Aircraft cluster confrontation method based on dynamic game and related device

Abstract

The application relates to the technical field of aircrafts, and provides an aircraft cluster confrontation method based on dynamic game and related devices. A first target function of each defense aircraft is determined according to a defense task, a second target function of each invasion aircraft is determined according to an invasion task, the second target function represents the relationship between the action control variable of the invasion aircraft and the total task cost of the invasion aircraft, a game confrontation function set of the aircraft cluster is obtained, the Nash equilibrium strategy set of the function set is solved based on the initial flight state of each defense aircraft, the initial flight state of each invasion aircraft and the region information of the protection region, the optimal action strategy of each defense aircraft and the optimal action strategy of each invasion aircraft are obtained, and each defense aircraft and each invasion aircraft can perform real-time confrontation according to the optimal action strategy of the aircraft, so that the interference efficiency on the invasion side is improved, and the success rate of the aircraft in executing the defense task is improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of aircraft technology, in particular to an aircraft cluster confrontation method based on dynamic game and related device. BACKGROUND

[0002] In recent years, aircraft performance continues to improve, and the types are increasingly diversified, which have been widely used in service support, security, environmental monitoring, etc. Due to the limited load capacity of a single aircraft, it is difficult to complete the task independently, and in recent years, a new combat mode of aircraft cluster confrontation has been proposed. As an important style of future combat, aircraft cluster confrontation is a typical multi-agent task, which regards the aircraft cluster formation as a multi-agent system. Aircraft cluster confrontation problems are generally divided into four categories: pursuit and evasion problems, interception problems, hunting problems and driving problems, which mainly focus on how the pursuer-escapee (defender-intruder) interacts in different task scenarios. Game theory is easy to establish a strategy interaction model between different game players, and the strategy selection process of the game player is the cooperation or competition process within the system. Therefore, using game theory to study aircraft cluster confrontation problems has gradually become a research hotspot in this field.

[0003] In the current common pursuit and evasion differential game strategy, differential game theory is usually combined with task allocation algorithm to study the defense problem of multiple pursuers and multiple escapees, and then the optimal strategy of the pursuer and the escapee is solved. However, it cannot be well expanded between the number of game players and the state dimension, and cannot be flexibly adapted to the confrontation strategy according to the number of enemy and ourselves and the real-time environment of the battlefield in missile attack and aircraft confrontation scenes. Moreover, when the number of game players is large, it is difficult to solve, and cannot meet the real-time demand of game confrontation. SUMMARY

[0004] Therefore, the purpose of the present application is to provide an aircraft cluster confrontation method based on dynamic game and related device.

[0005] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0006] In the first aspect, the present application provides an aircraft cluster confrontation method based on dynamic game, which comprises:

[0007] According to the task of the defense party, a first target function of each defense party aircraft is determined; the first target function represents the relationship between the action control variable of the defense party aircraft and the total task cost thereof;

[0008] determine a second objective function of each of the intruder aircrafts according to the intruder task, and obtain a function group comprising each of the first objective function and each of the second objective function; the second objective function represents a relationship between an action control variable of the intruder aircraft and a total task cost of the intruder aircraft, and the function group represents a game confrontation function of a cluster of aircrafts composed of all the defense aircrafts and all the intruder aircrafts;

[0009] solve a Nash equilibrium strategy set of the function group based on the initial flight state of each of the defense aircrafts, the initial flight state of each of the intruder aircrafts and the region information of the protection region, and obtain an optimal action strategy of each of the defense aircrafts and an optimal action strategy of each of the intruder aircrafts, so that each of the defense aircrafts and each of the intruder aircrafts perform real-time confrontation according to the optimal action strategy thereof.

[0010] In an optional embodiment, the defense task is that the defense aircrafts track the intruder aircrafts and perform continuous jamming attack on the intruder aircrafts.

[0011] The step of determining the first objective function of each of the defense aircrafts according to the defense task comprises:

[0012] For each of the defense aircrafts, determine a cost function of the defense aircraft based on a preset tracking incentive rule, an energy consumption constraint condition, a safety boundary constraint condition and an attack incentive rule, wherein the cost function of the defense aircraft represents a relationship between an action control variable of the defense aircraft at each time and a task cost of the defense aircraft.

[0013] determine the first objective function of the defense aircraft based on a preset game duration and the cost function of the defense aircraft, and obtain the first objective function of each of the defense aircrafts.

[0014] In an optional embodiment, the cost function of the defense aircraft has the following expression:

[0015]

[0016]

[0017] wherein g i (t, u 1: (t)) represents the cost function of the i th defense aircraft; t represents a time; N represents a total number of aircrafts in the cluster of aircrafts; u 1: (t) represents an action control variable of each of the aircrafts in the cluster of aircrafts at the time t; N1 represents a total number of the defense aircrafts; s Dgoal represents a distance vector between the i th defense aircraft and a target intruder aircraft tracked by the i th defense aircraft; (sDgoal ) T denotes the transpose of s Dgoal ; Q i (t) denotes the first positive definite matrix of the i-th defender aircraft at time t; denotes the energy consumption incentive parameter of the i-th defender aircraft; u h (t) denotes the action control variable of the h-th aircraft in the aircraft swarm at time t; [u h (t)] T denotes the transpose of u h (t); R h () denotes the second positive definite matrix of the h-th aircraft in the aircraft swarm at time t; denotes the safety boundary distance of the i-th defender aircraft from other defender aircrafts; denotes the safety boundary distance incentive parameter of the i-th defender aircraft; denotes the attack incentive parameter of the i-th defender aircraft; Q denotes a three-dimensional task space; q denotes the position of a target intruder aircraft in the three-dimensional task space; φ(q, t) denotes the position probability density function of the target intruder aircraft at time t; P(q) denotes the joint attack probability of the i-th defender aircraft and other defender aircrafts on the target intruder aircraft;

[0018] The expression of the first objective function of the defender aircraft is as follows:

[0019]

[0020] wherein J i denotes the first objective function of the i-th defender aircraft; t s denotes a preset game duration.

[0021] In an optional implementation, the expression of the joint attack probability is as follows:

[0022]

[0023]

[0024] wherein P(q) denotes the joint attack probability of M defender aircrafts on a target intruder aircraft, and the M defender aircrafts include the i-th defender aircraft; Q k denotes the attack range of the k-th defender aircraft; R denotes an upper limit value of an attack radius; Θ denotes an upper limit value of an attack horizontal angle; Ψ denotes an upper limit value of an attack pitch angle; d k denotes the distance difference between the k-th defender aircraft and the target intruder aircraft; α k denotes the horizontal angle difference between the k-th defender aircraft and the target intruder aircraft; represents the pitch angle difference between the kth defender aircraft and the target invader aircraft.

[0025] In an optional embodiment, the invader task is for the invader aircraft to enter the protected area and escape from the pursuit of the defender aircraft;

[0026] The step of determining the second objective function of each invader aircraft according to the invader task comprises:

[0027] For each invader aircraft, a cost function of the invader aircraft is determined based on a preset invader incentive rule, an energy consumption constraint condition, a safety boundary constraint condition and an escape incentive rule, the cost function of the invader aircraft representing a relationship between an action control variable of the invader aircraft at each time and a task cost of the invader aircraft;

[0028] A second objective function of the invader aircraft is determined based on a preset game duration and the cost function of the invader aircraft, to obtain the second objective function of each invader aircraft.

[0029] In an optional embodiment, the cost function of the invader aircraft has the following expression:

[0030]

[0031]

[0032] wherein g j (t, u 1: ()) represents the cost function of the jth invader aircraft; t represents time; N represents the total number of aircraft in the aircraft cluster; u 1: (t) represents the action control variable of each aircraft in the aircraft cluster at time t; N2 represents the total number of invader aircraft; s Igoal represents the distance vector of the jth invader aircraft from the protected area; ( Igoal ) T represents the transpose of s Igoal ; Q j (t) represents the first positive definite matrix of the jth invader aircraft at time t; represents the energy consumption incentive parameter of the jth invader aircraft; u h (t) represents the action control variable of the hth aircraft in the aircraft cluster at time t; [u h (t)] T represents the transpose of u h (t); r h () represents the second positive definite matrix of the hth aircraft in the aircraft cluster at time t; represents the distance between the jth intruder aircraft and the safety boundary of other intruder aircrafts; represents the safety boundary distance incentive parameter of the jth intruder aircraft; represents the escape incentive parameter of the jth intruder aircraft; mind i,j represents the shortest distance between the jth intruder aircraft and the defense aircraft within its perception range;

[0033] The expression of the second objective function of the intruder aircraft is as follows:

[0034]

[0035] Wherein, J j represents the second objective function of the jth intruder aircraft; t s represents the preset game duration.

[0036] In an optional implementation, the optimal action strategy includes an action control parameter at each time point;

[0037] The real-time confrontation of each defense aircraft and each intruder aircraft according to the optimal action strategy of itself is realized in the following manner:

[0038] For each defense aircraft, the defense aircraft adjusts the flight state in real time according to the action control parameter at each time point of itself and the preset dynamic model to perform real-time confrontation;

[0039] For each intruder aircraft, the intruder aircraft adjusts the flight state in real time according to the action control parameter at each time point of itself and the preset dynamic model to perform real-time confrontation.

[0040] In a second aspect, the application provides a kind of based on dynamic game's aircraft cluster confrontation device, the based on dynamic game's aircraft cluster confrontation device includes:

[0041] The determining module is used to determine the first objective function of each defense aircraft according to the defense task;The first objective function represents the relationship between the action control variable of the defense aircraft and its total task cost;

[0042] The second objective function of each intruder aircraft is determined according to the intruder task, and a function group including each first objective function and each second objective function is obtained;The second objective function represents the relationship between the action control variable of the intruder aircraft and its total task cost, and the function group represents the game confrontation function of the aircraft cluster composed of all defense aircrafts and all intruder aircrafts;

[0043] The computing module is configured to solve a Nash equilibrium strategy set of the function group based on the initial flight state of each of the defense aircraft, the initial flight state of each of the intrusion aircraft, and the region information of the protection region, to obtain an optimal action strategy of each of the defense aircraft and an optimal action strategy of each of the intrusion aircraft, so that each of the defense aircraft and each of the intrusion aircraft perform real-time confrontation according to the optimal action strategy thereof.

[0044] In a third aspect, the present application provides an electronic device, comprising a processor and a memory, wherein the memory stores a computer program, and the processor implements the method for aircraft cluster confrontation based on dynamic game according to any one of the preceding embodiments when executing the computer program.

[0045] In a fourth aspect, the present application provides a storage medium, wherein the storage medium stores a computer program, and the computer program is executed by a processor to implement the method for aircraft cluster confrontation based on dynamic game according to any one of the preceding embodiments.

[0046] The method for aircraft cluster confrontation based on dynamic game and the related device provided by the present application determine a first target function of each defense aircraft according to a defense task, and the first target function represents the relationship between the action control variable of the defense aircraft and the total task cost thereof; and determine a second target function of each intrusion aircraft according to an intrusion task, and the second target function represents the relationship between the action control variable of the intrusion aircraft and the total task cost thereof, that is, obtain a function group comprising each first target function and each second target function, and the function group represents the game confrontation function of the aircraft cluster composed of all defense aircraft and all intrusion aircraft; then solve the Nash equilibrium strategy set of the function group based on the initial flight state of each defense aircraft, the initial flight state of each intrusion aircraft, and the region information of the protection region, to obtain the optimal action strategy of each defense aircraft and the optimal action strategy of each intrusion aircraft, so that each defense aircraft and each intrusion aircraft perform real-time confrontation according to the optimal action strategy thereof. The present application establishes the function model of the game confrontation of the aircraft cluster by means of the game theory, and solves the Nash equilibrium strategy set to make each aircraft perform real-time confrontation according to the optimal action strategy, thereby improving the interference efficiency on the intrusion aircraft and improving the success rate of the defense task performed by the aircraft.

[0047] In order to make the above objectives, characteristics and advantages of the present application more apparent, comprehensible and easy to understand, the following preferred embodiments are specifically described below with reference to the accompanying drawings. BRIEF DESCRIPTION OF DRAWINGS

[0048] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows. It should be understood that the following drawings only show some of the embodiments of the present application, and therefore should not be regarded as a limitation to the scope, and other related drawings can also be obtained by those of ordinary skill in the art without any creative effort, on the premise of not paying any creative effort.

[0049] Figure 1 A flowchart of the aircraft cluster confrontation method based on dynamic game provided by the embodiments of the present application is shown.

[0050] Figure 2 One of the example diagrams of the aircraft cluster confrontation method based on dynamic game provided by the embodiments of the present application is shown.

[0051] Figure 3 The second example diagram of the aircraft cluster confrontation method based on dynamic game provided by the embodiments of the present application is shown.

[0052] Figure 4 The third example diagram of the aircraft cluster confrontation method based on dynamic game provided by the embodiments of the present application is shown.

[0053] Figure 5 The fourth example diagram of the aircraft cluster confrontation method based on dynamic game provided by the embodiments of the present application is shown.

[0054] Figure 6 The fifth example diagram of the aircraft cluster confrontation method based on dynamic game provided by the embodiments of the present application is shown.

[0055] Figure 7 The sixth example diagram of the aircraft cluster confrontation method based on dynamic game provided by the embodiments of the present application is shown.

[0056] Figure 8 A functional module diagram of the aircraft cluster confrontation device based on dynamic game provided by the embodiments of the present application is shown.

[0057] Figure 9 A schematic diagram of the electronic device provided by the embodiments of the present application is shown.

[0058] Icon: 100-electronic device; 110-memory; 120-processor; 300-aircraft cluster confrontation device based on dynamic game; 310-determination module; 330-computation module. DETAILED DESCRIPTION

[0059] The technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings can be arranged and designed in various different configurations.

[0060] Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed application, but merely represents selected embodiments of the application. Based on the embodiments of the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of the present application.

[0061] It should be noted that the relational terms such as "first" and "second" and the like are used only to differentiate one entity or action from another, and do not necessarily require or imply that these entities or actions exist in any such actual relationship or order. Moreover, the terms "comprising", "including" or any other variant thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus that includes a list of elements not only includes those elements, but also includes other elements not explicitly listed or inherent to such process, method, article or apparatus. Without more limitations, the element defined by the statement "comprising a" does not exclude the presence of additional identical elements in the process, method, article or apparatus that includes the element.

[0062] In recent years, aircraft performance has been continuously improved, and the types have become increasingly diversified, and has been widely used in service guarantee, security, environmental monitoring, etc. Due to the limited load capacity of a single aircraft, it is difficult to complete the task independently, and in recent years, a new combat mode of aircraft cluster confrontation has been proposed. As an important style of future combat, aircraft cluster confrontation is a typical multi-agent task, which regards the aircraft cluster formation as a multi-agent system. Aircraft cluster confrontation problems are generally divided into four categories: pursuit and evasion problems, interception problems, hunting problems and driving problems, which mainly focus on the strategies of the pursuer-escapee (defender-intruder) in different task scenarios. Game theory is easy to establish a strategy interaction model between different game players, and the strategy selection process of the game player is the cooperation or competition process within the system. Therefore, using game theory to study aircraft cluster confrontation problems has gradually become a research hotspot in this field.

[0063] In the current common pursuit and evasion differential game strategy, the differential game theory is usually combined with a task allocation algorithm to study the defense problem of multiple pursuers and multiple evaders, and then the optimal strategy of the pursuer and the evader is solved. However, it cannot be well expanded between the number of game players and the state dimension, and cannot be flexibly adapted to the confrontation strategy according to the number of enemy and ourselves and the real-time environment of the battlefield in the scene of missile strike and aircraft confrontation. In solving the differential game problem, the iterative best response (IBR) algorithm is a common method, but this method cannot guarantee the convergence of the algorithm for any initialization, and when the number of game players is large, it is difficult to solve, and cannot meet the real-time demand of game confrontation. Therefore, an aircraft cluster confrontation method based on dynamic game is provided to solve the above problems.

[0064] Please refer to Figure 1 , Figure 1 is a flowchart of an aircraft cluster confrontation method based on dynamic game provided by the embodiment of the application. It should be noted that the aircraft cluster confrontation method based on dynamic game provided by the application is not limited to the specific order shown in Figure 1 , and the order of some steps can be exchanged according to actual needs. The specific process shown in Figure 1 will be described in detail below.

[0065] Step S202, according to the defense task, determining a first target function of each defense aircraft; the first target function represents the relationship between the action control variable of the defense aircraft and the total task cost.

[0066] Step S204, according to the invasion task, determining a second target function of each invasion aircraft, obtaining a function group including each first target function and each second target function; the second target function represents the relationship between the action control variable of the invasion aircraft and the total task cost, and the function group represents the game confrontation function of the aircraft cluster composed of all defense aircraft and all invasion aircraft.

[0067] It can be understood that in the aircraft cluster confrontation scene, there are two types of aircraft, one is the defense aircraft of the defense party, and the other is the invasion aircraft of the invasion party.

[0068] For the defense party and the invasion party, each has a task target, that is, the defense task and the invasion task. The task target of the defense party usually has two types, one is to shoot down the invasion aircraft, that is, the hard-kill target, and the other is to maximize the cumulative interference of the invasion aircraft at a close distance, that is, the soft-kill target. In the embodiment of the application, the soft-kill target is taken as the task target of the defense party.

[0069] In the embodiment, the target function of each defense aircraft can be determined according to the defense task, that is, each first target function is obtained; and the target function of each intrusion aircraft can be determined according to the intrusion task, that is, each second target function is obtained. The function group composed of all the first target functions and all the second target functions is the game confrontation function of the aircraft cluster composed of all the defense aircrafts and all the intrusion aircrafts.

[0070] From the perspective of game theory, each aircraft in the aircraft cluster can be regarded as each game player, the target function of each aircraft is the target function of each game player, and the action control variable of each aircraft is the decision variable of each game player. The action control variable represents a variable parameter for controlling the action of the aircraft. In order to maximize the interests of the aircraft cluster confrontation, the relationship between the action control variable of each aircraft and the total cost of performing the task can be taken as the target function of the aircraft.

[0071] In step S206, the Nash equilibrium strategy set of the function group is solved based on the initial flight state of each defense aircraft, the initial flight state of each intrusion aircraft and the region information of the protection region, so as to obtain the optimal action strategy of each defense aircraft and the optimal action strategy of each intrusion aircraft, so that each defense aircraft and each intrusion aircraft can perform real-time confrontation according to the optimal action strategy thereof.

[0072] In the embodiment, the function group obtained in the foregoing steps is used to obtain the initial flight state of each defense aircraft, the initial flight state of each intrusion aircraft and the region information of the protection region, and then the Nash equilibrium strategy set of the function group is solved, that is, the optimal action strategy of each defense aircraft and the optimal action strategy of each intrusion aircraft are obtained.

[0073] The Nash equilibrium strategy set is a strategy combination, that is, the equilibrium strategy of each game player is to maximize the expected income, that is, to minimize the cost, and all game players follow such a strategy combination. In the embodiment, the Nash equilibrium strategy set refers to a set of solutions that can minimize the function value of each target function in the function group, that is, the total task cost of each aircraft is minimized, and the set of solutions represents the optimal action strategy of each aircraft. Each aircraft can perform real-time confrontation according to the optimal action strategy thereof.

[0074] From the perspective of game theory, the goal of solving the game confrontation function group of the aircraft cluster is to find the time-varying state feedback optimal action strategy of each game player, that is, each aircraft h Γ hrepresents a strategy space of the aircraft h, which is a set of observable functions that map the state of the system in the game-against process to the action control variable of the aircraft h, which can be represented as wherein, γ h represents the action strategy of the aircraft h; t s represents the game duration; represents the state of the system in the game-against process, represents a strategy space of the aircraft h.

[0075] It should be noted that the game player, i.e., the aircraft h, can only observe the state of the system at each time, and does not know the control strategy of the other game player. It is assumed that J h represents the target function of the hth aircraft, and then the Nash equilibrium strategy set can be solved by the following inequality group.

[0076]

[0077] wherein, N represents the total number of aircraft in the aircraft cluster; represents the minimum value of the target function of the hth aircraft; J h represents the target function of the hth aircraft; represents the optimal action strategy when the target function of the hth aircraft is the minimum value; γ h represents the action strategy of the hth aircraft.

[0078] It can be seen that based on the above steps, the first target function of each defense aircraft is determined according to the defense task, and the first target function represents the relationship between the action control variable of the defense aircraft and the total task cost; and the second target function of each invasion aircraft is determined according to the invasion task, and the second target function represents the relationship between the action control variable of the invasion aircraft and the total task cost, i.e., a function group including each first target function and each second target function is obtained, and the function group represents the game-against function of the aircraft cluster composed of all defense aircraft and all invasion aircraft; then based on the initial flight state of each defense aircraft, the initial flight state of each invasion aircraft and the region information of the protection region, the Nash equilibrium strategy set of the function group is solved to obtain the optimal action strategy of each defense aircraft and the optimal action strategy of each invasion aircraft, so that each defense aircraft and each invasion aircraft performs real-time confrontation according to the optimal action strategy. The function model of the aircraft cluster game-against is established by the game theory, and the Nash equilibrium strategy set is solved to make each aircraft perform real-time confrontation according to the optimal action strategy, so as to improve the interference efficiency on the invader and improve the success rate of the aircraft in performing the defense task.

[0079] Optionally, for the step S202, an implementation manner is provided by the embodiment of the present application.

[0080] In step S202-1, for each defender aircraft, a cost function of the defender aircraft is determined based on the preset tracking incentive rule, the energy consumption constraint condition, the safety boundary constraint condition and the attack incentive rule, the cost function of the defender aircraft representing a relationship between an action control variable of the defender aircraft at each time and a task cost of the defender aircraft.

[0081] In step S202-3, a first target function of the defender aircraft is determined based on the preset game duration and the cost function of the defender aircraft, and the first target function of each defender aircraft is obtained.

[0082] In the embodiment, the defender task is that the defender aircraft tracks the intruder aircraft and performs a sustained jamming attack on the intruder aircraft. The tracking incentive rule can be understood as an incentive rule for the defender aircraft to track the intruder aircraft. The energy consumption constraint condition can be understood as a constraint condition that needs to be met by the energy consumption of the defender aircraft in the game confrontation process. The safety boundary constraint condition can be understood as a constraint condition that needs to be met by the distance between the defender aircraft and the friendly aircraft in the game confrontation process. The attack incentive rule can be understood as an incentive rule for the defender aircraft to attack the intruder aircraft.

[0083] It can be understood that the manner of determining the first target function of each defender aircraft is similar, and for brevity, the determination of the first target function of one defender aircraft is taken as an example for description below.

[0084] Based on the defender task, the relationship between the action control variable of the defender aircraft at each time and the task cost of the defender aircraft, i.e., the cost function of the defender aircraft, can be determined according to the preset tracking incentive rule, the energy consumption constraint condition, the safety boundary constraint condition and the attack incentive rule; and then the first target function of the defender aircraft is determined based on the preset game duration and the cost function of the defender aircraft.

[0085] Optionally, the expression of the cost function of the defender aircraft is as follows:

[0086]

[0087]

[0088] wherein g i (t, u 1: (t)) represents the cost function of the i th defender aircraft; t represents time; N represents the total number of aircraft in the aircraft cluster; u 1:(t) represents the action control variable of each aircraft in the aircraft cluster at time t; N1 represents the total number of defense aircraft.

[0089] It can be understood that, is the tracking incentive function of the ith defense aircraft obtained according to the preset tracking incentive rule. Wherein, s Dgoal represents the distance vector between the ith defense aircraft and the target intruder aircraft tracked by the ith defense aircraft; (s Dgoal ) T represents the transpose of s Dgoal ; Q i (t) represents the first positive definite matrix of the ith defense aircraft at time t.

[0090] It can be understood that, is the energy consumption constraint function of the ith defense aircraft obtained according to the preset energy consumption constraint condition. Wherein, represents the energy consumption incentive parameter of the ith defense aircraft; h (t) represents the action control variable of the hth aircraft in the aircraft cluster at time t; [u h (t)] T represents the transpose of u h (t); R h () represents the second positive definite matrix of the hth aircraft in the aircraft cluster at time t.

[0091] It can be understood that, is the safety boundary constraint function of the ith defense aircraft obtained according to the preset safety boundary constraint condition. Wherein, represents the safety boundary distance between the ith defense aircraft and other defense aircrafts; represents the safety boundary distance incentive parameter of the ith defense aircraft.

[0092] It can be understood that, is the attack incentive function of the ith defense aircraft obtained according to the preset attack incentive rule. Wherein, represents the attack incentive parameter of the ith defense aircraft; Q represents a three-dimensional task space; q represents the position of the target intruder aircraft in the three-dimensional task space; φ(q, t) represents the position probability density function of the target intruder aircraft at time t; P(q) represents the joint attack probability of the ith defense aircraft and other defense aircrafts on the target intruder aircraft.

[0093] It can be understood that the cost function of the defense aircraft is composed of the tracking incentive function, the energy consumption constraint function, the safety boundary constraint function and the attack incentive function of the defense aircraft.

[0094] Optionally, the first objective function of the defense aircraft can be obtained by integrating the cost function at all time instants, i.e., the expression of the first objective function of the defense aircraft is as shown in the following formula:

[0095]

[0096] wherein J i represents the first objective function of the i th defense aircraft; t s represents the preset game duration.

[0097] It can be understood that, based on the task objective of the defense in the embodiment being a soft-killing target, i.e., the attack energy accumulated by the defense aircraft over time during the continuous tracking of the intrusion aircraft is sufficient to cause the intrusion aircraft to be disturbed to fall, the task is determined to be successful.

[0098] Assuming that the total attack energy that the intrusion aircraft can resist is known, the attack performance of the defense aircraft depends on the distance and direction of the defense aircraft and the target intrusion aircraft, and can be represented as:

[0099]

[0100] wherein p k (q) represents the attack performance index of the k th defense aircraft; Q k represents the attack range of the k th defense aircraft; represents the upper limit value of the attack radius; represents the upper limit value of the attack horizontal angle; represents the upper limit value of the attack pitch angle; d k represents the distance difference between the k th defense aircraft and the target intrusion aircraft; a k represents the horizontal angle difference between the k th defense aircraft and the target intrusion aircraft; represents the pitch angle difference between the k th defense aircraft and the target intrusion aircraft.

[0101] If there is an intrusion aircraft at q and it is within the attack range of multiple defense aircraft, then the joint attack probability of the multiple defense aircraft on the intrusion aircraft can be calculated, which can be represented as:

[0102]

[0103] wherein P(g) represents the joint attack probability of the M defense aircraft on the target intrusion aircraft located at q.

[0104] Optionally, for the above step S204, the embodiment of the application provides an implementation manner.

[0105] Step S204-1, for each intruder aircraft, determine the cost function of the intruder aircraft based on the preset intrusion incentive rule, the energy consumption constraint condition, the safety boundary constraint condition and the escape incentive rule, the cost function of the intruder aircraft representing the relationship between the action control variable of the intruder aircraft at each time and the task cost of the intruder aircraft;

[0106] Step S204-3, determine the second objective function of the intruder aircraft based on the preset game duration and the cost function of the intruder aircraft, and obtain the second objective function of each intruder aircraft.

[0107] In the embodiment, the intruder task is for the intruder aircraft to enter the protection area and escape from the tracking of the defender aircraft. The intrusion incentive rule can be understood as the incentive rule for the intruder aircraft to intrude into the protection area. The energy consumption constraint condition can be understood as the constraint condition required to be met by the energy consumption of the intruder aircraft in the game confrontation process. The safety boundary constraint condition can be understood as the constraint condition required to be met by the distance between the intruder aircraft and the friendly aircraft in the game confrontation process. The escape incentive rule can be understood as the incentive rule for the intruder aircraft to escape from the tracking of the defender aircraft.

[0108] It can be understood that the way of determining the second objective function of each intruder aircraft is similar. For brevity, the determination of the second objective function of one intruder aircraft is taken as an example for description below.

[0109] Based on the intruder task, the relationship between the action control variable of the intruder aircraft at each time and the task cost of the intruder aircraft can be determined according to the preset intrusion incentive rule, the energy consumption constraint condition, the safety boundary constraint condition and the escape incentive rule, that is, the cost function of the intruder aircraft is obtained; and then the second objective function of the intruder aircraft is determined based on the preset game duration and the cost function of the intruder aircraft.

[0110] Optionally, the expression of the cost function of the intruder aircraft is as follows:

[0111]

[0112]

[0113]

[0114] wherein g j (t, 1: ()) represents the cost function of the jth intruder aircraft; t represents the time; N represents the total number of aircrafts in the aircraft cluster; u 1: (t) represents the action control variable of each aircraft in the aircraft cluster at the time t; and N2 represents the total number of intruder aircrafts.

[0115] It can be understood that is the invasion incentive function of the jth invasion aircraft obtained according to the preset invasion incentive rule. Wherein, s Igoal represents the distance vector between the jth invasion aircraft and the protected area; (s Igoal ) T represents the transpose of s Igoal ; Q j (t) represents the first positive definite matrix of the jth invasion aircraft at time t.

[0116] It can be understood that is the energy consumption constraint function of the jth invasion aircraft obtained according to the preset energy consumption constraint condition. Wherein, represents the energy consumption incentive parameter of the jth invasion aircraft; h (t) represents the action control variable of the hth aircraft in the aircraft cluster at time t; [u h (t)] T represents the transpose of u h (t); R h () represents the second positive definite matrix of the hth aircraft in the aircraft cluster at time t.

[0117] It can be understood that is the safety boundary constraint function of the jth invasion aircraft obtained according to the preset safety boundary constraint condition. Wherein, represents the safety boundary distance between the jth invasion aircraft and other invasion aircrafts; represents the safety boundary distance incentive parameter of the jth invasion aircraft.

[0118] It can be understood that is the escape incentive function of the jth invasion aircraft obtained according to the preset escape incentive rule. Wherein, represents the escape incentive parameter of the jth invasion aircraft; mind i,j (t) represents the shortest distance between the jth invasion aircraft and the defense aircraft within its perception range.

[0119] It can be understood that the cost function of the invasion aircraft is composed of the invasion incentive function, the energy consumption constraint function, the safety boundary constraint function and the escape incentive function of the invasion aircraft.

[0120] Optionally, the second objective function of the invasion aircraft can be obtained by integrating the cost function of the invasion aircraft at all times, that is, the expression of the second objective function of the invasion aircraft is as follows:

[0121]

[0122] wherein J j denotes the second objective function of the jthintruder aircraft; t s denotes the preset game duration.

[0123] Optionally, for the process of real-time confrontation of each defense aircraft and each intruder aircraft according to the optimal action strategy of itself in the step S206, the embodiment of the application provides an implementation manner.

[0124] In the step S208, for each defense aircraft, the defense aircraft adjusts the flight state in real time according to the action control parameter of each moment and the preset dynamic model to perform real-time confrontation.

[0125] In the step S210, for each intruder aircraft, the intruder aircraft adjusts the flight state in real time according to the action control parameter of each moment and the preset dynamic model to perform real-time confrontation.

[0126] In the embodiment, the optimal action strategy of each defense aircraft and each intruder aircraft includes the action control parameter of each moment.

[0127] It can be understood that whether the defense aircraft or the intruder aircraft belongs to the aircraft in the aircraft cluster, and the way of real-time confrontation according to the optimal action strategy of itself is similar. For simplicity, one aircraft in the aircraft cluster is taken as an example for description below.

[0128] The flight state of the aircraft can be represented by a state vector, and the state vector includes three-dimensional coordinates of the aircraft in a three-dimensional task space, a horizontal angle, a pitch angle and an instantaneous speed.

[0129] The preset dynamic model is as follows:

[0130]

[0131] wherein, denotes the state vector of the aircraft at the t+1 moment; denotes the coordinates of the aircraft in the three-dimensional task space at the t+1 moment, denotes the horizontal angle of the aircraft at the t+1 moment, denotes the pitch angle of the aircraft at the t+1 moment, represents the instantaneous velocity of the aircraft at time t+1; [x, y, z, θ, β, v] represents the state vector of the aircraft at time t; x, y, z represent the coordinates of the aircraft in the three-dimensional task space at time t; θ represents the horizontal angle of the aircraft at time t; β represents the pitch angle of the aircraft at time t; v represents the instantaneous velocity of the aircraft at time t; ω, ξ, and v are action control parameters of the aircraft at time t, ω represents the horizontal angle change parameter of the aircraft at time t, ξ represents the pitch angle change parameter of the aircraft at time t, and v represents the acceleration of the aircraft at time t.

[0132] For each aircraft in the aircraft cluster, it can adjust its flight state in real time based on the action control parameter at each time and the preset dynamic model according to its own optimal action strategy to carry out real-time confrontation.

[0133] In order to better understand the present application, the following will take an example to illustrate the aircraft cluster confrontation method based on dynamic game provided by the embodiments of the present application. It should be noted that the aircraft cluster confrontation scenarios in the following examples are all as shown in FIG. 1, that is, there is a protection area in the three-dimensional task space, the invading aircraft invades from all directions to attack the protection area of our side, and the defending aircraft is dispersed around the protection area, tracks the invading aircraft, and continuously attacks the invading aircraft when the enemy enters the attack range. Figure 2

[0134] The following takes the scenario of 2V1 as an example, that is, including two defending aircraft and one invading aircraft. The initial flight state of the defending aircraft 1 is [-20, 0, 40, arcsin(0.2), π / 4, 20], the initial flight state of the defending aircraft 2 is [-60, -40, 40, arcsin(0.2), π / 4, 20], and the initial flight state of the invading aircraft is [30, 60, 40, 5π / 4, π / 4, 20]. There is a protection area in the three-dimensional task space, and the position of the protection area is [-20, 0, 100].

[0135] The objective of the defending aircraft is to track the invading aircraft and continuously attack it, the incentive rules thereof are tracking incentive rules and attack incentive rules, and the constraint conditions thereof are energy consumption constraint conditions and safety boundary constraint conditions. The objective of the invading aircraft is to enter the protection area and escape from the pursuit of the defending aircraft, the incentive rules thereof are invasion incentive rules and escape incentive rules, and the constraint conditions thereof are energy consumption constraint conditions and safety boundary constraint conditions.

[0136] ​Example 1: After the game confrontation function set of the aircraft cluster is established by the method provided in the embodiment of the present application, the iterative linear quadratic differential game (ILQG) algorithm is used to solve the Nash equilibrium strategy set, in the present example, the sampling time is 0.1s, 40 path points are selected, and the obtained result simulation diagram is as shown in FIG. 2. Figures 3 to 5

[0137] The starting point of the invading aircraft is represented by a circle, the starting point of the defending aircraft is represented by a diamond, the initial point R1 represents the starting point of the invading aircraft, the initial point F1 represents the starting point of the defending aircraft 1, and the initial point F2 represents the starting point of the defending aircraft 2.

[0138] In each iteration of the algorithm, the ILQG simulates the trajectory of the entire nonlinear system, calculates the discrete-time linear dynamic approximation and quadratic cost approximation, and solves the linear quadratic differential game sub-problem to generate the next action strategy. Figure 3 The simulation diagram for the first iteration of the algorithm is as shown in FIG. 3, Figure 4 The simulation diagram for the third iteration of the algorithm is as shown in FIG. 4, Figure 5 The simulation diagram after the algorithm converges through iteration is as shown in FIG. 5. The final defending aircraft achieves the optimization of continuous jamming attack on the enemy aircraft within the limited path under the constraint condition.

[0139] Example 2: Assuming that the aircraft cluster confrontation is a long-distance scenario, and the sensitivity of the enemy aircraft to the soft-kill attack on the aircraft is known, that is, the maximum attack amount that the enemy aircraft can withstand is accumulated. When the invading aircraft continuously receives the jamming attack wave intensity accumulated to a certain degree, that is, reaches the sensitivity value, it is determined that the present confrontation aircraft has succeeded.

[0140] After the game confrontation function set of the aircraft cluster is established by the method provided in the embodiment of the present application, the rolling horizon algorithm is used, in the present example, the sampling time is 0.1s, the prediction horizon is 30 steps, and the actual execution is 10 steps, and the obtained result simulation diagram is as shown in FIG. 6. Figures 6 to 7

[0141] The starting point of the invading aircraft is represented by a circle, the starting point of the defending aircraft is represented by a diamond, the initial point R1 represents the starting point of the invading aircraft, the initial point F1 represents the starting point of the defending aircraft 1, and the initial point F2 represents the starting point of the defending aircraft 2.

[0142] Figure 6 The simulation result diagram when the invading aircraft is not sensitive to the continuous soft-kill attack is as shown in FIG. 7, Figure 7 ​​The simulation result diagram when the intruding aircraft is sensitive to the continuous soft-kill attack. It can be seen that the sensitivity of the intruding aircraft to the soft-kill attack determines the length of the continuous rolling iteration number of the algorithm, and the more sensitive the enemy aircraft is to the attack, the more likely the enemy aircraft is to lose the action capability in a short time.

[0143] It should be understood that the method provided by the embodiment of the present application can be extended to any number of aircraft cluster confrontation scenes. Meanwhile, when the number of aircraft clusters is huge and the resources of the aircraft are limited, the clusters can be first assigned tasks, the game problem is grouped according to the closest distance between the enemy and the friend, the energy consumption and other factors, 1V1, 2V1, 3V2 game confrontation combinations are realized, and then the method provided by the embodiment of the present application is used to effectively interfere with the enemy.

[0144] In order to perform the corresponding steps in the above embodiment and each implementation mode, an implementation mode of an aircraft cluster confrontation device based on dynamic game is given below. Please refer to Figure 8 , Figure 8 A function module diagram of an aircraft cluster confrontation device 300 based on dynamic game provided by the embodiment of the present application. It should be noted that the aircraft cluster confrontation device 300 based on dynamic game provided by the embodiment has the same basic principles and technical effects as the above embodiment, and in order to briefly describe, the embodiment is not mentioned in the above embodiment. Please refer to the corresponding content in the above embodiment. The aircraft cluster confrontation device 300 based on dynamic game includes:

[0145] The determining module 310 is configured to determine a first target function of each defense aircraft according to a defense task, the first target function representing a relationship between an action control variable of the defense aircraft and a total task cost of the defense aircraft; determine a second target function of each intruding aircraft according to an intruding task, the second target function representing a relationship between an action control variable of the intruding aircraft and a total task cost of the intruding aircraft, and obtain a function group including each first target function and each second target function; the function group represents a game confrontation function of the aircraft cluster composed of all defense aircrafts and all intruding aircrafts;

[0146] The calculating module 330 is configured to solve a Nash equilibrium strategy set of the function group based on an initial flight state of each defense aircraft, an initial flight state of each intruding aircraft and region information of the protection region, and obtain an optimal action strategy of each defense aircraft and an optimal action strategy of each intruding aircraft, so that each defense aircraft and each intruding aircraft perform real-time confrontation according to the optimal action strategy of itself.

[0147] Optionally, the determining module 310 is further configured to: for each defender aircraft, determine a cost function of the defender aircraft based on preset tracking incentive rules, energy consumption constraints, safety boundary constraints and attack incentive rules, the cost function of the defender aircraft representing a relationship between an action control variable of the defender aircraft at each time and a task cost of the defender aircraft; determine a first objective function of the defender aircraft based on a preset game duration and the cost function of the defender aircraft, to obtain the first objective function of each defender aircraft.

[0148] Optionally, the determining module 310 is further configured to: for each intruder aircraft, determine a cost function of the intruder aircraft based on preset intrusion incentive rules, energy consumption constraints, safety boundary constraints and escape incentive rules, the cost function of the intruder aircraft representing a relationship between an action control variable of the intruder aircraft at each time and a task cost of the intruder aircraft; determine a second objective function of the intruder aircraft based on a preset game duration and the cost function of the intruder aircraft, to obtain the second objective function of each intruder aircraft.

[0149] Optionally, the real-time confrontation of each defender aircraft and each intruder aircraft according to the optimal action strategy of itself is implemented in the following manner:

[0150] For each defender aircraft, the defender aircraft adjusts a flight state in real time according to an action control parameter at each time of the defender aircraft and a preset dynamic model to perform the real-time confrontation; for each intruder aircraft, the intruder aircraft adjusts a flight state in real time according to an action control parameter at each time of the intruder aircraft and a preset dynamic model to perform the real-time confrontation.

[0151] Please refer to Figure 9 , Figure 9 The schematic diagram of the electronic device provided by the embodiment of the present application is shown in FIG. 1. The electronic device 100 includes a memory 110 and a processor 120. The memory 110 and the processor 120 are directly or indirectly electrically connected to realize the transmission or interaction of data. For example, these elements can be electrically connected through one or more communication buses or signal lines.

[0152] The memory 110 is used to store programs or data. The memory 110 may be, but is not limited to, random access memory (RAM), read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), etc.

[0153] The processor 120 is used to read / write data or programs stored in memory and to perform corresponding functions.

[0154] It should be understood that, Figure 9 The structure shown is only a schematic diagram of an electronic device; the electronic device may also include components that are larger than... Figure 9 The more or fewer components shown, or having the same Figure 9 The different configurations shown. Figure 9 The components shown can be implemented using hardware, software, or a combination thereof.

[0155] The electronic device provided in this embodiment of the invention has a memory that stores a computer program. When the processor executes the computer program, it implements the aircraft swarm confrontation method based on dynamic game theory disclosed in this embodiment of the invention.

[0156] This invention also provides a storage medium storing a computer program, which, when executed by a processor, implements the dynamic game-based aircraft swarm confrontation method disclosed in this invention.

[0157] In several embodiments provided by the present application, it should be understood that the disclosed apparatus and method can also be implemented in other manners. The described embodiments of the apparatus are merely exemplary, and the present application can be implemented in other manners. For example, the flowcharts and block diagrams in the accompanying drawings illustrate the possible implementation modes of the apparatus, method and computer program product according to the present application. In this regard, each block in the flowcharts or block diagrams can represent a module, a segment or a part of code, which comprises one or more executable instructions for implementing the specified logic function. It should also be noted that in some alternative implementation modes, the functions noted in the blocks can occur in a different order from that noted in the accompanying drawings. For example, two consecutive blocks can actually be executed in parallel, and they can also be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and the combination of blocks in the block diagrams and / or flowcharts, can be implemented by a dedicated hardware-based system for implementing the specified functions or actions, or can be implemented by a combination of dedicated hardware and computer instructions.

[0158] In addition, each functional module in the various embodiments of the present application can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0159] If the functions are implemented in the form of software function modules and sold or used as independent products, they can be stored in a computer readable storage medium. Based on this understanding, the technical solutions of the present application can be embodied in the form of a software product, and the computer software product is stored in a storage medium, and includes a number of instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present application. The aforementioned storage medium includes: a U disk, a mobile hard disk, a read-only memory (ROM, Read-Only Memory), a random access memory (RAM, Random Access Memory), a magnetic disk or an optical disk, and various media that can store program codes.

[0160] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. An aircraft cluster confrontation method based on dynamic game, characterized in that, The aircraft cluster confrontation method based on dynamic game includes: According to the defense task, based on the preset game duration, the preset tracking incentive rule, the energy consumption constraint condition, the safety boundary constraint condition and the attack incentive rule, the first objective function of each defense aircraft is determined; The first objective function represents the relationship between the action control variable of the defense aircraft and the total task cost thereof; According to the invasion task, based on the preset game duration, the preset invasion incentive rule, the energy consumption constraint condition, the safety boundary constraint condition and the escape incentive rule, the second objective function of each invasion aircraft is determined, and a function group including each first objective function and each second objective function is obtained; The second objective function represents the relationship between the action control variable of the invasion aircraft and the total task cost thereof, and the function group represents the game confrontation function of the aircraft cluster composed of all defense aircrafts and all invasion aircrafts; Based on the initial flight state of each defense aircraft, the initial flight state of each invasion aircraft and the region information of the protection region, the Nash equilibrium strategy set of the function group is solved, and the optimal action strategy of each defense aircraft and the optimal action strategy of each invasion aircraft are obtained, so that each defense aircraft and each invasion aircraft can perform real-time confrontation according to the optimal action strategy thereof.

2. The dynamic game-based aircraft swarm adversarial method according to claim 1, wherein, The defense task is that the defense aircraft tracks the invasion aircraft and continuously attacks the invasion aircraft; The step of determining the first objective function of each defense aircraft according to the defense task includes: For each defense aircraft, based on the preset tracking incentive rule, the energy consumption constraint condition, the safety boundary constraint condition and the attack incentive rule, the cost function of the defense aircraft is determined, and the cost function of the defense aircraft represents the relationship between the action control variable of the defense aircraft at each moment and the task cost thereof; Based on the preset game duration and the cost function of the defense aircraft, the first objective function of the defense aircraft is determined, and the first objective function of each defense aircraft is obtained.

3. The dynamic game-based aircraft swarm confrontation method according to claim 2, characterized in that, The expression of the cost function of the defense aircraft is as follows: ， ； wherein, denotes the cost function of the i th defender aircraft; t denotes the time instant; N denotes the total number of aircraft in the fleet of aircraft; denotes the action control variable of the t th aircraft in the fleet of aircraft at the time instant N1 denotes the total number of defender aircraft; denotes the distance vector of the i th defender aircraft to the target invader aircraft it is tracking; denotes the transpose of ; denotes the th defender aircraft; i denotes the first positive definite matrix of the t th defender aircraft at the time instant denotes the i th defender aircraft; denotes the action control variable of the h th aircraft in the fleet of aircraft at the time instant t ; denotes the th aircraft in the fleet of aircraft; denotes the transpose of ; denotes the h th aircraft in the fleet of aircraft; t denotes the second positive definite matrix of the th aircraft in the fleet of aircraft at the time instant i denotes the safety boundary distance of the th defender aircraft to other defender aircraft; i denotes the safety boundary distance incentive parameter of the th defender aircraft; i denotes the attack incentive parameter of the th defender aircraft; Q denotes the three-dimensional mission space; denotes the position of the target invader aircraft in the three-dimensional mission space; t denotes the position probability density function of the target invader aircraft at the time instant denotes the joint attack probability of the i th defender aircraft to other defender aircraft on the target invader aircraft; The expression of the first objective function of the defense aircraft is as follows: wherein, represents a first objective function of the i defender aircraft; represents a preset game duration.

4. The dynamic game based aircraft swarm confrontation method according to claim 3, characterized in that, The expression of the joint attack probability is as follows: 1- ， wherein, M a joint attack probability of the defending aircraft against the target aggressor aircraft, and M the defending aircraft comprises a first i defending aircraft; denotes an attack range of the first k defending aircraft; denotes an upper limit value of the attack radius; denotes an upper limit value of the attack horizontal angle; denotes an upper limit value of the attack pitch angle; denotes a distance difference between the first k defending aircraft and the target aggressor aircraft; denotes a horizontal angle difference between the first k defending aircraft and the target aggressor aircraft; denotes a pitch angle difference between the first k defending aircraft and the target aggressor aircraft.

5. The dynamic game based aircraft swarm adversarial method according to claim 1, wherein, The invasion task is that the invasion aircraft enters the protection region and escapes from the tracking of the defense aircraft; The step of determining the second objective function of each invasion aircraft according to the invasion task includes: For each invasion aircraft, based on the preset invasion incentive rule, the energy consumption constraint condition, the safety boundary constraint condition and the escape incentive rule, the cost function of the invasion aircraft is determined, and the cost function of the invasion aircraft represents the relationship between the action control variable of the invasion aircraft at each moment and the task cost thereof; Based on the preset game duration and the cost function of the invasion aircraft, the second objective function of the invasion aircraft is determined, and the second objective function of each invasion aircraft is obtained.

6. The dynamic game-based aircraft swarm adversarial method according to claim 5, wherein, The expression of the cost function of the invasion aircraft is as follows: ， ； wherein, represents a cost function of the j th intruder vehicle; t represents a time instant; N represents the total number of vehicles in the vehicle swarm; represents the action control variable of each vehicle in the vehicle swarm at time instant t N2 represents the total number of intruder vehicles; represents a distance vector between the j th intruder vehicle and the protected region; represents represents a first positive definite matrix of the j th intruder vehicle at time instant t represents an energy consumption incentive parameter of the j th intruder vehicle; represents the action control variable of the h th vehicle in the vehicle swarm at time instant t represents the transpose of represents a second positive definite matrix of the h th vehicle in the vehicle swarm at time instant t represents a safety boundary distance between the j th intruder vehicle and other intruder vehicles; represents a safety boundary distance incentive parameter of the j th intruder vehicle; represents an escape incentive parameter of the j th intruder vehicle; represents the shortest distance between the j th intruder vehicle and the defender vehicles within its perception range.​​​​​ An expression of the second objective function of the intruding aircraft is as follows: wherein, represents a second objective function of the i-th intruder aircraft; j represents a preset game duration.​ 7. The dynamic game based aircraft swarm adversarial method according to claim 1, wherein, The optimal action strategy includes an action control parameter at each time point; The real-time confrontation of each of the defense aircraft and each of the intruding aircraft in accordance with the optimal action strategy thereof is realized in the following manner: For each of the defense aircraft, the defense aircraft adjusts a flight state in real time in accordance with the action control parameter thereof at each time point and a preset dynamic model to perform real-time confrontation; For each of the intruding aircraft, the intruding aircraft adjusts a flight state in real time in accordance with the action control parameter thereof at each time point and a preset dynamic model to perform real-time confrontation.

8. An aircraft swarm countermeasure device based on dynamic game, characterized in that, The aircraft cluster confrontation device based on dynamic game includes: A determination module is configured to determine, in accordance with a defense task, a first objective function of each defense aircraft based on a preset game duration, a preset tracking incentive rule, an energy consumption constraint condition, a safety boundary constraint condition, and an attack incentive rule; the first objective function represents a relationship between an action control variable of the defense aircraft and a total task cost thereof; In accordance with an intruding task, a second objective function of each intruding aircraft is determined based on a preset game duration, a preset intruding incentive rule, an energy consumption constraint condition, a safety boundary constraint condition, and an escape incentive rule, to obtain a function group including each of the first objective functions and each of the second objective functions; the second objective function represents a relationship between an action control variable of the intruding aircraft and a total task cost thereof, and the function group represents a game confrontation function of an aircraft cluster composed of all defense aircraft and all intruding aircraft; A calculation module is configured to solve a Nash equilibrium strategy set of the function group based on an initial flight state of each of the defense aircraft, an initial flight state of each of the intruding aircraft, and region information of a protection region, to obtain an optimal action strategy of each of the defense aircraft and an optimal action strategy of each of the intruding aircraft, so that each of the defense aircraft and each of the intruding aircraft perform real-time confrontation in accordance with the optimal action strategy thereof.

9. An electronic device, comprising: The memory stores a computer program, and the processor, when executing the computer program, implements the aircraft cluster confrontation method based on dynamic game according to any one of claims 1 to 7.

10. A storage medium, characterized by The storage medium stores a computer program, and the processor, when executing the computer program, implements the aircraft cluster confrontation method based on dynamic game according to any one of claims 1 to 7.

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