party is the evader and the disadvantaged party is the pursuer, the total payment function J of the advantaged party is e for:

[0050]

[0051] in, It represents the weight of the pursuit payment part in the total payment function, represents the weight of the information advantage strategy in the total payment, when α o =0 means that the evader does not consider the benefits of the pursuit process, and the strategy becomes pure deception;

[0052] Maximizing this function can obtain the dominant party strategy under asymmetric information conditions;

[0053] With maneuverable guidance in a confrontation environment and the total payment function of the disadvantaged party J p for:

[0054]

[0055] By minimizing this function, we can obtain the risk avoidance strategy of the tracking party under asymmetric information conditions.

[0056] Preferably, a Hamiltonian function is constructed, and the control equation and the co-state equation are obtained through the first-order partial derivative to obtain the actual countermeasures for both the advantages and disadvantages.

[0057] Preferably, step S5 comprises:

[0058] Construct the Hamiltonian function of each party with information asymmetry. For the party with information advantage, the corresponding Hamiltonian function is expressed as:

[0059] H e =J e +λf e (x e (t),v(t))

[0060] For the party with information disadvantage, the corresponding Hamiltonian function is expressed as:

[0061] H p =J p +λf p (x p (t),u(t))

[0062] Where λ is the adjoint variable of the Hamiltonian equation;

[0063] The optimality condition is that the first-order partial derivative is zero, and the control equation is expressed as:

[0064]

[0065]

[0066] The co-state equation is expressed as:

[0067]

[0068] By combining the above equations, we can obtain the game strategy solutions of the advantageous and disadvantaged parties under the condition of asymmetric information.

[0069] A mobile confrontation system based on asymmetric information game provided by the present invention includes:

[0070] Module M1: Establish a mathematical model representation of the maneuvering game in the form of differential equations;

[0071] Module M2: Establishing feasible strategy space of maneuvering game based on the differential game representation;

[0072] Module M3: Establish a characterization description of the observation information asymmetry between the two parties, and design the target decision function for the party with information advantage and the party with information disadvantage to avoid risks;

[0073] Module M4: Computing the payoff function of asymmetric information games;

[0074] Module M5: Generate reliable differential game strategies based on the payment function.

[0075] Compared with the prior art, the present invention has the following beneficial effects:

[0076] 1. The present invention proposes a mathematical model in the form of discrete differential equations for maneuvering games and a characterization description of the information asymmetry observed by both parties, and provides a set of equations to characterize the game confrontation situation, which is more in line with the real scene of confrontation.

[0077] 2. Based on the performance constraint and sensitivity analysis method, the present invention establishes the target decision function of information advantage strategy of the information advantage party and risk aversion of the information disadvantage party, thus realizing the effective use of information under the asymmetric structure.

[0078] 3. The present invention adopts the differential game method to obtain the Nash equilibrium game result, which strongly supports the rapid and accurate solution of the game strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Other features, objects and advantages of the present invention will become more apparent from the detailed description of non-limiting embodiments made with reference to the following drawings:

[0080] Figure 1 It is a schematic diagram of the workflow of the present invention;

[0081] Figure 2 This is a schematic diagram of the asymmetric information game principle in the present invention;

[0082] Figure 3 This is a diagram of the mobile game results of the method embodiment of the present invention. DETAILED DESCRIPTION

[0083] The present invention is described in detail below in conjunction with specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those of ordinary skill in the art, several changes and improvements can also be made without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

[0084] like Figure 2 As shown, the present invention introduces an imperfect observation representation of information into the confrontation situation equation of the two parties in the game, constructs a mathematical expression of the asymmetric information advantages and disadvantages, and clarifies the boundary conditions of the game; establishes a risk function that is advantageous to the party with information advantages and risk-averse to the party with information disadvantages in an asymmetric situation, and adjusts to obtain an asymmetric payment function; based on the differential game method, solves the final mobile pursuit and confrontation strategy of each party in the asymmetric situation. The present invention proposes a discrete equation form of mobile game and a representation of the information asymmetric structure, and provides an improved payment function of asymmetric form, which provides an effective method for establishing a mobile confrontation model that better meets information conditions.

[0085] Embodiment 1

[0086] According to a mobile confrontation method based on asymmetric information game provided by the present invention, Figure 1 and Figure 2 As shown, the steps include:

[0087] Step S1: Establish a mathematical model representation of the maneuvering game in the form of differential equations. Establish a kinematic differential game representation of both parties in the game, confirm the control input variables, and convert the motion relationship under the fixed coordinate system into a relative motion equation. Step S1 includes establishing a kinematic differential game representation of both parties in the maneuvering pursuit, and the formula is as follows:

[0088]

[0089] Among them, x p (t) represents the state vector of the pursuer at time t during the pursuit process, and the initial state x p (t0) is fixed x e (t) represents the state vector of the evading party at time t during the pursuit process, and the initial state x e (t0) is fixed f p With f e They represent the kinematic forms of the two parties respectively. u(t) and v(t) represent the control strategies adopted by the two parties in pursuit and escape respectively.

[0090] Combining each state vector, the relative motion relationship is converted into the following formula:

[0091]

[0092] Among them, x(t) represents the relative distance, and the initial state x(t0) is a fixed x 0 The duration of the game t0 is the initial time of the game, t f The game ends time.

[0093] Step S2: Establishing a feasible strategy space for the maneuvering game based on the differential game representation, confirming the maneuvering performance constraints and motion state transformation equations for the game, including the start and end time of the game, and the feasible maneuvering performance variable range. Step S2 includes:

[0094] make and Represents the range of feasible maneuverability variables. Furthermore, a set of optional maneuver strategies for both parties is established, expressed in the form of constraints:

[0095] g ρ (x p (t),x w (t),t)≥0

[0096] h ρ (x e (t),x w (t),t)≥0

[0097] Among them, g ρ With h ρ They represent the trajectory constraint equations of the two parties, ρ represents the information set of the environment and control variables, and the implicit variable relationship between ρ and the trajectory constraint is represented by a subscript. ρ 、h ρThey are only related to the control inputs u(t) and v(t) respectively, maintaining orthogonality.

[0098] The terminal boundary conditions of the game are:

[0099] Φ(x(t f ),t f )=0 or

[0100] g ρ (x p (t),x w (t),t)<0 or

[0101] h ρ (x e (t),x w (t),t)<0

[0102] Among them, Φ(x(t f ),t f )=0 means the maneuvering game task is over, g ρ (x p (t),x w (t),t)<0 and h ρ (x e (t),x w (t),t)<0 represents a violation of the game performance constraint.

[0103] Step S3: Based on the game description of step S2, a characterization description of the asymmetric observation information between the two parties is established, and a target decision function is designed for the party with information advantage and the party with information disadvantage to avoid risks. Step S3 includes:

[0104] Step S3.1: The asymmetric observation information between the two parties is manifested in the difference in their understanding of the environment and the control variable parameter ρ.

[0105] Consider a situation where we assume that the evading party is the one with more information and has all the information about the parameter vector ρ. represents the true value of ρ; the tracking party is the party with missing information and only has partial information about the parameter vector ρ, using the nominal value In addition, it is assumed that the party with information advantage also has the information held by the party with disadvantage, that is, the nominal value of the parameter of the party with disadvantage known to the evading party

[0106] Step S3.2: According to the characteristics of information asymmetry in maneuvering, the advantaged party designs a favorable strategy, and the benefit function is expressed as:

[0107]

[0108] in, It represents the behavioral benefits of the advantaged party making targeted strategies after knowing the true value information of the environment and control variables and the biased information known by the disadvantaged party. represents information advantage. Advantageous party has a beneficial benefit function It actually represents the risk that the disadvantaged party may violate the constraint under the advantaged party strategy. The larger it is, the more likely the party with information disadvantage is to violate the constraint, which reduces the range of optional maneuvers for the disadvantaged party and is more beneficial to the advantaged escaping party.

[0109] Step S3.3: Correspondingly, the impact of parameter changes on the game boundary is estimated based on the first-order sensitivity function, and the risk avoidance strategy of the tracking party is designed. Integrate the kinematic equation to obtain the transfer equation of the motion state:

[0110]

[0111] Using the Leibniz formula to derive the transfer equation, we get:

[0112]

[0113] The risk sensitivity function S(t) is:

[0114]

[0115] as well as:

[0116] S(t0)=0

[0117] in, represents the information held by the disadvantaged party under the asymmetric information structure, U(t) and P(t) represent the coefficient and deviation term of the sensitivity function, respectively, as shown below:

[0118]

[0119] Since the initial conditions are given, the initial value of the sensitivity function is a zero matrix. From the sensitivity equation, we can see that When there is a very small fluctuation near This is done to a first order approximation:

[0120]

[0121] Similarly, the sensitivity function of the constraint can be written as:

[0122]

[0123] In order to highlight that the constraint sensitivity is greater at the boundary than at the non-boundary position, a nonlinear function γ(z) is introduced, which satisfies:

[0124]

[0125] in is a continuous function that increases monotonically in the interval (-∞,0). In actual calculation, the Gaussian kernel function can be used etc. functions to calculate.

[0126] Thus, the relative sensitivity function matrix S of the constraints is constructed. γ :

[0127] S γ (t) = RS g (t)

[0128] Where R is the amplification factor, Reason The diagonal array formed.

[0129] The risk measurement function of the disadvantaged party with asymmetric information can be finally expressed as:

[0130]

[0131] Risk aversion benefit function for the disadvantaged party The meaning of represents the risk of the information disadvantage party assessing itself to leave the feasible strategy space under the condition of unknown environment and control parameters. Therefore, the selected control strategy u makes The smaller it is, the lower the risk and the more conservative the strategy. This means that the disadvantaged party believes that the current information has a high degree of incomplete bias, and the selected strategy should be more conservative, so the benefit of adopting a risk-averse solution is higher.

[0132] Step S4: Based on step S3, the complete target decision function of the two is calculated, and the payment function of the asymmetric information game is adjusted according to the form and information structure of both parties. Step S4 includes:

[0133] The basic payment function of the mobile pursuit confrontation process is:

[0134]

[0135] Where H(·) represents the terminal payment function, G p (·) and G e (·) respectively represent the process payment functions of the two parties in pursuit and escape. The former represents the terminal distance in the pursuit process. The pursuit party hopes that the relative distance is small, while the escape party hopes that the relative distance is large. The latter usually represents the control consumption of both parties in the pursuit process. The two parties constitute a zero-sum game at the basic payment function level. The pursuit party hopes to minimize the payment, while the escape party hopes to maximize the payment.

[0136] The total payoff function of the game under asymmetric information is:

[0137]

[0138] Consider the information situation where the advantaged party is the evader and the disadvantaged party is the pursuer. The total payment function J of the advantaged party is e for:

[0139]

[0140] in, Represents the weight of the pursuit payment part in the total payment function, represents the weight of the information advantage strategy in the total payment. o =0, which means that the evading party does not consider the benefits of the pursuit process, and the strategy becomes pure deception.

[0141] Maximizing this function can obtain the dominant strategy under asymmetric information conditions.

[0142] Compared with the prior art, the present invention provides a total payment function J of the disadvantaged party with maneuverable guidance and in-competent guidance under confrontation environment based on the mathematical model representation of observation information asymmetry, differential game method and favorable control and risk avoidance design of information advantages and disadvantages. p for:

[0143]

[0144] By minimizing this function, we can obtain the risk avoidance strategy of the tracking party under asymmetric information conditions.

[0145] Step S5: Generate a reliable differential game strategy based on the payoff function. Construct a Hamiltonian function, and obtain the control equation and co-state equation through the first-order partial derivative to obtain the actual strategy of the superior and inferior parties. Step S5 includes:

[0146] Define the Hamiltonian function, solve the optimal solution through Hamilton-Jacobi-Isaacs theory, and combine the boundary conditions of the differential equation to obtain the analytical expression of the optimal strategy.

[0147] Construct the Hamiltonian function of each party with information asymmetry. For the party with information advantage, the corresponding Hamiltonian function is expressed as:

[0148] H e =J e +λf e (x e (t),v(t))

[0149] For the party with information disadvantage, the corresponding Hamiltonian function is expressed as:

[0150] H p =J p+λf p (x p (t),v(t))

[0151] Where λ is the adjoint variable of the Hamiltonian equation.

[0152] The optimality condition is that the first-order partial derivative is zero, and the control equation is expressed as:

[0153]

[0154] The co-state equation is expressed as:

[0155]

[0156] By combining the above equations, we can obtain the game strategy solutions of the advantageous and disadvantaged parties under the condition of asymmetric information.

[0157] The present invention aims to overcome the shortcomings of the prior art in which the decision-making utility is low and the decision-making behavior is easily predicted by the opponent when the underwater information is incomplete or insufficient, and solve the problem of mobile confrontation game with asymmetric information.

[0158] Furthermore, combined with Figure 3 The mobile confrontation method based on asymmetric information game of the present invention is specifically described as follows:

[0159] Firstly, a mathematical model of the maneuver confrontation game in the form of differential equations is established. Indicates the location coordinates of the tracking party, represents the position coordinates of the escaping party, while u(t) and v(t) represent the moving speeds of the chasing and escaping parties respectively, and the two-dimensional coordinates are represented by subscripts respectively. The speeds of the chasing and escaping parties are kept constant at u c and v c , with the ability to control the speed and direction of movement. In order to ensure the capture capability, let u c >v c .

[0160] The trajectory constraint form of the application example is:

[0161] g ρ =||x p (t)-x w (t)||2-r0 2 ≥0

[0162] h ρ =||x e (t)-x w (t)||2-r0 2 ≥0

[0163] In order to simplify the calculation results, the discretized upper and lower game equations are set. At this time, the kinematic equation is expressed as:

[0164] x p k+1 =x p k +u k Δt

[0165] x e k+1 =x e k +v k Δt

[0166]

[0167] Among them, k represents the current time step. In a fixed time window, the time window length is set to NΔt, and Δt represents the step size.

[0168] In a discrete time frame, the target payment function can be converted into the relative distance of the pursuit-escape game, and the payment within a certain time window can be rewritten as:

[0169] J ρ (u 1:N ,v 1:N )=||x p k+N -x e k+N ||2

[0170] Among them, u 1:N ,v 1:N represents the strategy pair adopted by the two parties in a time window, ||x p k+N -x e k+N ||2 represents the relative distance between the two parties after the current time window ends. As the time window moves forward, the game payout for each step can be continuously obtained.

[0171] Furthermore, the information advantage strategy of the evader is calculated. The evader assumes that the tracking party will refer to the bias value under the condition of incomplete information disadvantage. To adopt the strategy of approaching oneself as quickly as possible, the target position obtained according to the deviation value is:

[0172]

[0173] Get estimated tracking party The maneuver expression is:

[0174]

[0175] In the formula Represents the distance between the tracking party and the expected obstacle position. When the relative distance is greater than the set distance α, the tracking party adopts a pursuit strategy; when it is less than α, it chooses to avoid the obstacle.

[0176] The actual payoff of the evader is:

[0177]

[0178] The total payoff of the information advantage strategy is calculated as:

[0179]

[0180] Solve and obtain the information advantage strategy design results of the solution application case.

[0181] At the kth time step, the relative constraint sensitivity function of the tracking party is:

[0182]

[0183] The total payoff of the information disadvantage strategy is calculated as:

[0184]

[0185] Finally, the result of the maneuvering game is Figure 3 shown.

[0186] Embodiment 2

[0187] The present invention also provides a mobile confrontation system based on asymmetric information game. The mobile confrontation system based on asymmetric information game can be realized by executing the process steps of the mobile confrontation method based on asymmetric information game, that is, those skilled in the art can understand the mobile confrontation method based on asymmetric information game as a preferred implementation of the mobile confrontation system based on asymmetric information game.

[0188] A mobile confrontation system based on asymmetric information game provided by the present invention includes:

[0189] Module M1: Establish a mathematical model representation of the maneuvering game in the form of differential equations; the module M1 includes establishing a kinematic differential game representation of both parties in the game, confirming the control input variables, and converting the motion relationship under the fixed coordinate system into a relative motion equation, and the kinematic related differential game representation of both parties in the maneuvering pursuit confrontation, the formula is as follows:

[0190]

[0191] Among them, x p (t) represents the state vector of the pursuer at time t during the pursuit process, x e (t) represents the state vector of the evading party at time t during the pursuit process, fp With f e They represent the kinematic forms of both parties, u(t) and v(t) represent the control strategies adopted by the two parties respectively; the state vectors are combined and converted into the relative motion relationship as follows:

[0192]

[0193] Among them, x(t) represents the relative distance, and the initial state x(t0) is a fixed x 0 The duration of the game t0 is the initial time of the game, t f The game ends time.

[0194] Module M2: Establishing the feasible strategy space of the maneuvering game based on the differential game representation; the module M2 includes confirming the maneuvering performance constraints and motion state transformation equations of the game, including the start and end time of the game, and the feasible maneuvering performance variable range. and Represents the range of feasible maneuverability variables; establishes a set of optional maneuver strategies for both parties, expressed in the form of constraints:

[0195] g ρ (x p (t),x w (t),t)≥0

[0196] h ρ (x e (t),x w (t),t)≥0

[0197] Among them, g ρ With h ρ They represent the trajectory constraint equations of the two parties, and ρ represents the information set of the environment and control variables. The terminal boundary condition of the game is:

[0198] Φ(x(t f ),t f )=0 or

[0199] g ρ (x p (t),x w (t),t)<0 or

[0200] h ρ (x e (t),x w (t),t)<0

[0201] Among them, Φ(x(t f ),t f )=0 means the mobile game task is over, g ρ(x p (t),x w (t),t)<0 and h ρ (x e (t),x w (t),t)<0 indicates a violation of the game performance constraint.

[0202] Module M3: Establish a characterization description of the observation information asymmetry between the two parties, and design a target decision function for the information advantage of the information advantage party and the risk aversion of the information disadvantage party; the module M3 includes: Module M3.1: According to the characteristics of mobile confrontation information asymmetry, the advantage party designs a favorable strategy, and the benefit function is expressed as:

[0203]

[0204] in, It represents the behavioral benefits of the advantaged party making targeted strategies after knowing the true value information of the environment and control variables and the biased information known by the disadvantaged party. Represents information advantage; Module M3.2: Estimate the impact of parameter changes on the game boundary based on the first-order sensitivity function and design the risk avoidance strategy of the tracking party; Construct the relative sensitivity function matrix S of the constraint γ :

[0205] S γ (t) = RS g (t)

[0206] Where R is the amplification factor, Reason The diagonal matrix formed by the information asymmetry disadvantageous party risk measurement function can be finally expressed as:

[0207]

[0208] Risk aversion benefit function for the disadvantaged party The meaning of represents the risk of the information disadvantage party assessing its own departure from the feasible strategy space under the condition of unknown environment and control parameters. The asymmetric observation information between the two parties is manifested in the difference in the understanding of the environment and control variable parameters ρ between the two parties.

[0209] Module M4: Calculate the payment function of the asymmetric information game; the module M4 includes: the basic payment function of the mobile pursuit confrontation process is:

[0210]

[0211] Where H(·) represents the terminal payment function, G p (·) and G e(·) represent the process payment functions of the two parties in pursuit and escape, respectively; the total payment function of the game under the condition of asymmetric information is:

[0212]

[0213] Considering the information situation where the advantaged party is the evader and the disadvantaged party is the pursuer, the total payment function J of the advantaged party is e for:

[0214]

[0215] in, It represents the weight of the pursuit payment part in the total payment function, represents the weight of the information advantage strategy in the total payment, when α o =0 means that the evading party does not consider the benefits of the pursuit process, and the strategy becomes pure deception; maximizing this function can obtain the strategy of the dominant party under asymmetric information conditions; it has the total payment function J of the disadvantaged party and the maneuverable guidance in the confrontation environment p for:

[0216]

[0217] By minimizing this function, we can obtain the risk avoidance strategy of the tracking party under asymmetric information conditions.

[0218] Module M5: Generate reliable differential game strategies based on the payment function. Based on the state estimation and saddle point solution system, the Hamiltonian function is constructed, and the control equation and co-state equation obtained by the first-order partial derivative are used to obtain the actual strategies of the two parties with advantages and disadvantages. Module M5 includes: constructing the Hamiltonian functions of the two parties with asymmetric information. For the party with information advantage, the corresponding Hamiltonian function is expressed as:

[0219] H e =J e +λf e (x e (t),v(t))

[0220] For the party with information disadvantage, the corresponding Hamiltonian function is expressed as:

[0221] H p =J p +λf p (x p (t),u(t))

[0222] Where λ is the adjoint variable of the Hamiltonian equation; the optimality condition is that the first-order partial derivative is zero, and the control equation is expressed as:

[0223]

[0224] The co-state equation is expressed as:

[0225]

[0226] By combining the above equations, we can obtain the game strategy solutions of the advantageous and disadvantaged parties under the condition of asymmetric information.

[0227] Those skilled in the art know that, in addition to realizing the system and its various devices, modules, and units provided by the present invention in a purely computer-readable program code, it is entirely possible to realize the same functions in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered as a hardware component, and the devices, modules, and units included therein for realizing various functions can also be regarded as structures within the hardware component; the devices, modules, and units for realizing various functions can also be regarded as both software modules for realizing the method and structures within the hardware component.

[0228] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, which does not affect the essence of the present invention. In the absence of conflict, the embodiments of the present application and the features in the embodiments can be combined with each other arbitrarily.

Claims

1. A mobile confrontation method based on asymmetric information game, characterized in that: include: Step S1: Establish a mathematical model representation of the maneuvering game in the form of a differential equation; Step S2: establishing a feasible strategy space of the maneuvering game based on the differential game representation; Step S3: Establish a characterization description of the observation information asymmetry between the two parties, and design a target decision function for the party with information advantage and the party with information disadvantage to avoid risks; Step S4: Calculate the payoff function of the asymmetric information game; Step S5: Generate a reliable differential game strategy based on the payment function.

2. The mobile confrontation method based on asymmetric information game according to claim 1 is characterized in that: The step S1 includes establishing a kinematic differential game expression for both parties in the game, confirming the control input variables, and converting the motion relationship in the fixed coordinate system into a relative motion equation. The kinematic differential game expression for both parties in the mobile pursuit is as follows: Among them, x p (t) represents the state vector of the pursuer at time t during the pursuit process, x e (t) represents the state vector of the evading party at time t during the pursuit process, f p With f e They represent the kinematic forms of the two parties respectively, u(t) and v(t) represent the control strategies adopted by the two parties in pursuit and escape respectively; Combining each state vector, the relative motion relationship is converted into the following formula: Among them, x(t) represents the relative distance, and the initial state x(t0) is a fixed x 0 The duration of the game t0 is the initial time of the game, t f The game ends time.

3. The mobile confrontation method based on asymmetric information game according to claim 1 is characterized in that: The step S2 includes confirming the game maneuverability constraints and motion state conversion equations, including the game start and end time, and the feasible maneuverability variable range.

4. The mobile confrontation method based on asymmetric information game according to claim 3 is characterized in that: make and represents the range of feasible maneuverability variables; Establish a set of optional maneuver strategies for both parties, expressed in the form of constraints: g ρ (x p (t),x w (t),t)≥0 h ρ (x e (t),x w (t),t)≥0 Among them, g ρ With h ρ They represent the trajectory constraint equations of the two parties, and ρ represents the information set of the environment and control variables; The terminal boundary conditions of the game are: Φ(x(t f ),t f )=0 or g ρ (x p (t),x w (t),t)<0 or h ρ (x e (t),x w (t),t)<0 Among them, Φ(x(t f ),t f )=0 means the mobile game task is over, g ρ (x p (t),x w (t),t)<0 and h ρ (x e (t),x w (t),t)<0 indicates a violation of the game performance constraint.

5. The mobile confrontation method based on asymmetric information game according to claim 1 is characterized in that: The step S3 comprises: Step S3.1: According to the characteristics of information asymmetry in maneuver confrontation, the advantaged party designs a favorable strategy, and the benefit function is expressed as: in, It represents the behavioral benefits of the advantaged party making targeted strategies after knowing the true value information of the environment and control variables and the biased information known by the disadvantaged party. Indicates information advantage; Step S3.2: Estimate the impact of parameter changes on the game boundary based on the first-order sensitivity function and design the risk avoidance strategy of the tracking party; construct the relative sensitivity function matrix S of the constraint γ : S γ (t)=RS g (t) Where R is the amplification factor, Reason The diagonal matrix formed by The risk measurement function of the disadvantaged party with asymmetric information can be finally expressed as: Risk aversion benefit function for the disadvantaged party The meaning of represents the risk that the party with information disadvantage assesses itself to leave the feasible strategy space under the condition of unknown environment and control parameters.

6. The mobile confrontation method based on asymmetric information game according to claim 1 is characterized in that: The asymmetric observation information between the two parties is manifested in the difference in their understanding of the environment and the control variable parameter ρ.

7. The mobile confrontation method based on asymmetric information game according to claim 1 is characterized in that: The step S4 comprises: The basic payment function of the mobile pursuit confrontation process is: Where H(·) represents the terminal payment function, G p (·) and G e (·) represents the process payment function of the two parties in pursuit and escape; The total payoff function of the game under asymmetric information conditions is: Considering the information situation where the advantaged party is the evader and the disadvantaged party is the pursuer, the total payment function J of the advantaged party is e for: in, It represents the weight of the pursuit payment part in the total payment function, represents the weight of the information advantage strategy in the total payment, when α o =0 means that the evader does not consider the benefits of the pursuit process, and the strategy becomes pure deception; Maximizing this function can obtain the dominant party strategy under asymmetric information conditions; With maneuverable guidance in a confrontation environment and the total payment function of the disadvantaged party J p for: By minimizing this function, we can obtain the risk avoidance strategy of the tracking party under asymmetric information conditions.

8. The mobile confrontation method based on asymmetric information game according to claim 1 is characterized in that: The Hamiltonian function is constructed, and the control equation and co-state equation are obtained through the first-order partial derivative to obtain the actual countermeasures for both the advantaged and disadvantaged parties.

9. The mobile confrontation method based on asymmetric information game according to claim 8 is characterized in that: Step S5 includes: Construct the Hamiltonian function of each party with information asymmetry. For the party with information advantage, the corresponding Hamiltonian function is expressed as: H e =J e +λf e (x e (t),v(t)) For the party with information disadvantage, the corresponding Hamiltonian function is expressed as: H p =J p +λf p (x p (t),u(t)) Where λ is the adjoint variable of the Hamiltonian equation; The optimality condition is that the first-order partial derivative is zero, and the control equation is expressed as: The co-state equation is expressed as: By combining the above equations, we can obtain the game strategy solutions of the advantageous and disadvantaged parties under the condition of asymmetric information.

10. A mobile confrontation system based on asymmetric information game, characterized in that: include: Module M1: Establish a mathematical model representation of the maneuvering game in the form of differential equations; Module M2: Establishing feasible strategy space of maneuvering game based on the differential game representation; Module M3: Establish a characterization description of the observation information asymmetry between the two parties, and design the target decision function for the party with information advantage and the party with information disadvantage to avoid risks; Module M4: Computing the payoff function of asymmetric information games; Module M5: Generate reliable differential game strategies based on the payment function.

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