Fast solution method and system for multi-uav attack-defense game

Abstract

The application provides a quick solution method and system for multi-UAV attack and defense game. The method calculates a strict game matrix through a zero-sum game matrix model to obtain a Nash equilibrium solution. According to the Nash equilibrium solution, a first initial strategy group of a first UAV formation and a second initial strategy group of a second UAV formation are selected, a first optimal strategy group of the first UAV formation is solved based on attack and defense strategy probability and the second initial strategy group, and a second optimal strategy group of the second UAV formation is solved based on attack and defense strategy probability and the first initial strategy group. If the calculated first optimal strategy group and / or the second optimal strategy group is not in the strict game matrix, the strict game matrix is updated, and the Nash equilibrium solution is recalculated. If the optimal strategy groups are all in the strict game matrix, the strategy groups of the multi-UAV formation are set according to the Nash equilibrium solution. The application improves the solution efficiency of multi-UAV target allocation scheme by introducing attack and defense strategies.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) technology, and specifically to a rapid solution method and system for multi-UAV attack-defense game. Background Technology

[0002] Unmanned aerial vehicles (UAVs) can autonomously complete given tasks in various environments, effectively reducing manpower costs. Compared to manned aircraft, UAVs have advantages such as no personnel casualties, high maneuverability, lighter weight, and lower cost. However, due to the limited number and performance of weapons and sensors carried by a single UAV, its ability to perform air combat missions is correspondingly limited. Effective coordination among multiple UAVs can better accomplish air combat missions; therefore, multi-UAV formations for coordinated mission execution have received increasing attention. How to set target allocations for coordinated combat in UAV formations remains a major challenge.

[0003] In existing technologies, most experts and scholars use game theory methods to solve multi-UAV target allocation models built based on game theory, including exact solution algorithms and heuristic solution algorithms.

[0004] Due to the high complexity of these problems, their size grows exponentially with the number of drones. Most existing algorithms are only suitable for small to medium-sized problems, or cannot simultaneously achieve both high efficiency and fast processing time. Exact algorithms are only suitable for small-scale weapon target allocation problems and struggle to find optimal solutions for medium to large-scale problems within a reasonable timeframe. Heuristic algorithms can fully utilize domain knowledge to improve efficiency, but the quality of the solution depends on the heuristic rules, resulting in performance fluctuations and a tendency to get trapped in local optima, leading to low efficiency in solving allocation schemes. Summary of the Invention

[0005] (a) Technical problems to be solved

[0006] To address the shortcomings of existing technologies, this invention provides a fast solution method and system for multi-UAV attack and defense game, solving the technical problem of low solution efficiency when obtaining target allocation schemes for multiple UAVs in existing technologies.

[0007] (II) Technical Solution

[0008] To achieve the above objectives, the present invention provides the following technical solution:

[0009] This invention provides a fast solution method for multi-UAV attack-defense game theory, which solves its technical problem. The fast solution method is executed by a computer and includes the following steps:

[0010] A zero-sum game matrix model is constructed. This model includes multi-drone formation information (first and second drone formations), multi-drone strategy information, and a payoff matrix. The multi-drone strategy information includes a set of strategy groups for the drone formations, where each strategy group contains strategy pairs for multiple drones within the formation. These strategy pairs characterize offensive and defensive strategies and their objectives. The offensive and defensive strategies include attack strategies, evasion strategies, and interference strategies. The multi-drone formation information includes drone information within the formations, and this drone information includes the probabilities of offensive and defensive strategies.

[0011] The strict game matrix is ​​calculated based on the zero-sum game matrix model, and the Nash equilibrium solution is solved based on the strict game matrix.

[0012] Based on the Nash equilibrium solution, select the first initial strategy group for the first drone formation and the second initial strategy group for the second drone formation; the initial strategy group is the strategy group with the highest probability in the strict game matrix.

[0013] Based on the attack and defense strategy probabilities and the second initial strategy set, the first optimal strategy set for the first UAV formation is solved, and based on the attack and defense strategy probabilities and the first initial strategy set, the second optimal strategy set for the second UAV formation is solved;

[0014] If the first optimal strategy group and / or the second optimal strategy group are not in the strict game matrix, then update the strict game matrix and re-execute the step of solving for the Nash equilibrium solution based on the strict game matrix based on the updated strict game matrix.

[0015] If both the first optimal strategy group and the second optimal strategy group are in the strict game matrix, then the strategy group for the multi-drone formation is set according to the Nash equilibrium solution.

[0016] Preferably, the revenue matrix includes:

[0017]

[0018] Among them, S R s represents the first drone formation strategy group set. R ∈S R S represents a strategy group of the first drone formation. B Indicates the second drone formation strategy group set, s B ∈S B This represents a strategy group for the second drone formation;

[0019] (s R ,s B This indicates that the first drone formation adopted strategy group s R The second drone formation adopted a strategy group sB Strategy group combination; u(s) R ,s B ) for the first drone formation in the strategy group combination (s R ,s B The returns under )

[0020] u(s R ,s B )=u R (s R ,s B )-u B (s R ,s B )

[0021]

[0022] Among them, u R (s R ,s B ) and u B (s R ,s B () represent the expected survival value of a drone formation and a drone formation, respectively.

[0023] v i v represents the value of drone i in the first drone formation. j Let m represent the value of drone j in the second drone formation; drone j is the strategic target of drone i; m represents the number of drones in the first drone formation, and n represents the number of drones in the second drone formation.

[0024] q i h represents the probability of drone i avoiding the second drone formation. i The parameter q represents the avoidance parameters of drone i against the second drone formation. j h represents the probability that drone j will avoid the first drone formation. j This represents the avoidance parameters of drone j against the first drone formation;

[0025] t ij Let l represent the probability of drone i interfering with drone j. ij The parameter t represents the interference parameter of UAV i on UAV j. ji Let l represent the probability of drone j interfering with drone i. ji This represents the interference parameters of drone j on drone i;

[0026] p ji b represents the probability of drone j killing drone i. ji p represents the attack parameters of drone j against drone i; ijLet a represent the probability of drone i killing drone j. ij This represents the attack parameters of drone i against drone j.

[0027] Preferably, calculating the strict game matrix based on the zero-sum game matrix model includes:

[0028] Select p strategy groups from the first set of UAV formation strategy groups and q strategy groups from the second set of UAV formation strategy groups; where p≥2 and q≥2.

[0029] A strict game matrix is ​​generated based on the p strategy groups and the q strategy groups.

[0030] Preferably, the step of solving for the Nash equilibrium solution based on the strict game matrix includes:

[0031] The strict game matrix is ​​processed based on a preset probability distribution algorithm to solve for the Nash equilibrium solution; the Nash equilibrium solution includes the first probability distribution of the p strategy groups and the second probability distribution of the q strategy groups.

[0032] The first initial strategy group for the first UAV formation and the second initial strategy group for the second UAV formation are selected based on the Nash equilibrium solution, including:

[0033] Traverse the Nash equilibrium solutions, obtain the strategy group with the highest probability according to the first probability distribution, and determine it as the first initial strategy group; obtain the strategy group with the highest probability according to the second probability distribution, and determine it as the second initial strategy group.

[0034] Preferably, solving for the first optimal strategy group of the first UAV formation based on the attack and defense strategy probabilities and the second initial strategy group includes:

[0035] Initialize a first drone vector for a first drone formation; the first drone vector is used to characterize the policy pair state of each drone in the first drone formation, the policy pair state includes a determined state indicating that the drone has determined a policy pair and an undetermined state indicating that the drone has not determined a policy pair; in the initialized first drone vector, the policy pair state of all drones is undetermined.

[0036] Calculate the initial survival probability of the UAV; based on the first UAV vector, obtain the first target UAV in the first UAV formation that is in an uncertain state; obtain multiple target UAV policy pairs of the target UAV from the multi-UAV policy information;

[0037] The marginal reward value of the target drone strategy pair is calculated based on the initial survival probability of the drone, and the target drone strategy pair with the largest marginal reward value is set as the target strategy pair of the target drone.

[0038] Update the policy pair state of the target UAV in the first UAV vector to a determined state, and detect the updated first UAV vector;

[0039] If there is a drone in the updated first drone vector that is in an uncertain state, then the step of obtaining the first target drone in the first drone formation that is in an uncertain state based on the first drone vector is re-executed based on the updated first drone vector.

[0040] If all drones in the updated first drone vector are in a deterministic state, then the first optimal policy group is determined based on the target policy pairs of all drones.

[0041] Preferably, the calculation of the initial survival probability of the drone includes:

[0042] Set the first initial avoidance probability for the first drone formation and the second initial avoidance probability for the second drone formation; calculate the first initial probability of a drone in the first drone formation not being destroyed and the second initial probability of a drone in the second drone formation not being destroyed:

[0043]

[0044] in,

[0045] B_uninterference[j] represents the probability that drone j is not interfered with by the first drone formation;

[0046] R_undes[i] represents the initial probability that drone i is not destroyed;

[0047] R_uninterference[i] represents the probability that drone i is not interfered with by the second drone formation;

[0048] B_undes[j] represents the second initial probability that drone j is not destroyed;

[0049] The initial survival probability of a first UAV in the first UAV formation is calculated based on the first initial avoidance probability and the first initial survival probability; the initial survival probability of a second UAV in the second UAV formation is calculated based on the second initial avoidance probability and the second initial survival probability; including:

[0050] R_survival[i]=1-(1-R_evasive[i])·(1-R_undes[i])

[0051] B_survival[j]=1-(1-B_evasive[j])·(1-B_undes[j])

[0052] Where R_survival[i] represents the first initial survival probability of drone i, R_evasive[i] represents the first initial evasion probability of drone i, and R_undes[i] represents the first initial probability of drone i not being destroyed;

[0053] B_survival[j] represents the second initial survival probability of drone j, and B_evasive[j] represents the second initial avoidance probability of drone j.

[0054] Preferably, the step of calculating the marginal reward value of the target drone strategy pair based on the initial survival probability of the drone includes:

[0055] Based on the target UAV strategy, solve for the attack and defense strategy;

[0056] The updated survival probability of the drone is calculated based on the described attack and defense strategy.

[0057] The marginal reward value of the target drone strategy pair is calculated based on the updated survival probability of the drone and the initial survival probability of the drone.

[0058] Preferably, the step of solving the drone's updated survival probability according to the attack and defense strategy includes:

[0059] Determine the target drone strategy to match the first and second drones;

[0060] If the attack and defense strategy is an attack strategy, the updated survival probability of the first drone is set to be equal to the initial survival probability of the first drone; and the updated survival probability of the second drone is calculated as follows:

[0061] j_survival=1-(1-q j )·(1-Δ B_undes [ipj])

[0062] Δ B_undes [i,p,j]=B_undes[j]·(1-R_uninterference[i]·p ij )

[0063] Where j_survival represents the updated survival probability of the second drone;

[0064] [i,p,j] represents the drone triplet formed by the first drone i and the target drone policy pair [p,j]; q jThis represents the probability that the second drone j will avoid the formation of the first drone;

[0065] If the attack and defense strategy is an evasion strategy, the updated survival probability of the second drone is set to be equal to the initial survival probability of the second drone; and, in the second initial strategy group, it is detected whether any drone uses an attack strategy to attack the first drone; if not, the updated survival probability of the first drone is set to be equal to the initial survival probability of the first drone; if so, the updated survival probability of the first drone is calculated as follows:

[0066] i_survival=1-(1-q i )·(1-R_undes[i])

[0067] Where i_survival represents the survival probability of the first drone; q i This represents the probability that the first drone i will avoid the formation of the second drone;

[0068] If the attack and defense strategy is an interference strategy, the updated survival probability of the first drone is set to be equal to the initial survival probability of the first drone, and the updated survival probability of the second drone is set to be equal to the initial survival probability of the second drone.

[0069] The attack and defense strategy of the second UAV is solved according to the second initial strategy set; and when the attack and defense strategy is an attack strategy, the attack target of the second UAV is obtained; and the association probability set of the UAV triple is calculated according to the attack target; the association probability set includes:

[0070] [i,p,j]=[j_target,j_target_undes,j_target_survival]

[0071]

[0072] j_target_survival=1-(1-R_evasive[j_target])·(1-j_target_undes)

[0073] in,

[0074] j_target represents the attack target, j_target_undes represents the probability that the first drone of the attack target was not destroyed, and j_target_survival represents the updated survival probability of the first drone of the attack target.

[0075] The step of calculating the marginal reward value of the target drone strategy pair based on the updated survival probability of the drone and the initial survival probability of the drone includes:

[0076] δipj =u' R -u R

[0077]

[0078] Where, δ ipj This represents the marginal return value of the target drone strategy pair;

[0079] This indicates the value of the first drone. This indicates the value of the second drone.

[0080] Preferably, before detecting the updated first drone vector, the process further includes:

[0081] Obtain the target attack and defense strategy, the first target UAV, and the second target UAV of the target strategy pair;

[0082] The initial survival probability of the drone is updated according to the target attack and defense strategy, including:

[0083] If the target's attack and defense strategy is an attack strategy, then the second initial probability of the target's second drone not being destroyed and the second initial survival probability of the drone are updated as follows:

[0084] B_undes[j * ]=Δ B_undes [i * ,p * ,j * ]

[0085] B_survival[j * ]=j * _survival

[0086] Among them, i * Indicates the first target drone, p * To represent the target's offensive and defensive strategy, j * Indicates the target is the second drone;

[0087] If the target's attack and defense strategy is an evasion strategy, then the initial evasion probability and the initial survival probability of the first drone are updated as follows:

[0088] R_evasive[i * ] = q i*

[0089] R_survival[i * ] = i * _survival

[0090] If the target attack and defense strategy is an interference strategy, then obtain the target association probability group of the first UAV and the UAV triple formed by the target strategy pair; obtain the attack target in the target association probability group, and update the first initial undestroyed probability of the attack target and the initial survival probability of the first UAV according to the target association probability group.

[0091] This invention provides a fast solution system for multi-UAV attack-defense game theory, which addresses the technical problem of the invention. The system includes:

[0092] The model generation module is configured to construct a zero-sum game matrix model. The zero-sum game matrix model includes multi-drone formation information, multi-drone strategy information, and a payoff matrix for the first and second drone formations. The multi-drone strategy information includes a set of strategy groups for the drone formations, where each strategy group includes strategy pairs for multiple drones within the formation. These strategy pairs represent offensive and defensive strategies and their objectives. The offensive and defensive strategies include attack strategies, evasion strategies, and interference strategies. The multi-drone formation information includes drone information for the drone formations, and the drone information includes the probabilities of the offensive and defensive strategies.

[0093] The rigorous game matrix acquisition module is configured to calculate the rigorous game matrix based on the zero-sum game matrix model and solve for the Nash equilibrium solution based on the rigorous game matrix.

[0094] The initial strategy group module is configured to select the first initial strategy group of the first drone formation and the second initial strategy group of the second drone formation based on the Nash equilibrium solution; the initial strategy group is the strategy group with the highest probability in the strict game matrix.

[0095] The optimal strategy group module is configured to solve for the first optimal strategy group of the first UAV formation based on the attack and defense strategy probability and the second initial strategy group, and to solve for the second optimal strategy group of the second UAV formation based on the attack and defense strategy probability and the first initial strategy group.

[0096] The scheme allocation module is configured to update the strict game matrix if the first optimal strategy group and / or the second optimal strategy group are not in the strict game matrix, and re-execute the step of solving the Nash equilibrium solution based on the strict game matrix based on the updated strict game matrix.

[0097] If both the first and second optimal strategy groups are in the strict game matrix, then the strategy groups for the multi-drone formation are set according to the Nash equilibrium solution.

[0098] (III) Beneficial Effects

[0099] This invention provides a fast solution method and system for multi-UAV attack-defense game. Compared with existing technologies, it has the following advantages:

[0100] This invention calculates the strict game matrix using a zero-sum game matrix model and solves for the Nash equilibrium. Based on the Nash equilibrium, a first initial strategy group for a first drone formation and a second initial strategy group for a second drone formation are selected. The first optimal strategy group for the first drone formation is solved based on the attack / defense strategy probabilities and the second initial strategy group. The second optimal strategy group for the second drone formation is solved based on the attack / defense strategy probabilities and the first initial strategy group. If the first optimal strategy group and / or the second optimal strategy group are not in the strict game matrix, the strict game matrix is ​​updated, and the Nash equilibrium is solved again. If both are in the strict game matrix, the strategy groups for the multi-drone formation are set according to the Nash equilibrium. This invention considers attack and defense strategies, improving the solution efficiency for target allocation schemes involving multiple drones. Attached Figure Description

[0101] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0102] Figure 1 This is a schematic diagram illustrating a scenario for a fast solution method for multi-UAV attack-defense game provided in an embodiment of the present invention. Detailed Implementation

[0103] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are described clearly and completely. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0104] To better understand the above technical solutions, the following will provide a detailed explanation of the technical solutions in conjunction with the accompanying drawings and specific implementation methods.

[0105] This invention provides a fast solution method for multi-UAV attack-defense game, which is executed by a computer and includes the following steps:

[0106] S1. Construct a zero-sum game matrix model; the zero-sum game matrix model includes multi-drone formation information, multi-drone strategy information, and payoff matrix for the first and second drone formations; the multi-drone strategy information includes a set of strategy groups for the drone formations, each strategy group consisting of strategy pairs for multiple drones within the formation, and strategy pairs representing offensive and defensive strategies and strategic objectives; offensive and defensive strategies include attack strategies, evasion strategies, and interference strategies; the multi-drone formation information includes drone information for the drone formations, and the drone information includes the probabilities of offensive and defensive strategies;

[0107] S2. Calculate the strict game matrix based on the zero-sum game matrix model, and solve for the Nash equilibrium solution based on the strict game matrix;

[0108] S3. Select the first initial strategy group of the first drone formation and the second initial strategy group of the second drone formation based on the Nash equilibrium solution; the initial strategy group is the strategy group with the highest probability in the strict game matrix.

[0109] S4. Solve the first optimal strategy group of the first UAV formation based on the attack and defense strategy probability and the second initial strategy group, and solve the second optimal strategy group of the second UAV formation based on the attack and defense strategy probability and the first initial strategy group.

[0110] S5. If the first optimal strategy group and / or the second optimal strategy group are not in the strict game matrix, then update the strict game matrix and re-execute the steps of solving the Nash equilibrium solution based on the strict game matrix based on the updated strict game matrix.

[0111] If both the first and second optimal strategy groups are in the strict game matrix, then the strategy groups for the multi-drone formation are set according to the Nash equilibrium solution.

[0112] Figure 1 This is a schematic diagram illustrating a scenario for the rapid solution method of multi-UAV attack-defense game provided in an embodiment of the present invention. The following is a detailed analysis of each step.

[0113] In step S1, a zero-sum game matrix model is constructed. Considering that the strategies adopted by both drone formations will affect the other's payoff, a zero-sum game matrix model G = (P, S, U) is constructed. This game model includes the drone component, the strategy component, and the payoff component.

[0114] Where P = {R, B} represents the multi-drone formation information, symbolizing the participants in the game. The multi-drone formation information includes drone information. The game involves two multi-drone formations, referred to as the red side and the blue side in this embodiment. R represents the red side, referred to as the first drone formation in this embodiment. B represents the blue side, referred to as the second drone formation in this embodiment.

[0115] It should be noted that each drone in the first drone formation is collectively referred to as the first drone; each drone in the second drone formation is collectively referred to as the second drone. Each drone formation may include a number of drones. The red team has m drones, and the blue team has n drones.

[0116] The drone information also includes the value of each drone. The value of R's drones is expressed as... The value of Party B's drone is expressed as:

[0117] The strategy component S includes multi-UAV strategy information. Strategy component S = SuAV R ×S B , representing the set of strategies employed by the two drone formations in a game. S R Let s represent the set of strategy groups for the first drone formation, i.e., the set of strategy groups for the red side. R ∈S R S represents a strategy group for the red team. B s represents the second drone formation strategy set, i.e., the strategy set of the blue team. B ∈S B This represents a strategy group for the blue team. A strategy group consists of the strategy pairs for each drone in the drone formation.

[0118] The strategy pair includes the current drone, the offensive and defensive strategy, and the strategy target; the offensive and defensive strategy includes attack strategy, evasion strategy, and interference strategy; the strategy group includes strategy pairs of multiple drones in a multi-drone formation.

[0119] In multi-drone games, each drone can adopt three strategies: attack, evasion, and interference. A drone can also use a strategy against any of its opponents; the target is called the strategy objective. Drones can be equipped with both offensive and electronic warfare weapons. A drone can attack an enemy drone, evade an attack from an enemy drone, or interfere with an enemy drone's attack, but can only choose one strategy at a time. Drones can also engage in strategy pairs, which refer to a drone's offensive / defensive strategy and its strategy objective.

[0120] Taking the i-th drone of the red team as an example, its strategy pair is (p,j), indicating that it adopts attack / defense strategy p, and the strategy target is the j-th drone of the blue team. Since the red team drones can adopt 3 strategies, and the strategy target can be set to any one of the n blue team drones, each red team drone can have (3×n) strategy pairs. Similarly, the blue team drones can adopt 3 strategies, and the strategy target can be set to any one of the m red team drones, so each blue team drone can have (3×m) strategy pairs.

[0121] It should be noted that for a drone swarm, each drone adopts a strategy pair during mission execution, and the strategy pairs adopted by all drones together constitute the current strategy group of the drone swarm. As the strategy pairs adopted by each drone may be different, the overall strategy group of the drone swarm will also be different.

[0122] In this embodiment of the application, the use of This represents a strategy group for player R.

[0123] This indicates the strategy pair adopted by drone i of side R, including offensive and defensive strategies and strategic objectives. This indicates the strategy adopted by drone i. These represent three offensive and defensive strategies: attack, evasion, and interference. This represents the strategic objectives of R-side drone i in attacking, evading, and interfering with other drones. For example, if the strategy group formed by R-side's attack and defense strategy is [(1,2),(2,3),(3,3)], it means that R-side drone 1 attacks B-side drone 2, R-side drone 2 evades the attack of B-side drone 3, and R-side drone 3 interferes with B-side drone 3.

[0124] use This can represent a strategy group of Party B. This indicates the strategy adopted by drone j of party B. This indicates the offensive and defensive strategies adopted by drone j. These represent three offensive and defensive strategies: attack, evasion, and interference. This indicates the target that the drone is attacking, evading, or interfering with.

[0125] For a drone swarm, each drone selects a strategy pair. The strategy pairs of all drones are counted to form a strategy group for the drone swarm. Different strategy groups can be obtained by considering the different strategy pairs selected by the drones. All possible strategy group combinations are counted to generate a set of strategy groups, which represents the game strategies that the drone swarm can employ.

[0126] For the red team formation, since each of the m red team drones can have (3×n) policy pairs, the number of policy pairs in the red team formation is τ. R (3×n) m Similarly, the number of strategies τ for the blue team's formation. B (3×m) n The strategy space of an adversary is equal to the product of the number of possible strategy pairs that each adversary can take. Therefore, the size of the strategy space for this game is...

[0127] S|=τ R ·τ B = (3×n)m ·(3×m) n .

[0128] In some embodiments, each attack and defense strategy can be configured with a strategy probability, including the kill probability of an attack strategy, the evasion probability of an evasion strategy, and the interference probability of an interference strategy. The three strategy probabilities are represented as follows:

[0129] Kill probability represents the probability that one drone successfully destroys another drone. The kill probability of Rf1 against Bf1j can be expressed as: The kill probability matrix of R against B can be expressed as: Where p ij Let $\frac{i}{R}$ represent the probability of killing UAV $j from UAV $B$. Similarly, the probability of killing UAV $j from UAV $R$ can be expressed as: The probability matrix of B's ​​kill on R can be expressed as:

[0130] The evasion probability represents the probability that one drone successfully evades an attack from another drone. The evasion probability of Ri against Bi's attack can be expressed as: The avoidance probability matrix of R against B is expressed as follows: Similarly, the probability of B's ​​j avoiding an attack from R can be expressed as: The avoidance probability matrix of Party B against Party R can be expressed as follows:

[0131] The interference probability represents the probability that one drone successfully interferes with an attack by another drone. The interference probability of Rsquarei against Bsquarej can be expressed as: The interference probability matrix of R to B can be expressed as: Similarly, the probability of interference from B_j to R_i can be expressed as: The interference probability matrix of B to R can be expressed as:

[0132] Each probability can be pre-generated, and the probability of each strategy for the drone can be randomly generated.

[0133] The payoff component U is the payoff matrix. The payoff matrix is ​​represented as:

[0134]

[0135] Among them, S R s represents the first drone formation strategy group set. R ∈S R S represents a strategy group of the first drone formation. B Indicates the second drone formation strategy group set, s B ∈S BThis refers to a strategy group within the second drone formation.

[0136] (s R ,s B This indicates that the first drone formation adopted strategy group s R The second drone formation adopted a strategy group s B Strategy group combination; u(s) R ,s B ) for the first drone formation in the strategy group combination (s R ,s B The returns under )

[0137] u(s R ,s B )=u R (s R ,s B )-u B (s R ,s B )

[0138]

[0139] Among them, u R (s R ,s B ) and u B (s R ,s B () represent the expected survival value of a drone formation and a drone formation, respectively.

[0140] v i v represents the value of drone i in the first drone formation. j Let m represent the value of drone j in the second drone formation; drone j is the strategic target of drone i; m represents the number of drones in the first drone formation, and n represents the number of drones in the second drone formation.

[0141] q i h represents the probability of drone i avoiding the second drone formation. i The parameter q represents the avoidance parameters of drone i against the second drone formation. j h represents the probability that drone j will avoid the first drone formation. j This represents the avoidance parameters of drone j against the first drone formation;

[0142] t ij Let l represent the probability of drone i interfering with drone j. ij The parameter t represents the interference parameter of UAV i on UAV j. ji Let l represent the probability of drone j interfering with drone i. jiThis represents the interference parameters of drone j on drone i;

[0143] p ji b represents the probability of drone j killing drone i. ji p represents the attack parameters of drone j against drone i; ij Let a represent the probability of drone i killing drone j. ij This represents the attack parameters of drone i against drone j.

[0144] This represents the total expected survival value of all drones owned by R.

[0145] Let i represent the survival probability of drone i from side R; This indicates the probability that drone i failed to evade and was destroyed. This indicates the probability that drone i failed to evade the attack.

[0146] This represents the probability that drone i will be destroyed;

[0147] This indicates the probability that drone i will not be destroyed;

[0148] This represents the probability that drone i is not destroyed by drone j from side B. Let represent the probability that drone i is destroyed by drone j. This represents the probability that drone j was not successfully interfered with by drone R.

[0149] The three parameter settings are as follows:

[0150]

[0151] Among them, a ij This represents the attack parameters of drone i in the first drone formation against drone j in the second drone formation; m represents the number of drones in the first drone formation, and n represents the number of drones in the second drone formation.

[0152] This indicates the offensive and defensive strategies adopted by drone i; These represent attack strategies, evasion strategies, and interference strategies, respectively. This indicates the strategic target targeted by the offensive and defensive strategies employed by drone i.

[0153] The first evasion strategy parameter matrix is ​​as follows:

[0154]

[0155] Among them, h iThis represents the avoidance parameters of drone i against the second drone formation.

[0156]

[0157] Among them, l ij This represents the interference parameters of drone i on drone j.

[0158] The second strategy parameter matrix includes the second attack strategy parameter matrix, the second evasion strategy parameter matrix, and the second interference strategy parameter matrix.

[0159]

[0160] Among them, b ji This represents the attack parameters of drone j against drone i;

[0161] This indicates the offensive and defensive strategies adopted by drone j. These represent attack strategies, evasion strategies, and interference strategies, respectively. This represents the strategic objective of drone j.

[0162]

[0163] Among them, h j This represents the avoidance parameters of drone j against the first drone formation.

[0164]

[0165] Among them, l ji This represents the interference parameters of drone j on drone i.

[0166] For the payoff matrix of the game, u(s) R ,s B ) is R's strategy combination (s R ,s B The profit value for Party B under the given condition is -u(s). R ,s B ).

[0167] In step S2, a strict game matrix is ​​calculated based on the zero-sum game matrix model, and a Nash equilibrium solution is obtained based on the strict game matrix.

[0168] Select p strategy groups from the first set of UAV formation strategy groups, and select q strategy groups from the second set of UAV formation strategy groups. Where p≥2, q≥2.

[0169] A strict game matrix is ​​generated based on the p strategy groups and the q strategy groups. A first strict game set for the first drone formation is generated based on the p strategy groups, and a second strict game set for the second drone formation is generated based on the q strategy groups.

[0170] The strict game matrix is ​​processed using a pre-defined probability distribution algorithm to solve for the Nash equilibrium. The Nash equilibrium solution comprises a first probability distribution of the p strategy groups and a second probability distribution of the q strategy groups.

[0171] In step S3, a first initial strategy group for the first drone formation and a second initial strategy group for the second drone formation are selected based on the Nash equilibrium solution. The initial strategy group is the strategy group with the highest probability in the strict game matrix.

[0172] Specifically, the Nash equilibrium solutions can be traversed, and the strategy group with the highest probability can be obtained according to the first probability distribution and determined as the first initial strategy group; the strategy group with the highest probability can be obtained according to the second probability distribution and determined as the second initial strategy group.

[0173] In step S4, the first optimal strategy group for the first UAV formation is solved based on the attack and defense strategy probabilities and the second initial strategy group, and the second optimal strategy group for the second UAV formation is solved based on the attack and defense strategy probabilities and the first initial strategy group.

[0174] We can first solve for the first optimal strategy group of the first drone formation, including the following steps:

[0175] S401. Initialize the first drone vector of the first drone formation. The first drone vector is used to characterize the policy pair state of each drone in the first drone formation. The policy pair state includes a determined state indicating that the drone has determined a policy pair and an undetermined state indicating that the drone has not determined a policy pair. In the initialized first drone vector, the policy pair state of all drones is undetermined.

[0176] In this embodiment of the application, the first UAV vector bool_R = [b i ] 1×m This is used to record whether the drones in the first drone formation have determined their policy pairs. If a policy pair has been determined, the policy pair state is set to the determined state, represented by 1; if the policy pair has not yet been determined, the policy pair state is set to the undetermined state, represented by 0. The first drone vector contains m elements, each element corresponding to one first drone. The policy pair state of the drone is represented by setting the element to 1 or 0. Initially, all elements are 0, meaning that all drones have not yet determined their policy pairs.

[0177] S402. Calculate the initial survival probability of the drone. This includes the following steps:

[0178] Set a first initial avoidance probability for the first drone formation and a second initial avoidance probability for the second drone formation. The initial avoidance probability can be directly adopted from the aforementioned avoidance probability.

[0179] Calculating the first initial probability of a drone not being destroyed in the first drone formation and the second initial probability of a drone not being destroyed in the second drone formation includes:

[0180]

[0181] Where B_uninterference[j] represents the probability that drone j is not interfered with by the first drone formation; R_undes[i] represents the initial probability that drone i is not destroyed.

[0182] R_uninterference[i] represents the probability that drone i is not interfered with by the second drone formation;

[0183] B_undes[j] represents the second initial probability that drone j is not destroyed.

[0184] Calculate the initial survival probability of the first UAV in the first UAV formation based on the first initial avoidance probability and the first initial survival probability; calculate the initial survival probability of the second UAV in the second UAV formation based on the second initial avoidance probability and the second initial survival probability; including:

[0185] R_survival[i]=1-(1-R_evasive[i])·(1-R_undes[i])

[0186] B_survival[j]=1-(1-B_evasive[j])·(1-B_undes[j])

[0187] Where R_survival[i] represents the first initial survival probability of drone i, R_evasive[i] represents the first initial evasion probability of drone i, and R_undes[i] represents the first initial probability of drone i not being destroyed;

[0188] B_survival[j] represents the second initial survival probability of drone j, and B_evasive[j] represents the second initial avoidance probability of drone j.

[0189] S403. Based on the vector of the first UAV, obtain the first target UAV in the first UAV formation that is in an undetermined state.

[0190] S404. Obtain multiple policy pairs of the target drone from the multi-drone policy information, referred to as target drone policy pairs in this embodiment.

[0191] S405. Calculate the marginal reward value of the target drone strategy pair based on the initial survival probability of the drone, and set the target drone strategy pair with the largest marginal reward value as the target strategy pair of the target drone. The steps for obtaining the marginal reward value are as follows:

[0192] S4051. Obtain the attack and defense strategy according to the target UAV strategy pair, that is, determine the attack and defense strategy in the target UAV strategy pair.

[0193] For each target drone policy pair, a triple can be generated based on the first drone (i.e., the target drone) adopting the policy pair and the policy pair itself. This triple is represented as the current drone - attack / defense policy - policy target, denoted as [i, p, j], which represents the combination of the drone and the policy pair adopted.

[0194] S4052. Obtain the updated drone survival probability based on the attack and defense strategy. This includes the following steps:

[0195] Determine the first and second drones that match the target drone strategy pair, that is, determine the current target drone (the first drone in the first drone formation) and the strategy target in the target drone strategy pair (the second drone in the second drone formation).

[0196] If the attack and defense strategy is an attack strategy, the updated survival probability of the first drone is set to be equal to the initial survival probability of the first drone; and the updated survival probability of the second drone is calculated as follows:

[0197] j_survival=1-(1-q j )·(1-Δ B_undes [ipj])

[0198] Δ B_undes [i,p,j]=B_undes[j]·(1-R_uninterference[i]*p ij )

[0199] Where j_survival represents the updated survival probability of the second drone;

[0200] [i,p,j] represents the drone triple formed by the first drone i and the current target drone strategy pair [p,j]. j This represents the probability that the second drone j will avoid the formation of the first drone.

[0201] If the attack and defense strategy is an evasion strategy, the updated survival probability of the second drone is set to be equal to the initial survival probability of the second drone; and, in the second initial strategy group, it is detected whether any drone uses an attack strategy to attack the first drone; if not, the updated survival probability of the first drone is set to be equal to the initial survival probability of the first drone; if so, the updated survival probability of the first drone is calculated as follows:

[0202] i_survival=1-(1-q i )·(1-R_undes[i])

[0203] Where i_survival represents the survival probability of the first drone; q i This represents the probability that the first drone i will avoid the formation of the second drone;

[0204] If the attack and defense strategy is an interference strategy, the updated survival probability of the first drone is set to be equal to the initial survival probability of the first drone, and the updated survival probability of the second drone is set to be equal to the initial survival probability of the second drone.

[0205] When the offensive and defensive strategy is a jamming strategy, some data can also be calculated.

[0206] The offensive and defensive strategies of the second UAV are obtained based on the second initial strategy group. Within the current target UAV strategy pair, the strategic target of the target UAV (i.e., the second UAV) can be determined. In the second initial strategy group, the strategy pair for each second UAV is determined, thus the offensive and defensive strategies of that second UAV can be obtained.

[0207] When the attack / defense strategy of the second UAV is an attack strategy, the attack target of the second UAV is obtained (the strategy target is determined according to the strategy pair). Based on the attack target, an associated probability set of UAV triples is obtained. The associated probability set includes:

[0208] [i,p,j]=[j_target,j_target_undes,j_target_survival]

[0209]

[0210] j_target_survival=1-(1-R_evasive[j_target])·(1-j_target_undes)

[0211] in,

[0212] j_target represents the attack target, j_target_undes represents the probability that the first drone of the attack target was not destroyed, and j_target_survival represents the updated survival probability of the first drone of the attack target.

[0213] S4053. Calculate the marginal reward value of the target drone strategy pair based on the updated survival probability of the drone and the initial survival probability of the drone. This includes:

[0214] δ ipj =u' R -u R

[0215]

[0216] Where, δ ipj This represents the marginal return value of the target drone strategy pair;

[0217] This indicates the value of the first drone. This indicates the value of the second drone.

[0218] S406. Update the policy pair state of the target UAV in the first UAV vector to a determined state, and detect the updated first UAV vector.

[0219] In some embodiments, before detecting the updated first drone vector, some probability data may also be updated, including:

[0220] After setting the target drone strategy pair with the maximum marginal return as the target drone strategy pair, the target attack and defense strategy, the first target drone, and the second target drone can be obtained. Here, the attack and defense strategy in the target strategy pair is the target attack and defense strategy, the policy target in the target strategy pair is the second target drone, and the first drone currently using this target strategy pair (i.e., the target drone in the previous step) is the first target drone. The drone triple formed by the first drone and the adopted target strategy pair is represented as [i...]. * ,p * ,j * ].

[0221] The initial survival probability of the drone can be updated based on the target's offensive and defensive strategy, including the following steps:

[0222] If the target's attack and defense strategy is an attack strategy, then the second initial probability of the target's second drone not being destroyed and the second initial survival probability of the drone are updated as follows:

[0223] B_undes[j * ]=Δ B_undes [i* ,p * ,j * ]

[0224] B_survival[j * ]=j * _survival

[0225] Among them, i * Indicates the first target drone, p * To represent the target's offensive and defensive strategy, j * This indicates the target is the second drone.

[0226] If the target's attack and defense strategy is an evasion strategy, then the initial evasion probability and the initial survival probability of the first drone are updated as follows:

[0227] R_evasive[i * ] = q i*

[0228] R_survival[i * ] = i * _survival

[0229] If the target attack and defense strategy is an interference strategy, then the target association probability group of the first target UAV and the target strategy pair forming the UAV triplet is obtained. In the aforementioned steps, multiple association probability groups of UAV triplets can be obtained. Therefore, through the current UAV triplet [i * ,p * ,j * You can query the corresponding target-related probability group.

[0230] The target association probability set can be represented as [j * _target,j * _target_undes,j * _target_survival]. Where, j * _target is the attack target, j * _target_undes represents the probability that the first drone of the target was not destroyed, j * _target_survival updates the survival probability of the first drone of the attack target.

[0231] It can obtain the attack targets in the target association probability group and update the first initial survivability probability of the attack targets and the first initial survival probability of the first UAV according to the target association probability group. Specifically, updating the first initial survivability probability of the attack targets to the first UAV survivability probability includes: R_undes[j* _target]=j * _target_undes.

[0232] Update the initial survival probability of the first drone of the attack target to the updated survival probability of the first drone, including: R_survival[j * _target]=j * _target_survival.

[0233] S407. If there is a drone in the updated first drone vector that is in an undetermined state, then the step of obtaining the first target drone in the first drone formation that is in an undetermined state based on the first drone vector is re-executed based on the updated first drone vector.

[0234] If all drones in the updated first drone vector are in a deterministic state, then a first optimal policy group is determined based on the target policy pairs of all drones. The target policy pairs of all drones constitute the first optimal policy group.

[0235] The above steps disclose how to solve for the first optimal strategy group of the first UAV formation based on the attack and defense strategy probabilities and the second initial strategy group. Referring to the above steps, the second optimal strategy group of the second UAV formation can be solved based on the attack and defense strategy probabilities and the first initial strategy by simply replacing the information of the first and second UAVs; this will not be elaborated further here.

[0236] In step S5, if the first optimal strategy group and / or the second optimal strategy group are not in the strict game matrix, the strict game matrix is ​​updated, and the step of solving for the Nash equilibrium based on the updated strict game matrix is ​​re-executed. This includes the following cases:

[0237] The first optimal strategy group is in the strict game matrix, but the second optimal strategy group is not. The first optimal strategy group is not in the strict game matrix, but the second optimal strategy group is. Neither the first nor the second optimal strategy group is in the strict game matrix. In these cases, the first and / or second optimal strategy groups that are not in the strict game set can be added to the strict game set, and the steps in S2 to find the Nash equilibrium solution can be repeated.

[0238] If both the first and second optimal strategy groups are within the strict game matrix, then the strategy groups for the multi-drone formation are set according to the Nash equilibrium solution. For example, the strategy group with the highest probability in the Nash equilibrium solution can be determined as the final strategy group.

[0239] This invention also provides a fast solution system for multi-UAV attack and defense game, characterized in that the system includes:

[0240] The model generation module is configured to construct a zero-sum game matrix model. The zero-sum game matrix model includes multi-drone formation information, multi-drone strategy information, and a payoff matrix for the first and second drone formations. The multi-drone strategy information includes a set of strategy groups for the drone formations, where each strategy group includes strategy pairs for multiple drones within the formation. These strategy pairs represent offensive and defensive strategies and their objectives. The offensive and defensive strategies include attack strategies, evasion strategies, and interference strategies. The multi-drone formation information includes drone information for the drone formations, and the drone information includes the probabilities of the offensive and defensive strategies.

[0241] The rigorous game matrix acquisition module is configured to calculate the rigorous game matrix based on the zero-sum game matrix model and solve for the Nash equilibrium solution based on the rigorous game matrix.

[0242] The initial strategy group module is configured to select the first initial strategy group of the first drone formation and the second initial strategy group of the second drone formation based on the Nash equilibrium solution; the initial strategy group is the strategy group with the highest probability in the strict game matrix.

[0243] The optimal strategy group module is configured to solve for the first optimal strategy group of the first UAV formation based on the attack and defense strategy probability and the second initial strategy group, and to solve for the second optimal strategy group of the second UAV formation based on the attack and defense strategy probability and the first initial strategy group.

[0244] The scheme allocation module is configured to update the strict game matrix if the first optimal strategy group and / or the second optimal strategy group are not in the strict game matrix, and re-execute the step of solving the Nash equilibrium solution based on the strict game matrix based on the updated strict game matrix.

[0245] If both the first and second optimal strategy groups are in the strict game matrix, then the strategy groups for the multi-drone formation are set according to the Nash equilibrium solution.

[0246] It is understood that the target allocation system provided in this embodiment of the invention corresponds to the fast solution method. The explanation, examples, and beneficial effects of the relevant content can be referred to the corresponding content in the fast solution method of multi-UAV attack and defense game, and will not be repeated here.

[0247] It should be noted that, through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms. The technical solutions described above, in essence or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods of various embodiments or certain parts of embodiments. Numerous specific details are set forth in the specification provided herein. However, it is understood that embodiments of the present invention can be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0248] In this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, without necessarily requiring or implying any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the element.

[0249] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A fast solution method for multi-UAV attack-defense game, wherein the fast solution method is executed by a computer, characterized in that, Includes the following steps: A zero-sum game matrix model is constructed. This model includes multi-drone formation information (first and second drone formations), multi-drone strategy information, and a payoff matrix. The multi-drone strategy information includes a set of strategy groups for the drone formations, where each strategy group contains strategy pairs for multiple drones within the formation. These strategy pairs characterize offensive and defensive strategies and their objectives. The offensive and defensive strategies include attack strategies, evasion strategies, and interference strategies. The multi-drone formation information includes drone information within the formations, and this drone information includes the probabilities of offensive and defensive strategies. The strict game matrix is ​​calculated based on the zero-sum game matrix model, and the Nash equilibrium solution is solved based on the strict game matrix. Based on the Nash equilibrium solution, select the first initial strategy group for the first drone formation and the second initial strategy group for the second drone formation; the initial strategy group is the strategy group with the highest probability in the strict game matrix. Based on the attack and defense strategy probabilities and the second initial strategy set, the first optimal strategy set for the first UAV formation is solved, and based on the attack and defense strategy probabilities and the first initial strategy set, the second optimal strategy set for the second UAV formation is solved; If the first optimal strategy group and / or the second optimal strategy group are not in the strict game matrix, then update the strict game matrix and re-execute the step of solving for the Nash equilibrium solution based on the strict game matrix based on the updated strict game matrix. If both the first optimal strategy group and the second optimal strategy group are in the strict game matrix, then the strategy group for the multi-drone formation is set according to the Nash equilibrium solution. The payout matrix includes: Among them, S R s represents the first drone formation strategy group set. R ∈S R S represents a strategy group of the first drone formation. B Indicates the second drone formation strategy group set, s B ∈S B This represents a strategy group for the second drone formation; (s R ,s B This indicates that the first drone formation adopted strategy group s R The second drone formation adopted a strategy group s B Strategy group combination; u(s) R ,s B ) for the first drone formation in the strategy group combination (s R ,s B The returns under ) u(s R ,s B )=u R (s R ,s B )-u B (s R ,s B ) in, u R (s R ,s B ) and u B (s R ,s B () represent the expected survival value of a drone formation and a drone formation, respectively. v i v represents the value of drone i in the first drone formation. j Let m represent the value of drone j in the second drone formation; drone j is the strategic target of drone i; m represents the number of drones in the first drone formation, and n represents the number of drones in the second drone formation. q i h represents the probability of drone i avoiding the second drone formation. i The parameter q represents the avoidance parameters of drone i against the second drone formation. j h represents the probability that drone j will avoid the first drone formation. j This represents the avoidance parameters of drone j against the first drone formation; t ij Let l represent the probability of drone i interfering with drone j. ij The parameter t represents the interference parameter of UAV i on UAV j. ji Let l represent the probability of drone j interfering with drone i. ji This represents the interference parameters of drone j on drone i; p ji b represents the probability of drone j killing drone i. ji p represents the attack parameters of drone j against drone i; ij Let a represent the probability of drone i killing drone j. ij This represents the attack parameters of drone i against drone j.

2. The fast solution method according to claim 1, characterized in that, The calculation of the strict game matrix based on the zero-sum game matrix model includes: Select p strategy groups from the first set of UAV formation strategy groups and q strategy groups from the second set of UAV formation strategy groups; where p≥2 and q≥2. A strict game matrix is ​​generated based on the p strategy groups and the q strategy groups.

3. The fast solution method according to claim 2, characterized in that, Solving for the Nash equilibrium based on the rigorous game matrix includes: The strict game matrix is ​​processed based on a preset probability distribution algorithm to calculate the Nash equilibrium solution; the Nash equilibrium solution includes the first probability distribution of the p strategy groups and the second probability distribution of the q strategy groups; The first initial strategy group for the first UAV formation and the second initial strategy group for the second UAV formation are selected based on the Nash equilibrium solution, including: The Nash equilibrium solutions are traversed, and the strategy group with the highest probability is obtained according to the first probability distribution and determined as the first initial strategy group; the strategy group with the highest probability is obtained according to the second probability distribution and determined as the second initial strategy group.

4. The fast solution method according to claim 1, characterized in that, Solving for the first optimal strategy group of the first UAV formation based on the attack and defense strategy probabilities and the second initial strategy group includes: Initialize a first drone vector for a first drone formation; the first drone vector is used to characterize the policy pair state of each drone in the first drone formation, the policy pair state includes a determined state indicating that the drone has determined a policy pair and an undetermined state indicating that the drone has not determined a policy pair; in the initialized first drone vector, the policy pair state of all drones is undetermined. Calculate the initial survival probability of the drone; Based on the first UAV vector, obtain the first target UAV in the first UAV formation that is in an undetermined state; Multiple target drone strategy pairs are obtained from the multi-drone strategy information of the target drone; The marginal reward value of the target drone strategy pair is calculated based on the initial survival probability of the drone, and the target drone strategy pair with the largest marginal reward value is set as the target strategy pair of the target drone. Update the policy pair state of the target UAV in the first UAV vector to a determined state, and detect the updated first UAV vector; If there is a drone in the updated first drone vector that is in an uncertain state, then the step of obtaining the first target drone in the first drone formation that is in an uncertain state based on the first drone vector is re-executed based on the updated first drone vector. If all drones in the updated first drone vector are in a deterministic state, then the first optimal policy group is determined based on the target policy pairs of all drones.

5. The fast solution method according to claim 4, characterized in that, The calculation of the initial survival probability of the drone includes: Set the first initial avoidance probability for the first drone formation and the second initial avoidance probability for the second drone formation; Calculating the first initial probability of a drone not being destroyed in the first drone formation and the second initial probability of a drone not being destroyed in the second drone formation includes: in, B_uninterference[j] represents the probability that drone j is not interfered with by the first drone formation; R_undes[i] represents the initial probability that drone i is not destroyed; R_uninterference[i] represents the probability that drone i is not interfered with by the second drone formation; B_undes[j] represents the second initial probability that drone j is not destroyed; The initial survival probability of a first UAV in the first UAV formation is calculated based on the first initial avoidance probability and the first initial survival probability; the initial survival probability of a second UAV in the second UAV formation is calculated based on the second initial avoidance probability and the second initial survival probability; including: R_survival[i]=1-(1-R_evasive[i])·(1-R_undes[i]) B_survival[j]=1-(1-B_evasive[j])·(1-B_undes[j]) in, R_survival[i] represents the first initial survival probability of drone i, R_evasive[i] represents the first initial evasion probability of drone i, and R_undes[i] represents the first initial probability that drone i is not destroyed. B_survival[j] represents the second initial survival probability of drone j, and B_evasive[j] represents the second initial avoidance probability of drone j.

6. The fast solution method according to claim 5, characterized in that, Calculating the marginal reward value of the target drone strategy pair based on the initial survival probability of the drone includes: Based on the target UAV strategy, solve for the attack and defense strategy; The updated survival probability of the drone is calculated based on the described attack and defense strategy. The marginal reward value of the target drone strategy pair is calculated based on the updated survival probability of the drone and the initial survival probability of the drone.

7. The fast solution method according to claim 6, characterized in that, The updated survival probability of the drone is calculated based on the aforementioned attack and defense strategy, including: Determine the target drone strategy to match the first and second drones; If the attack and defense strategy is an attack strategy, the updated survival probability of the first drone is set to be equal to the initial survival probability of the first drone; and the updated survival probability of the second drone is calculated as follows: j_survival=1-(1-q j )·(1-Δ B_undes [i,p,j]) Δ B_undes [i,p,j]=B_undes[j]·(1-R_uninterference[i]·p ij ) in, j_survival represents the updated survival probability of the second drone; [i,p,j] represents the drone triplet formed by the first drone i and the target drone policy pair [p,j]; q j This represents the probability that drone j will avoid the first drone formation; If the attack and defense strategy is an evasion strategy, the updated survival probability of the second drone is set to be equal to the initial survival probability of the second drone; and, in the second initial strategy group, it is detected whether any drone uses an attack strategy to attack the first drone; if not, the updated survival probability of the first drone is set to be equal to the initial survival probability of the first drone; if so, the updated survival probability of the first drone is calculated as follows: i_survival=1-(1-q i )·(1-R_undes[i]) in, i_survival represents the survival probability of the first drone; q i This represents the probability that the first drone i will avoid the formation of the second drone; If the attack and defense strategy is an interference strategy, the updated survival probability of the first drone is set to be equal to the initial survival probability of the first drone, and the updated survival probability of the second drone is set to be equal to the initial survival probability of the second drone. The attack and defense strategy of the second UAV is solved according to the second initial strategy set; and when the attack and defense strategy is an attack strategy, the attack target of the second UAV is obtained; the association probability set of the UAV triple is calculated according to the attack target; the association probability set includes: [i,p,j]=[j_target,j_target_undes,j_target_survival] j_target_survival=1-(1-R_evasive[j_target])·(1-j_target_undes) in, j_target represents the attack target, j_target_undes represents the probability that the first drone of the attack target was not destroyed, and j_target_survival represents the updated survival probability of the first drone of the attack target. The step of calculating the marginal reward value of the target drone strategy pair based on the updated survival probability of the drone and the initial survival probability of the drone includes: δ ipj =in' R -in R in, δ ipj This represents the marginal return value of the target drone strategy pair; This indicates the value of the first drone. This indicates the value of the second drone.

8. The fast solution method according to claim 5, characterized in that, Before detecting the updated first drone vector, the following is also included: Obtain the target attack and defense strategy, the first target UAV, and the second target UAV of the target strategy pair; The initial survival probability of the drone is updated according to the target attack and defense strategy, including: If the target's attack and defense strategy is an attack strategy, then the second initial probability of the target's second drone not being destroyed and the second initial survival probability of the drone are updated as follows: B_undes[j * ]=D B_undes [i * ,p * ,j * ] B_survival[j * ]=j * _survival in, i * Indicates the first target drone, p * To represent the target's offensive and defensive strategy, j * Indicates the target is the second drone; If the target's attack and defense strategy is an evasion strategy, then the initial evasion probability and the initial survival probability of the first drone are updated as follows: R_evasive[i * ]=q i * R_survival[i * ]=i * _survival If the target attack and defense strategy is an interference strategy, then obtain the target association probability group of the first UAV and the UAV triple formed by the target strategy pair; obtain the attack target in the target association probability group, and update the first initial undestroyed probability of the attack target and the initial survival probability of the first UAV according to the target association probability group.

9. A fast solution system for multi-UAV attack-defense game, characterized in that, The system includes: The model generation module is configured to construct a zero-sum game matrix model. The zero-sum game matrix model includes multi-drone formation information for a first drone formation and a second drone formation, multi-drone strategy information, and a payoff matrix. The multi-drone strategy information includes a set of strategy groups for the drone formation, where each strategy group includes strategy pairs for multiple drones within the formation. These strategy pairs characterize attack and defense strategies and strategy objectives. The attack and defense strategies include attack strategies, evasion strategies, and interference strategies. The multi-drone formation information includes drone information for the drone formation, and the drone information includes attack and defense strategy probabilities. The rigorous game matrix acquisition module is configured to calculate the rigorous game matrix based on the zero-sum game matrix model, and solve for the Nash equilibrium solution based on the rigorous game matrix. The initial strategy group module is configured to select a first initial strategy group for the first UAV formation and a second initial strategy group for the second UAV formation based on the Nash equilibrium solution; the initial strategy group is the strategy group with the highest probability in the strict game matrix. The optimal strategy group module is configured to solve for the first optimal strategy group of the first UAV formation based on the attack and defense strategy probabilities and the second initial strategy group, and to solve for the second optimal strategy group of the second UAV formation based on the attack and defense strategy probabilities and the first initial strategy group. The scheme allocation module is configured to update the strict game matrix if the first optimal strategy group and / or the second optimal strategy group are not in the strict game matrix, and re-execute the step of solving for the Nash equilibrium solution based on the strict game matrix based on the updated strict game matrix. If both the first optimal strategy group and the second optimal strategy group are in the strict game matrix, then the strategy group for the multi-drone formation is set according to the Nash equilibrium solution. The payout matrix includes: Among them, S R s represents the first drone formation strategy group set. R ∈S R S represents a strategy group of the first drone formation. B Indicates the second drone formation strategy group set, s B ∈S B This represents a strategy group for the second drone formation; (s R ,s B This indicates that the first drone formation adopted strategy group s R The second drone formation adopted a strategy group s B Strategy group combination; u(s) R ,s B ) for the first drone formation in the strategy group combination (s R ,s B The returns under ) u(s R ,s B )=u R (s R ,s B )-u B (s R ,s B ) in, u R (s R ,s B ) and u B (s R ,s B () represent the expected survival value of a drone formation and a drone formation, respectively. v i v represents the value of drone i in the first drone formation. j Let m represent the value of drone j in the second drone formation; drone j is the strategic target of drone i; m represents the number of drones in the first drone formation, and n represents the number of drones in the second drone formation. q i h represents the probability of drone i avoiding the second drone formation. i The parameter q represents the avoidance parameters of drone i against the second drone formation. j h represents the probability that drone j will avoid the first drone formation. j This represents the avoidance parameters of drone j against the first drone formation; t ij Let l represent the probability of drone i interfering with drone j. ij The parameter t represents the interference parameter of UAV i on UAV j. ji Let l represent the probability of drone j interfering with drone i. ji This represents the interference parameters of drone j on drone i; p ji b represents the probability of drone j killing drone i. ji p represents the attack parameters of drone j against drone i; ij Let a represent the probability of drone i killing drone j. ij This represents the attack parameters of drone i against drone j.

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