A dual-ship formation 2v2 cooperative air combat auxiliary decision generation method

Abstract

The application discloses a kind of dual-machine formation 2v2 cooperative air combat auxiliary decision generation method, which realizes the efficiency promotion of dual-machine cooperative combat by the dual optimization of tactics and maneuver, and the dynamic analysis of air battlefield situation is realized by cooperative tactical decision-making, and the tactical formulation is carried out according to the situation relationship of enemy and our side, and then the combat target is selected;According to the tactics and the distribution of the combat target tactical role;Based on the target maneuver action library, the target prediction state is calculated, and then the final target prediction state is selected;Then the final target prediction state and the current state of our aircraft are input, the control amount of our aircraft in continuous domain is optimized by improved EDA algorithm, and the optimal flight trajectory of our aircraft is obtained.

Description

Technical Field

[0001] This invention belongs to the field of autonomous decision-making technology for air combat. Specifically, it designs an auxiliary decision-making system suitable for dual-aircraft cooperative air combat, realizing tactical and maneuver dual decision-making in cooperative operations. Background Technology

[0002] In modern air combat, two-aircraft formations have become the basic combat unit. Compared with single-aircraft combat, two-aircraft coordinated operations can, on the one hand, cover each other's blind spots and eliminate the threat of enemy aircraft attacking from behind; on the other hand, two-aircraft formations can carry out a variety of mutual cover tactics and have an overwhelming advantage when facing enemy single aircraft.

[0003] Air combat decision-making requires decision-makers to react quickly to the situation on both sides of the battlefield, thereby implementing optimal flight maneuvers to achieve target acquisition and positioning. The decision-making problem in two-aircraft coordinated air combat cannot be viewed as a simple superposition of one-on-one combat; it emphasizes the application of coordinated tactics and decision-making. Especially under disadvantageous conditions, two-aircraft formations must adopt correct tactical and maneuver decisions to quickly establish a local numerical advantage and rapidly transform the formation's disadvantageous situation into an advantageous one.

[0004] In general, compared to one-on-one air combat decision-making, the difficulty of dual-aircraft coordinated combat decision-making lies in the following aspects:

[0005] ① The dual-aircraft coordinated formation combat exponentially increases the dimensions of decision-making problems, further exacerbating the difficulty for pilots in situation analysis;

[0006] ② The real-time requirements for air combat decision-making are extremely high. The relative situational relationship in two-aircraft air combat changes rapidly, and pilots cannot give the optimal response in real time.

[0007] ③ The situational relationships in dual-aircraft cooperative combat are diverse, and pilots cannot experience all situations. Under certain conditions, they cannot make the optimal decision based on experience.

[0008] Since the 1960s, the problem of autonomous air combat has received widespread attention and numerous studies. Air combat is generally viewed as a pursuit-escape game, and various theoretical methods and optimal control strategies have provided solutions for autonomous air combat. Ardema MD, Park H, and Jarmark B, among others, used differential game theory to simulate air combat as a deterministic and complete pursuit-escape game problem. Isaacs R, Bellman R, and others used dynamic programming to solve the pursuit-escape game model, thus deriving the optimality principle. McGrew JS used an approximate dynamic programming method to conduct in-plane indoor flight tests based on optimal strategies. Han S et al. used differential game theory to solve the two-on-one air combat problem and established a simplified adversarial model. Eklund JM and Moon J et al. respectively studied the nonlinear control and guidance laws of aircraft, employing methods including model predictive control and sliding mode guidance. The aforementioned theoretical methods make it possible to provide a mathematical explanation of the air combat problem. However, the problem-solving process employs overly simplified combat models and assumptions, which fail to effectively map the complexity of the two-aircraft air combat confrontation situation, resulting in non-optimal results.

[0009] Another approach to combat decision-making research is to build rule-based heuristic systems by simulating pilot behavior. Responses to each combat situation are standardized, and these methods are validated through adversarial simulations against human pilots. NASA has proposed a rule-based adaptive maneuver logic called "Paladin," which demonstrates air combat capabilities similar to those of human pilots. Similarly, influence map strategies have been used to simulate pilots' decision-making processes for maneuvers at different times during air combat. While rule-based systems, supported by prior knowledge, can provide reasonable feedback on the battlefield situation, the complexity of two-aircraft air combat situations cannot be fully traversed, resulting in insufficient robustness of decision-making outcomes under finite rule conditions.

[0010] Currently, artificial algorithms such as reinforcement learning and genetic algorithms have emerged as new strategies for solving air combat maneuver decision-making problems, demonstrating better decision-making performance. Genetic-based machine learning methods can achieve the ability to solve model-free decision-making problems in air combat environments. Q-learning strategies generate maneuvers by designing reward-penalty functions for discrete maneuvers. However, achieving high-level combat capabilities requires a large number of operational training samples. Furthermore, the physical meaning and interpretability of the algorithm models need to be addressed, and the portability of the trained models is limited by the specific scenarios. In addition, mature methods and strategies for solving dual-aircraft cooperative combat decision-making problems are still lacking.

[0011] Based on the above analysis, the shortcomings of the current dual-aircraft maneuver decision-making method can be summarized in three aspects: First, the air combat situation model cannot reflect the complex situation of dual-aircraft cooperative combat; second, the decision-making model is too simplified and cannot reflect the synergistic characteristics of tactical and maneuver decisions in dual-aircraft confrontation; and third, the discrete maneuver decision-making model does not possess decision-optimization.

[0012] Due to the challenges of the aforementioned dual-aircraft cooperative air combat decision-making problem, the inventors have designed a dual-aircraft formation 2v2 cooperative air combat auxiliary decision generation method to achieve rapid assessment of complex battlefield situations and rapid generation of cooperative tactical and maneuver decisions, thereby improving the pilot's response speed and decision-making level to dynamic changes on the battlefield and enhancing the combat effectiveness of dual-aircraft cooperative air combat. Summary of the Invention

[0013] To overcome the aforementioned problems, the inventors conducted in-depth research and designed a dual-aircraft formation 2v2 cooperative air combat auxiliary decision generation method. This method improves the effectiveness of dual-aircraft cooperative combat through dual optimization of tactics and maneuvers. Cooperative tactical decision-making enables dynamic analysis of the air battlefield situation, formulates tactics based on the situational relationship between the enemy and friendly forces, and selects combat targets. Tactical roles are assigned based on tactics and combat targets. The target prediction state is calculated based on the target maneuver library, and the final target prediction state is then selected. The final target prediction state and the current state of our aircraft are then used as inputs, and the control variables of our aircraft in the continuous domain are optimized through an improved EDA algorithm to obtain the optimal flight trajectory of our aircraft, thus completing this invention.

[0014] Specifically, the purpose of this invention is to provide a method for generating auxiliary decision-making in 2v2 cooperative air combat with two aircraft formations, the method comprising the following steps:

[0015] Step 1: Obtain the angle and distance elements of enemy and friendly aircraft in real time, and construct a situation assessment model by combining the weighting factors of the two to complete the situation analysis of two-on-two air combat.

[0016] Step 2: Formulate tactics based on the situational relationship between the enemy and ourselves, and then select combat targets;

[0017] Step 3: Assign tactical roles based on tactical and operational objectives;

[0018] Step 4: Calculate the target prediction state based on the target maneuver library, and then select the final target prediction state;

[0019] Step 5: Using the final target prediction state and the current state of our aircraft as input, we optimize the control variables of our aircraft in the continuous domain using the improved EDA algorithm to obtain the optimal flight trajectory of our aircraft.

[0020] The angular elements include the approach angles of our aircraft and the enemy aircraft.

[0021] Step 1 includes the following sub-steps:

[0022] Sub-step 1-1: Evaluate the orientation and situation using the following formula (i);

[0023]

[0024] Where, η Q Q represents the positional situation assessment value. U Q represents the angle of entry of our aircraft. T Indicates the angle of entry of the enemy aircraft;

[0025] Sub-steps 1-2 evaluate the distance situation using the following formula (ii);

[0026]

[0027] Where, η Q R represents the distance situation assessment value. G D represents the effective kill radius of the weapons on our aircraft. UT Indicates the distance between our aircraft and the enemy aircraft;

[0028] Sub-steps 1-3 construct the following situation assessment model (III);

[0029] η=a1·η Q +a2·η D (three)

[0030] Where η represents the overall situation assessment value, and a1 and a2 both represent weighting factors;

[0031] Sub-steps 1-4 involve constructing the dual-aircraft confrontation situation assessment matrix in equation (iv) to conduct situation analysis of two-on-two air combat.

[0032]

[0033] Where S represents the set matrix of two-on-two air combat situation evaluation values, s ij Let η represent the overall situational assessment value of our i-th friendly aircraft against the j-th enemy aircraft.

[0034] In step 2, when any s ij When all values ​​are greater than or equal to 0.5, the tactic is an offensive tactic, and s is selected. ij The enemy aircraft corresponding to the maximum value in the middle is taken as the combat target and attacked, i.e., combat target J. A The column containing the maximum value of an element in matrix S is selected as shown in equation (V) below:

[0035]

[0036] When there is an s value less than 0.5 ij At that time, the tactic described is a defensive tactic, in which the enemy aircraft posing the greatest threat to our aircraft is selected as the operational target for attack, i.e., operational target J. A The column containing the minimum value of an element in matrix S is selected as shown in equation (vi) below:

[0037]

[0038] In step 3,

[0039] In offensive tactics, after selecting the combat target, the J-th element in matrix S is selected. A The aircraft with the larger element value in the column is designated as the attack aircraft, as shown in equation (VII):

[0040]

[0041] Among them, I F Indicates an attack aircraft;

[0042] In offensive tactics, after selecting the combat target, the J-th element in matrix S is selected. A The aircraft with smaller element values ​​in the column are designated as auxiliary attack aircraft, as shown in equation (8) below:

[0043]

[0044] Among them, I AF This refers to an auxiliary attack aircraft.

[0045] In step 3,

[0046] In defensive tactics, after selecting the combat target, the J-th element in matrix S is selected. A The aircraft with the larger element value in the column is designated as the attack aircraft, as shown in equation (VII):

[0047]

[0048] Among them, I F Indicates an attack aircraft;

[0049] In defensive tactics, after selecting the combat target, the J-th element in matrix S is selected. A The aircraft with the smaller element value in the column is used as a decoy, as shown in equation (IX):

[0050]

[0051] Among them, I B This refers to a bait machine.

[0052] Step 4 includes the following sub-steps:

[0053] Sub-step 4-1: Establish a target maneuver library;

[0054] Sub-step 4-2: Based on the current target state, iterate through the target prediction state after each flight action;

[0055] Sub-step 4-3 calculates the situational value of the predicted target state. In offensive tactics, it calculates the situational value of the attacking aircraft relative to the predicted target state; in defensive tactics, it calculates the situational value of the decoy aircraft relative to the predicted target state.

[0056] Sub-step 4-4: Select the target prediction state corresponding to the minimum value among all situation values ​​as the final target prediction state.

[0057] Step 5 includes the following sub-steps:

[0058] Sub-step 5-1: Update the control variables of our aircraft within the control variable constraints;

[0059] Sub-step 5-2: For the control quantity of our aircraft obtained in each update, calculate the aircraft state at the next moment based on the current state of our aircraft, and then combine it with the final target prediction state to solve the situation value. Record and select the control quantity of our aircraft that makes the situation value the highest as the optimal solution.

[0060] Sub-step 5-3: The optimal solution is used as an auxiliary decision suggestion, and the aircraft can be controlled according to the decision suggestion to generate the optimal flight trajectory of the aircraft.

[0061] In sub-step 5-1, the control variable is used as a population individual in the improved EDA algorithm. In the improved EDA algorithm, the population distribution information of n consecutive generations and of size NP is stored as a set A.

[0062] During the iterative process of the improved EDA algorithm, the top NP optimal individuals in set A are used as the parent population and participate in obtaining the Gaussian distribution model of equation (x):

[0063]

[0064] Where g represents the g-th iteration, ω i represents the coefficient used to calculate the mean of the weighted maximum likelihood estimation distribution; i represents the i-th element in set A;

[0065] A (g) Let A represent the set after the g-th iteration;

[0066] This represents the i-th element in set A corresponding to the g-th iteration.

[0067] μ (g) This represents the mean of the distribution corresponding to the g-th iteration;

[0068] C (g) This represents the covariance matrix corresponding to the g-th iteration;

[0069] During the iterative process of the improved EDA algorithm, offspring individuals are generated by sampling according to the Gaussian distribution model, as shown in equation (XI):

[0070]

[0071] in, This represents the i-th solution corresponding to the (g+1)-th iteration.

[0072] y i This represents the distribution vector corresponding to the i-th solution;

[0073] y i ~N(0,C (g) ) indicates that it follows a Gaussian distribution with a mean of 0.

[0074] In sub-step 5-1, the improved EDA algorithm stalls when the average fitness value of the top half of the best individuals in the current population is not less than the average value of the previous generation.

[0075] Offspring individuals are obtained through equations (12) and (13);

[0076]

[0077]

[0078] in, This represents the i-th solution corresponding to the (g+1)-th iteration;

[0079] Let represent the mean of the distribution improved by the MSD strategy corresponding to the g-th iteration;

[0080] B (g) This represents the eigenvector matrix corresponding to the g-th iteration;

[0081] D (g) This represents the eigenvalue matrix corresponding to the g-th iteration;

[0082] z i Represents the i-th random vector;

[0083] z i ~N(0,I 1×D ) indicates that the distribution follows a Gaussian distribution with a mean of 0;

[0084] This represents the elite solution randomly selected from set L corresponding to the g-th iteration; This represents the i-th solution corresponding to g iterations;

[0085] When the improved EDA algorithm stalls, the search range is narrowed by reducing the distribution variance, i.e., by narrowing the search range using the following equation (xiv):

[0086] D (g) =(1-g / g) max ) 0.5 ·D (g) (fourteen)

[0087] Among them, D (g) Represents the eigenvalue matrix;

[0088] g max This indicates the maximum number of iterations.

[0089] The beneficial effects of this invention include:

[0090] (1) The dual-aircraft formation 2v2 cooperative air combat auxiliary decision generation method provided by the present invention can realize the dual optimization of tactical and maneuver decisions and improve combat effectiveness;

[0091] (2) The dual-aircraft formation 2v2 cooperative air combat auxiliary decision generation method provided by the present invention can complete the one-step prediction of the target status and improve the decision advantage;

[0092] (3) The dual-aircraft formation 2v2 cooperative air combat auxiliary decision generation method provided by the present invention is simple, has a fast calculation speed, and can support the online generation of dual-aircraft cooperative combat maneuvers;

[0093] (4) In the dual-aircraft formation 2v2 cooperative air combat auxiliary decision generation method provided by the present invention, the control quantity is updated by an improved EDA algorithm. In each iteration, the distribution characteristics of the dominant individuals are extracted for model estimation. When it is determined to be convergent, the distribution variance is reduced to enhance the local development capability of the algorithm. The distribution model is improved by using the elite solution to diversify the search range and enhance the diversity of the population distribution. Then, the historical distribution information is saved by external archives to correct the abnormal distribution of the population. Thus, the exploration and development capabilities of the improved EDA algorithm can be effectively balanced, avoiding premature convergence of the algorithm and improving the global optimization capability. Attached Figure Description

[0094] Figure 1 This invention presents an overall logic flowchart of the improved dual-aircraft formation 2v2 cooperative air combat auxiliary decision generation method.

[0095] Figure 2 A schematic diagram showing the flight trajectories of enemy and friendly aircraft in an embodiment of the present invention is provided.

[0096] Figure 3 This diagram illustrates the trend of target situational assessment changes in a dual-aircraft formation according to an embodiment of the present invention. Detailed Implementation

[0097] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Through these descriptions, the features and advantages of the present invention will become clearer and more apparent.

[0098] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments. Although various aspects of embodiments are shown in the accompanying drawings, the drawings are not necessarily drawn to scale unless specifically indicated otherwise.

[0099] According to the present invention, a method for generating auxiliary decision-making in 2v2 cooperative air combat with dual aircraft formations is provided, such as... Figure 1 As shown, the method includes the following steps:

[0100] Step 1: Obtain the angle and distance elements of enemy and friendly aircraft in real time, and construct a situation assessment model by combining the weighting factors of the two to complete the situation analysis of two-on-two air combat.

[0101] Preferably, the angle element includes the approach angles of our aircraft and the enemy aircraft; the approach angle of our aircraft is the angle between the velocity direction of our aircraft and the line of sight from our aircraft to the enemy aircraft, and the approach angle of the enemy aircraft is the angle between the velocity direction of the enemy aircraft and the line of sight from our aircraft to the enemy aircraft; the distance element refers to the straight-line distance between our aircraft and the enemy aircraft.

[0102] Step 1 includes the following sub-steps:

[0103] Sub-step 1-1: Evaluate the orientation and situation using the following formula (i);

[0104]

[0105] Where, η Q Q represents the positional situation assessment value. U Q represents the angle of entry of our aircraft. T Indicates the angle of entry of the enemy aircraft;

[0106] Sub-steps 1-2 evaluate the distance situation using the following formula (ii);

[0107]

[0108] Where, η Q R represents the distance situation assessment value. G D represents the effective kill radius of the weapons on our aircraft.UT Indicates the distance between our aircraft and the enemy aircraft;

[0109] Sub-steps 1-3 construct the following situation assessment model (III);

[0110] η=a1·η Q +a2·η D (three)

[0111] Where η represents the overall situation assessment value, and a1 and a2 both represent weighting factors. The weighting factors can be selected and set according to the tactical objectives, for example, a1 = a2 = 0.5.

[0112] Sub-steps 1-4 involve constructing the dual-aircraft confrontation situation assessment matrix in equation (iv) to conduct situation analysis of two-on-two air combat; that is, in two-on-two air combat, it is necessary to analyze the four sets of overall situation evaluation values.

[0113]

[0114] Where S represents the set matrix of two-on-two air combat situation evaluation values, s ij Let η represent the overall situational assessment value of our i-th friendly aircraft against the j-th enemy aircraft.

[0115] Step 2: Formulate tactics based on the situational relationship between the enemy and ourselves, and then select combat targets;

[0116] Where, when any s ij When all values ​​are greater than or equal to 0.5, the tactic is an offensive tactic, and s is selected. ij The enemy aircraft corresponding to the maximum value in the middle is taken as the combat target and attacked, i.e., combat target J. A The column containing the maximum value of an element in matrix S is selected as shown in equation (V) below:

[0117]

[0118] At this point, our formation members are in a relatively advantageous position compared to the enemy. We should choose the target with the greatest relative advantage to attack, and eliminate the target as soon as possible to create a two-on-one advantage.

[0119] When there is an s value less than 0.5 ij At that time, the tactic described is a defensive tactic, in which the enemy aircraft posing the greatest threat to our aircraft is selected as the operational target for attack, i.e., operational target J. A The column containing the minimum value of an element in matrix S is selected as shown in equation (vi) below:

[0120]

[0121] At this point, our two-aircraft formation has members who are at a relative disadvantage compared to the enemy. We should choose the target that poses the greatest threat to the formation members and attack it. By eliminating the target as soon as possible, we can ensure the survival rate of the formation members.

[0122] Step 3: Assign tactical roles based on tactical and operational objectives;

[0123] Preferably, in offensive tactics, after selecting the combat target, the J-th element in matrix S is selected. A The aircraft with the larger element value in the column is designated as the attack aircraft, as shown in equation (VII):

[0124]

[0125] Among them, I F Indicates an attack aircraft;

[0126] In offensive tactics, after selecting the combat target, the J-th element in matrix S is selected. A The aircraft with smaller element values ​​in the column are designated as auxiliary attack aircraft, as shown in equation (8) below:

[0127]

[0128] Among them, I AF This refers to an auxiliary attack aircraft.

[0129] Preferably, in defensive tactics, after selecting the combat target, the J-th element in matrix S is selected. A The aircraft with the larger element value in the column is designated as the attack aircraft, as shown in equation (VII):

[0130]

[0131] Among them, I F Indicates an attack aircraft;

[0132] In defensive tactics, after selecting the combat target, the J-th element in matrix S is selected. A The aircraft with the smaller element value in the column is used as a decoy, as shown in equation (IX):

[0133]

[0134] Among them, I B This refers to a bait machine.

[0135] Step 4: Calculate the target prediction state based on the target maneuver library, and then select the final target prediction state;

[0136] Step 4 includes the following sub-steps:

[0137] Sub-step 4-1: Establish a target maneuver library;

[0138] Sub-step 4-2: Based on the current target state, iterate through the target prediction state after each flight action;

[0139] Sub-step 4-3 calculates the situational value of the predicted target state. In offensive tactics, it calculates the situational value of the attacking aircraft relative to the predicted target state; in defensive tactics, it calculates the situational value of the decoy aircraft relative to the predicted target state.

[0140] Sub-step 4-4: Select the target prediction state corresponding to the minimum value among all situation values ​​as the final target prediction state.

[0141] Preferably, the target maneuver database represents the target's potential state information at the next moment. The aircraft's state information includes six elements: velocity components in three directions, velocity, track inclination angle in the track coordinate system, and track deflection angle in the track coordinate system. For an aircraft in normal flight, the means to change its state are control variables, which generally include angle of attack, roll angle in the track coordinate system, and thrust. Thrust equals the product of maximum thrust and throttle stick coefficient. Since the maximum thrust of an aircraft is generally known, the throttle stick coefficient can be used as the control variable, i.e., the control variable is u = [αφc]. T The update frequency of the target maneuver library can be selected and set according to the actual situation, such as updating 1-5 times per second, etc.

[0142] Taking the F4 "Ghost" model as an example, its mass value range can be... c∈(0,1);

[0143] Each flight maneuver in the target maneuver library is essentially a combination of different control variable assignments. After discretizing the three control variables according to the table below, a target maneuver library containing 5*5*6=150 flight maneuvers can be obtained.

[0144] Control quantity Value α -π / 18,0,π / 18,π / 9,π / 6 φ -π / 3,-π / 6,0,π / 6,π / 3 c 0,0.2,0.4,0.6,0.8,1

[0145] In this application, for a specific target, a target maneuver library corresponding to the target can be pre-stored, or a target maneuver library of other types of targets with similar parameters can be selected.

[0146] Step 5: Using the final target prediction state and the current state of our aircraft as input, we optimize the control variables of our aircraft in the continuous domain using the improved EDA algorithm to obtain the optimal flight trajectory of our aircraft.

[0147] The control variables of our aircraft are similar to those of the enemy aircraft, both including angle of attack, roll angle in the track coordinate system, and throttle push coefficient;

[0148] The improved EDA algorithm is obtained by adjusting and modifying the traditional classic EDA algorithm. Step 5 in this application specifically includes the following sub-steps:

[0149] Sub-step 5-1: Update the control variables of our aircraft within the control variable constraints;

[0150] Sub-step 5-2: For the control quantity of our aircraft obtained in each update, calculate the aircraft state at the next moment based on the current state of our aircraft, and then combine it with the final target prediction state to solve the situation value. Record and select the control quantity of our aircraft that makes the situation value the highest as the optimal solution.

[0151] Sub-step 5-3: The optimal solution is used as an auxiliary decision suggestion, and the aircraft can be controlled according to the decision suggestion to generate the optimal flight trajectory of the aircraft.

[0152] Preferably, in sub-step 5-1, the control quantity constraint range is selected and set according to the operational performance of our aircraft. For example, the control quantity constraint range of the F4 "Phantom" model mentioned above can be... c∈(0,1);

[0153] Preferably, in sub-step 5-1, the control variable is used as a population individual in the improved EDA algorithm. In the improved EDA algorithm, the population distribution information of n consecutive generations and of size NP is stored as a set A, i.e., A (g) =X (g) ∪X (g-1) ∪...∪X (g-n+1) , where X (g) Let A represent the offspring population in the g-th iteration; preferably, the set A is an external archive, and if the external archive A exceeds its maximum capacity, the earliest parent population X is removed. (g-n+1) A (g+1) =X (g+) ∪X (g) ∪...∪X (g-n+)2 .

[0154] In this application, the storage capacity of the set A is preset, generally 2-5 times the population size NP. For example, if it is selected to be 3 times, that is, n equals 3.

[0155] During the iterative process of the improved EDA algorithm, the top NP optimal individuals in set A are used as the parent population and participate in obtaining the Gaussian distribution model of equation (x):

[0156]

[0157] Where g represents the g-th iteration, ω iThe coefficient representing the weighted maximum likelihood estimate for calculating the mean of the distribution is obtained by the following equation (xv);

[0158]

[0159] The NP can be selected and set according to the actual computing power, and is generally set to 15 to 20 times the population dimension, such as 18 times; in this application, there are 3 control variables, that is, the population dimension is 54.

[0160] i represents the i-th element in set A;

[0161] A (g) Let A represent the set after the g-th iteration;

[0162] This represents the i-th element in set A corresponding to the g-th iteration;

[0163] μ (g) This represents the mean of the distribution corresponding to the g-th iteration;

[0164] C (g) This represents the covariance matrix corresponding to the g-th iteration;

[0165] During the iterative process of the improved EDA algorithm, offspring individuals are generated by sampling according to the Gaussian distribution model, as shown in equation (XI):

[0166]

[0167] in, The i-th solution corresponding to the (g+1)-th iteration

[0168] y i This represents the distribution vector corresponding to the i-th solution;

[0169] y i ~N(0,C (g) ) indicates that it follows a Gaussian distribution with a mean of 0.

[0170] By combining the above set A with equations (x) and (xi), the abnormal distribution of the population can be corrected, and the final screening effect can be improved.

[0171] In this application, the solutions in the set A are sorted according to their fitness values, and the top NP best individuals are used as the parent population.

[0172] In a preferred embodiment, in sub-step 5-1, the improved EDA algorithm stalls when the average fitness value of the top half of the best individuals in the current population is not less than the average value of the previous generation. That is, each time a new offspring individual is obtained in an iteration, the average fitness value of the top half of the best individuals in the current population and the average value of the previous generation must be calculated accordingly.

[0173] When the improved EDA algorithm stalls, offspring individuals are obtained through equations (12) and (13);

[0174]

[0175]

[0176] in, This represents the i-th solution corresponding to the (g+1)-th iteration;

[0177] Let represent the mean of the distribution improved by the MSD strategy corresponding to the g-th iteration;

[0178] B (g) Let represent the eigenvector matrix corresponding to the g-th iteration; it is obtained by decomposing the covariance matrix C, as shown in equation (xvii):

[0179] C (g) = (B (g) ·D (g) )·(B (g) ·D (g) ) T (sixteen).

[0180] B (g) This represents the eigenvector matrix corresponding to the g-th iteration;

[0181] D (g) This represents the eigenvalue matrix corresponding to the g-th iteration;

[0182] z i Represents the i-th random vector;

[0183] z i ~N(0,I 1×D ) indicates that it follows a normal distribution;

[0184] This represents the elite solution randomly selected from set L corresponding to the g-th iteration;

[0185] This represents the i-th solution corresponding to g iterations;

[0186] The set L is a set that stores the |L| top optimal solutions in the current population NP; initially, L contains only one element, and whenever the algorithm stalls, the number of elements in L increases by 1, until the maximum size |L| is reached. max The value will not change afterward; preferably, |L| max The value of is one-tenth of the population size NP, and it is set to 5 in this application.

[0187] In a preferred embodiment, when the improved EDA algorithm stalls, the search range is narrowed by reducing the distribution variance, i.e., by narrowing the search range using the following equation (xiv):

[0188] D (g) =(1-g / g) max ) 0.5 ·D (g) (fourteen)

[0189] Among them, D (g) Represents the eigenvalue matrix;

[0190] g max This represents the maximum number of iterations, which is related to the computation speed and the required reaction time. In this application, it is preferably set to 50 iterations.

[0191] Example:

[0192] Initially, the enemy's two-aircraft formation is positioned behind ours, possessing a situational advantage. During the 100-second engagement, both of our aircraft perform maneuvering control based on control variables generated by the 2v2 cooperative air combat auxiliary decision generation method for two-aircraft formations. This method performs a calculation every second, outputting a set of control variables, and then controls our aircraft according to these variables. Specifically, this method includes:

[0193] Step 1: Obtain the angle and distance parameters of enemy and friendly aircraft in real time, and evaluate the bearing situation using the following formula (I);

[0194]

[0195] Where, η Q Q represents the positional situation assessment value. U Q represents the angle of entry of our aircraft. T Indicates the angle of entry of the enemy aircraft;

[0196] The distance situation is evaluated using the following formula (ii);

[0197]

[0198] Where, η Q R represents the distance situation assessment value. G D represents the effective kill radius of the weapons on our aircraft.UT Indicates the distance between our aircraft and the enemy aircraft;

[0199] Construct the situation assessment model according to formula (iii);

[0200] η=a1·η Q +a2·η D (three)

[0201] Where η represents the overall situation assessment value, and both a1 and a2 are 0.5;

[0202] Sub-steps 1-4 involve constructing the dual-aircraft confrontation situation assessment matrix in equation (iv) to conduct situation analysis of two-on-two air combat.

[0203]

[0204] Step 2 involves formulating tactics based on the situational relationship between the enemy and ourselves, and then selecting operational targets; among these steps,

[0205]

[0206]

[0207] J A Indicate the operational objectives;

[0208] Step 3: Assign tactical roles based on tactical and operational objectives:

[0209] Among them, when equation (5) is satisfied,

[0210] attack aircraft

[0211] Auxiliary attack aircraft

[0212] When equation (vi) is satisfied,

[0213] attack aircraft

[0214] bait machine

[0215] Step 4: Calculate the target predicted state based on the target maneuver library, and then select the final target predicted state; this includes the following sub-steps:

[0216] Sub-step 4-1: Establish a target maneuver library;

[0217] Sub-step 4-2: Based on the current target state, iterate through the target prediction state after each flight action;

[0218] Sub-step 4-3 calculates the situational value of the predicted target state. In offensive tactics, it calculates the situational value of the attacking aircraft relative to the predicted target state; in defensive tactics, it calculates the situational value of the decoy aircraft relative to the predicted target state.

[0219] Sub-step 4-4: Select the target prediction state corresponding to the minimum value among all situation values ​​as the final target prediction state.

[0220] Step 5 involves taking the final target prediction state and the current state of our aircraft as inputs, and optimizing the control variables of our aircraft in the continuous domain using an improved EDA algorithm to obtain the optimal flight trajectory of our aircraft. Step 5 includes the following sub-steps:

[0221] Sub-step 5-1: Update the control variables of our aircraft within the control variable constraints;

[0222] Sub-step 5-2: For the control quantity of our aircraft obtained in each update, calculate the aircraft state at the next moment based on the current state of our aircraft, and then combine it with the final target prediction state to solve the situation value. Record and select the control quantity of our aircraft that makes the situation value the highest as the optimal solution.

[0223] Sub-step 5-3 involves using the optimal solution as an auxiliary decision suggestion, and being able to control our aircraft according to this decision suggestion.

[0224] In sub-step 5-1, the control quantity is used as the population individual of the improved EDA algorithm. In the improved EDA algorithm, the population distribution information of three consecutive generations with a size of 54 is saved as set A, and the archive capacity of set A is 162 sets of data.

[0225] During the iterative process of the improved EDA algorithm, the top 54 optimal individuals in set A are used as the parent population and participate in obtaining the Gaussian distribution model of equation (x):

[0226]

[0227] Where g represents the g-th iteration, ω i represents the coefficient used to calculate the mean of the weighted maximum likelihood estimation distribution; i represents the i-th element in set A;

[0228] A (g) Let A represent the set after the g-th iteration;

[0229] This represents the i-th element in set A corresponding to the g-th iteration;

[0230] μ (g) This represents the mean of the distribution corresponding to the g-th iteration;

[0231] C (g) This represents the covariance matrix corresponding to the g-th iteration;

[0232] During the iterative process of the improved EDA algorithm, offspring individuals are generated by sampling according to the Gaussian distribution model, as shown in equation (XI):

[0233]

[0234] in, This represents the i-th solution corresponding to the (g+1)-th iteration.

[0235] y i The distribution vector corresponding to the i-th solution;

[0236] y i ~N(0,C (g) ) indicates that it follows a normal distribution.

[0237] In sub-step 5-1, when the average fitness value of the top half of the excellent individuals in the current population is not less than the average value of the previous generation, the improved EDA algorithm stalls, and the offspring individuals are obtained through equations (12) and (13).

[0238]

[0239]

[0240] in, This represents the i-th solution corresponding to the (g+1)-th iteration;

[0241] The distribution mean improved by the MSD strategy corresponding to the g-th iteration;

[0242] B (g) This represents the eigenvector matrix corresponding to the g-th iteration;

[0243] D (g) The eigenvalue matrix corresponding to the g-th iteration;

[0244] z i Represents the i-th random vector;

[0245] z i ~N(0,I 1×D ) indicates that it follows a normal distribution;

[0246] This represents the elite solution randomly selected from set L for the g-th iteration, with a value of 6.

[0247] Let represent the i-th solution corresponding to g iterations.

[0248] When the improved EDA algorithm stalls, the search range is narrowed using the following formula (XIV):

[0249] D (g) =(1-g / g) max ) 0.5 ·D (g) (fourteen)

[0250] Among them, D (g) Represents the eigenvalue matrix;

[0251] g max This represents the maximum number of iterations, with a value of 50.

[0252] By controlling our aircraft using the control variables obtained through the above method, we continuously record the movement trajectories of both our and enemy aircraft over 100 seconds. Figure 2 As shown in the figure, the trend of the target situation score change of the dual-aircraft formation within 100 seconds is statistically analyzed to form... Figure 3 ;from Figure 2 aircraft trajectory and Figure 3 The trend of the situation score change shows that from the initial relative disadvantage, that is, the situation evaluation value was basically below 0.5, after maneuver optimization decision adjustment, the attack aircraft R2 finally achieved the attack advantage over the target T1. Figure 2 and Figure 3 In the diagram, R represents our aircraft, R2 is the attack aircraft, R1 is the decoy aircraft, T represents the enemy aircraft, and T1 is the tactical target.

[0253] As can be seen from the above embodiments, the decision suggestions provided by the dual-aircraft formation 2v2 cooperative air combat auxiliary decision generation method, that is, the control variables provided, can help the aircraft overcome the disadvantageous situation relative to the enemy aircraft and gradually turn into an advantageous situation.

[0254] The present invention has been described above with reference to preferred embodiments; however, these embodiments are merely exemplary and illustrative. Various substitutions and modifications can be made to the present invention based on these embodiments, all of which fall within the scope of protection of the present invention.

Claims

1. A method for generating auxiliary decision-making in 2v2 cooperative air combat with dual aircraft formations, characterized in that, The method includes the following steps: Step 1: Obtain the angle and distance elements of enemy and friendly aircraft in real time, and construct a situation assessment model by combining the weighting factors of the two to complete the situation analysis of two-on-two air combat. Step 2: Formulate tactics based on the situational relationship between the enemy and ourselves, and then select combat targets; Step 3: Assign tactical roles based on tactical and operational objectives; Step 4: Calculate the target prediction state based on the target maneuver library, and then select the final target prediction state; Step 5: Using the final target prediction state and the current state of our aircraft as input, optimize the control variables of our aircraft in the continuous domain using an improved EDA algorithm to obtain the optimal flight trajectory of our aircraft. The angular elements include the approach angles of our aircraft and the enemy aircraft. Step 1 includes the following sub-steps: Sub-step 1-1: Evaluate the orientation and situation using the following formula (i); (one) in, This indicates the positional situation assessment value. Indicates the angle of approach of our aircraft. Indicates the angle of entry of the enemy aircraft; Sub-steps 1-2 evaluate the distance situation using the following formula (ii); (two) in, This represents the distance situation assessment value. This indicates the effective kill radius of the weapons on our aircraft. Indicates the distance between our aircraft and the enemy aircraft; Sub-steps 1-3 construct the following situation assessment model (III); (three) in, This represents the overall situation assessment value. and Both represent weighting factors; Sub-steps 1-4 involve constructing the dual-aircraft confrontation situation assessment matrix in equation (iv) to conduct situation analysis of two-on-two air combat. (Four) in, This represents the set matrix of evaluation values ​​for two-on-two air combat situations. Indicates the first Our aircraft against the first Overall situation assessment value of enemy aircraft , Step 4 includes the following sub-steps: Sub-step 4-1: Establish a target maneuver library; Sub-step 4-2: Based on the current target state, iterate through the target prediction state after each flight action; Sub-step 4-3 calculates the situational value of the predicted target state. In offensive tactics, it calculates the situational value of the attacking aircraft relative to the predicted target state; in defensive tactics, it calculates the situational value of the decoy aircraft relative to the predicted target state. Sub-step 4-4: Select the target prediction state corresponding to the minimum value among all situation values ​​as the final target prediction state. Step 5 includes the following sub-steps: Sub-step 5-1: Update the control variables of our aircraft within the control variable constraints; Sub-step 5-2: For the control quantity of our aircraft obtained in each update, calculate the aircraft state at the next moment based on the current state of our aircraft, and then combine it with the final target prediction state to solve the situation value. Record and select the control quantity of our aircraft that makes the situation value the highest as the optimal solution. Sub-step 5-3: The optimal solution is used as an auxiliary decision suggestion, and the aircraft can be controlled according to the decision suggestion to generate the optimal flight trajectory of the aircraft.

2. The dual-aircraft formation 2v2 cooperative air combat auxiliary decision generation method according to claim 1, characterized in that, In step 2, When any When all values ​​are greater than or equal to 0.5, the tactic is an offensive tactic. The enemy aircraft corresponding to the maximum value is designated as the operational target for attack, i.e., the operational target. Select as matrix The column containing the maximum value of the element is shown in equation (5) below: (five); When there is less than 0.5 At that time, the tactic described is a defensive tactic, in which the enemy aircraft posing the greatest threat to our aircraft is selected as the operational target for attack, i.e., the operational objective. Select as matrix The column containing the minimum value of the elements is shown in equation (vi) below: (six).

3. The dual-aircraft formation 2v2 cooperative air combat auxiliary decision generation method according to claim 2, characterized in that, In step 3, In offensive tactics, after selecting the combat target, a matrix is ​​selected. The Middle The aircraft with the larger element value in the column is designated as the attack aircraft, as shown in equation (VII): (seven) in, Indicates an attack aircraft; In offensive tactics, after selecting the combat target, a matrix is ​​selected. The Middle The aircraft with the smaller element value in the column are used as auxiliary attack aircraft, as shown in equation (8) below: (eight) in, This refers to an auxiliary attack aircraft.

4. The dual-aircraft formation 2v2 cooperative air combat auxiliary decision generation method according to claim 2, characterized in that, In step 3, In defensive tactics, after selecting the combat objective, a matrix is ​​selected. The Middle The aircraft with the larger element value in the column is designated as the attack aircraft, as shown in equation (VII): (seven) in, Indicates an attack aircraft; In defensive tactics, after selecting the combat objective, a matrix is ​​selected. The Middle The aircraft with the smaller element value in the column is used as a decoy, as shown in equation (IX): (Nine) in, This refers to a bait machine.

5. The dual-aircraft formation 2v2 cooperative air combat auxiliary decision generation method according to claim 1, characterized in that, In sub-step 5-1, the control quantity is used as a population of individuals in the improved EDA algorithm. In the improved EDA algorithm, continuous... The population distribution information of each generation is stored in set A. During the iterative process of the improved EDA algorithm, the top NP optimal individuals in set A are used as the parent population and participate in obtaining the Gaussian distribution model of equation (x): (ten) in, Indicates the first iteration This represents the coefficient used to calculate the mean of the distribution in the weighted maximum likelihood estimation; Describe the first element in set A. One element; Indicates the first Set A after the next iteration; Indicates the first The set A corresponding to the nth iteration is the th i One element; Indicates the first The mean of the distribution corresponding to the next iteration; Indicates the first The distribution covariance matrix corresponding to the next iteration; During the iterative process of the improved EDA algorithm, offspring individuals are generated by sampling according to the Gaussian distribution model, as shown in equation (XI): (eleven) in, Indicates the first The iteration corresponding to the ... One solution; Indicates the corresponding number The distribution vector of the solutions; This indicates that it follows a Gaussian distribution with a mean of 0.

6. The dual-aircraft formation 2v2 cooperative air combat auxiliary decision generation method according to claim 5, characterized in that, In sub-step 5-1, the improved EDA algorithm stalls when the average fitness value of the top half of the best individuals in the current population is not less than the average value of the previous generation. At this point, offspring individuals are obtained through equations (12) and (13); (twelve) (Thirteen) in, Indicates the first The iteration corresponding to the ... One solution; No. The distribution mean improved by the MSD strategy for the next iteration; Indicates the first The eigenvector matrix corresponding to the next iteration; Indicates the first The eigenvalue matrix corresponding to the next iteration; Indicates the first 1 random vector; This indicates that it follows a Gaussian distribution with a mean of 0. Indicates the first The next iteration corresponds to an elite solution randomly selected from set L; express The iteration corresponding to the ... i One solution.

7. The dual-aircraft formation 2v2 cooperative air combat auxiliary decision generation method according to claim 6, characterized in that, When the improved EDA algorithm stalls, the search range is narrowed by reducing the distribution variance, i.e., by narrowing the search range using the following equation (xiv): (fourteen) in, Represents the eigenvalue matrix; This indicates the maximum number of iterations.

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