A dynamic tactical control domain solution method based on three-party game in air combat simulation environment

Abstract

The present invention discloses a method for solving a dynamic tactical control domain based on a three-party game in an air combat simulation environment, comprising: establishing and solving a three-party game system model to obtain an optimal pursuit and escape guidance strategy; constructing motion models of the three-party aircraft and setting simulation constraints to obtain a simulation model; for each set of simulation data obtained, on the basis of all three parties in the air combat executing the optimal pursuit and escape guidance strategy, using an improved advance and retreat method to search for the boundary of the dynamic tactical control domain to obtain an outer boundary dynamic tactical control distance value and an inner boundary dynamic tactical control distance value; sequentially connecting the same dynamic tactical control distance values obtained from each set of simulation data under the same air combat simulation environment and with continuous situations to obtain the inner boundary and outer boundary of the dynamic tactical control domain, thereby forming a dynamic tactical control domain. The present invention effectively fills the loopholes in the perception of air combat confrontation situation information in an active defense scenario, can improve the combat effectiveness of fighter jets in air combat confrontation simulation systems, and has strong engineering practicality and effectiveness.

Description

Technical Field

[0001] The present invention belongs to the technical field of computer simulation and artificial intelligence, and specifically relates to a method for solving a dynamic tactical control domain based on a three-party game in an air combat simulation environment. Background Art

[0002] Air combat games and simulation systems both utilize computer simulations to create detailed and realistic simulations of the entire combat process. To effectively enhance the user experience and controllability of these games and simulations, they must be designed from the perspective of actual air combat. More importantly, tactical simulation and convenient interactive design are crucial. This ensures that the user experience is both realistic and user-friendly.

[0003] In air combat games and simulations, fighter jets typically navigate two types of air combat environments: beyond-visual-range (BVR) and close-range (CLR) combat. Compared to CLR, BVR combat begins head-on and at greater distances, making attack and positioning angles easier to meet and placing a greater emphasis on distance-based competition and confrontation. The dynamic tactical control domain (DTC) revolves around combat distance, guiding fighters in selecting appropriate methods and timing for transitioning between attack and defense, providing the core information guiding tactical behavior. The accuracy of the DTC calculation plays a crucial role in enabling users to accurately grasp the course of combat and directly impacts the effectiveness of BVR combat in air combat simulations. Therefore, designing a highly competitive and timely DTC calculation method is crucial for improving the fidelity, credibility, and user control of air combat simulation systems.

[0004] Designing reference quantitative information for tactical decision-making in air combat confrontation simulation systems has always been one of the key research issues in the field of air combat simulation. Currently, the relevant theoretical models mainly include air-to-air missile attack zone and dynamic escape zone.

[0005] Air-to-air missile attack zones analyze the distance boundaries of tactical control from an offensive perspective. Key research findings include coordinated attack zones, three-dimensional attack zones, and omnidirectional attack zones. These methods, based on the dynamic equations and mathematical models of air-to-air missile guidance laws, combined with three- or six-degree-of-freedom models of the carrier aircraft, rapidly search for attack zone boundaries, achieving promising results. Related research includes "A New Method for Real-Time Calculation of Air-to-Air Missile Attack Zones" proposed by Zhang Ping, Fang Yangwang, and others, and "An Air-to-Air Missile Attack Zone Calculation Method Based on Adaptive Step Size" proposed by Huang Wei, Ren Yang, and others.

[0006] In terms of solution methods, attack zone calculation methods mainly include bisection, exponential search, translational numerical method, polynomial fitting, table interpolation, and neural network fitting. For example, the study "Research on a High-Precision and Fast Algorithm for Air-to-Air Missile Dynamic Attack Zone" uses the translational numerical method to search for missile dynamic attack zones in actual combat environments with wind field interference and target maneuvering, achieving relatively accurate calculation results. The study "Simulation Analysis of Exponential Optimization Search for Missile Launch Envelopes" comprehensively considers air combat motion parameters when calculating the attack zone and constructs an exponential polynomial function to roughly estimate the initial search space, effectively avoiding the blind search for initial values of the attack zone.

[0007] From a defensive perspective, dynamic escape zones (DEZs) quantify the distance between friendly and enemy aircraft when typical air combat events are triggered. This provides crucial information for pilots making escape maneuver decisions. Based on differential game theory and simplified geometric models, this approach devises a fast method for determining the timing of evasive maneuvers. This method serves as a basis for distinguishing between adventurous offensive and conservative defensive tactics, thus providing a theoretical basis for ensuring aircraft safety in beyond-visual-range air combat tactical control. For more information on this method, please refer to papers such as "Dynamic-escape-zone to avoid energy-bleeding coasting missiles" and "Simulation of the Defense Zone of Airborne Active Defense Systems."

[0008] However, because BVR air combat is a highly coordinated and coupled process of offense and defense, analyzing the tactical distances of attack and escape zones from a single perspective, such as attack or defense, fails to fully reflect the changing situational dynamics of both combatants and accurately predicts the transition timing between offense and defense in BVR air combat, severely impacting the quality of air combat simulations. In terms of solution methods, the translational numerical method and exponential search method offer high accuracy but slow convergence, making them inadequate for highly dynamic air combat environments. While the bisection method improves simulation timeliness, its solution results suffer from large errors and the search process is prone to falling into attack zone black holes, failing to meet the accuracy requirements of air combat simulations. Regarding model building, existing methods often assume a steady state or a given maneuvering state, resulting in results that are significantly inconsistent with the actual battlefield situation. The errors caused by ignoring target maneuvers are particularly prominent in BVR air combat, significantly reducing combat effectiveness in high-security air combat simulations. In terms of combat style, with the continuous improvement of air-to-air missile performance, traditional passive and inactive evasion and escape can no longer effectively guarantee the survival of the carrier aircraft.

[0009] Currently, active defense tactics, which effectively improve the survivability of carrier aircraft in air combat simulations by launching defensive missiles to intercept incoming air-to-air missiles, have gradually developed into a new form of air combat confrontation. However, there is currently no research on quantitative reference information for air combat offense and defense confrontation in scenarios where carrier aircraft launch defensive missiles. Summary of the Invention

[0010] To address the aforementioned problems in the prior art, the present invention provides a method for solving a dynamic tactical control domain in an air combat simulation environment based on a three-party game, which is applied to a beyond-visual-range air combat simulation environment under active defense tactics. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0011] Based on differential game theory, a three-party game system model is established to characterize the game confrontation relationship between three aircraft. The three-party game system model is solved to obtain the control vectors of each aircraft to represent the solved optimal pursuit and escape guidance strategy. The three aircraft are the target aircraft, the defense missile, and the attack missile; the control vectors are the acceleration vectors of the aircraft.

[0012] Construct the motion model of the three aircraft and set simulation constraints to obtain the simulation model;

[0013] For each set of simulation data obtained, based on the implementation of the optimal pursuit-escape guidance strategy by all three parties in the air combat, the boundary of the dynamic tactical control domain is searched using the set of simulation data, the simulation model, and the improved advance-retreat method, to obtain the outer boundary dynamic tactical control distance value and the inner boundary dynamic tactical control distance value corresponding to the set of simulation data;

[0014] The same dynamic tactical control distance values obtained from each set of simulation data with continuous situations in the same air combat simulation environment are connected in sequence to obtain the inner and outer boundaries of the dynamic tactical control domain, and the area enclosed by the inner and outer boundaries constitutes the dynamic tactical control domain; wherein, any set of simulation data represents the motion state of the three-party aircraft; the each set of simulation data with continuous situations in the same air combat simulation environment only has different target entry angles, which are used to represent different situations.

[0015] In one embodiment of the present invention, the three-party game system model based on differential game theory to characterize the three-party aircraft game confrontation relationship includes:

[0016] Establishing the motion equations of the three aircraft in an inertial coordinate system;

[0017] Rewriting the equation of motion into a state-space equation yields a differential game model;

[0018] A performance index function for the differential game model is set, and the maximum and minimum optimization problem for solving the optimal pursuit and escape guidance strategy is transformed into a minimization problem. The solution assumption of the differential game model is made to obtain a three-party game system model.

[0019] In one embodiment of the present invention, solving the three-party game system model to obtain the control vectors of each party's aircraft to represent the solved optimal pursuit and escape guidance strategy includes:

[0020] The three-party game system model is solved using the Hamiltonian function and the matrix Riccati differential equations to obtain an optimal pursuit and escape guidance strategy in the form of state feedback gain;

[0021] The constraints of the control system are imposed on the optimal pursuit and escape guidance strategy in the form of state feedback gain, and the control vectors of the aircraft of each party are obtained to represent the solved optimal pursuit and escape guidance strategy.

[0022] In one embodiment of the present invention, the step of constructing a motion model of the three-party aircraft includes:

[0023] The motion models of three-party aircraft are constructed by constructing the three-degree-of-freedom motion model of the aircraft and the three-degree-of-freedom motion model of the missile.

[0024] In one embodiment of the present invention, the simulation constraints include:

[0025] If the missile-target distance is less than the missile's maximum damage radius and neither the time limit nor the speed limit is triggered, the missile is deemed to have successfully hit the target; otherwise, the missile attack is deemed to have failed.

[0026] The time limit condition is: when the missile flight time is greater than the missile controllable flight time, the missile energy is exhausted and cannot hit the target;

[0027] The speed limit condition is: when the missile speed is less than the minimum flight speed of the missile, the missile's maneuverability is reduced and it cannot hit the target;

[0028] The missiles include the defense missiles and the attack missiles; the targets are objects attacked by the missiles; the objects attacked by the defense missiles are the attack missiles, and the objects attacked by the attack missiles are the target aircraft.

[0029] In one embodiment of the present invention, for each set of simulation data obtained, on the basis that all three parties in the air combat execute the optimal pursuit and escape guidance strategy, the boundary of the dynamic tactical control domain is searched using the set of simulation data, the simulation model, and the improved advance and retreat method, to obtain the outer boundary dynamic tactical control distance value and the inner boundary dynamic tactical control distance value corresponding to the set of simulation data, including:

[0030] For each set of simulation data obtained, based on the implementation of the optimal pursuit-and-escape guidance strategy by all three parties in the air combat, the outer boundary of the dynamic tactical control domain is searched using the set of simulation data, the simulation model, and the advance-and-retreat method to obtain the outer boundary dynamic tactical control distance value corresponding to the set of simulation data;

[0031] The inner boundary of the dynamic tactical control domain is searched using the outer boundary dynamic tactical control distance value corresponding to the group of simulation data and the dichotomy method to obtain the inner boundary dynamic tactical control distance value corresponding to the group of simulation data.

[0032] In one embodiment of the present invention, for each set of simulation data obtained, on the basis that all three parties in the air combat execute the optimal pursuit and escape guidance strategy, the outer boundary of the dynamic tactical control domain is searched using the set of simulation data, the simulation model, and the advance and retreat method to obtain the outer boundary dynamic tactical control distance value corresponding to the set of simulation data, including:

[0033] For each set of simulation data obtained, on the basis of all three parties in the air combat executing the optimal pursuit-and-escape guidance strategy, an air combat confrontation simulation under a corresponding situation is performed using the simulation model based on the set of simulation data and the obtained initial distance between the attacking missile and the target aircraft, to obtain an initial miss distance simulation result between the attacking missile and the target aircraft; and an initial outer boundary search point is set according to the initial miss distance simulation result;

[0034] Perform an air combat confrontation simulation using the outer boundary search point used in the current iteration, and output a miss distance simulation result of the current iteration; wherein the outer boundary search point used in the first iteration is the initial outer boundary search point;

[0035] Based on the numerical comparison relationship between the miss amount simulation result of the current iteration and the lower limit value and the upper limit value in the preset outer boundary search point range, the outer boundary search point used in the next iteration is obtained. When the miss amount simulation result of the current iteration does not fall within the outer boundary search point range, the air combat confrontation simulation is continued according to the outer boundary search point used in the next iteration until the miss amount simulation result falls within the outer boundary search point range. The iteration is stopped and the outer boundary search point used in the next iteration is used as the outer boundary dynamic tactical control distance value corresponding to the group of simulation data.

[0036] In one embodiment of the present invention, obtaining the outer boundary search point used in the next iteration based on the numerical comparison relationship between the miss distance simulation result of the current iteration and the lower limit value and the upper limit value in the preset outer boundary search point range includes:

[0037] Determine whether the miss distance simulation result of the current iteration is less than the lower limit value in the outer boundary search point range; if so, determine the outer boundary search point used in the next iteration using the first formula;

[0038] If not, determine whether the miss distance simulation result of the current iteration is greater than or equal to the upper limit value in the outer boundary search point range, and if so, use the second formula to determine the outer boundary search point used in the next iteration; if not, use the third formula to determine the outer boundary search point used in the next iteration;

[0039] Among them, the first formula is R k+1 =R k +d-0.5MD k : The second formula is R k+1 =R k -d-0.5MD k : The third formula is R k+1 =R k -0.5MD k ; R k Indicates the outer boundary search point used in the kth iteration; MD k is the k-th miss distance simulation result; d is the preset reverse boundary search step; k is a natural number greater than 0.

[0040] In one embodiment of the present invention, the inner boundary of the dynamic tactical control domain is searched using the outer boundary dynamic tactical control distance value corresponding to the set of simulation data and the dichotomy method to obtain the inner boundary dynamic tactical control distance value corresponding to the set of simulation data, including:

[0041] Calculate the binary split point based on the inner boundary search point range used in the current iteration; the lower limit of the inner boundary search point range used in the first iteration is 0, and the upper limit is the outer boundary dynamic tactical control distance value corresponding to the set of simulation data;

[0042] According to the dichotomy split point corresponding to the current iteration and the set of simulation data, a three-party game confrontation simulation is performed using the simulation model to obtain a simulation value of the miss amount;

[0043] determining whether the miss distance simulation value indicates that the target aircraft is not hit by the attack missile, and narrowing the inner boundary search point range used in the current iteration accordingly based on different determination results;

[0044] Determine whether the narrowed inner boundary search point range meets the preset error requirements;

[0045] If not, using the narrowed inner boundary search point range as the inner boundary search point range used in the next iteration, and returning to the step of calculating the binary segmentation point based on the inner boundary search point range used in the current iteration;

[0046] If so, the binary division point of the narrowed inner boundary search point range is calculated as the inner boundary dynamic tactical control distance value corresponding to the set of simulation data.

[0047] In one embodiment of the present invention, the step of narrowing the inner boundary search point range used in the current iteration based on different judgment results includes:

[0048] If the miss distance simulation value indicates that the target aircraft is hit by the attack missile, the upper limit value in the outer boundary search point range used in the current iteration is replaced by the dichotomy segmentation point corresponding to the current iteration;

[0049] If the miss distance simulation value indicates that the target aircraft is not hit by the attack missile, determining whether at least one of the time limit condition and the speed limit condition is satisfied;

[0050] If not satisfied, returning to the step of performing a three-party game confrontation simulation using the simulation model based on the dichotomy split point corresponding to the current iteration and the set of simulation data and re-simulating with the original input data;

[0051] If satisfied, the lower limit value in the outer boundary search point range used in the current iteration is replaced with the binary segmentation point corresponding to the current iteration.

[0052] To address the issue of decision-making information support in beyond-visual-range air combat simulations, an embodiment of the present invention proposes a quantitative characterization scheme for the dynamic tactical control zone (DTCZ) with adaptive, timely, and high-precision features. First, a three-party game system model is established based on differential game theory to characterize the three-party aircraft game confrontation relationship. Based on this, the optimal pursuit and escape guidance strategy for the three parties in the air combat is calculated. Then, a simulation model for boundary search is constructed. Based on the optimal pursuit and escape guidance strategy executed by each party in the air combat, a real-time DTCZ solution method based on an improved advance-and-retreat method is designed. This method can obtain the corresponding outer and inner boundary dynamic tactical control distance values for each set of simulation data in different situations, thereby obtaining the dynamic tactical control zone. The simulation results can meet the decision-making information solution requirements in scenarios with drastic situation changes in the air combat simulation environment. The embodiment of the present invention fully considers the decision-making requirements of fighter jets in beyond-visual-range air combat simulations, balancing their own safety and mission completion. Based on air combat process analysis, a theoretical model of the dynamic tactical control zone is established, and a DTCZ solution method based on the three-party game is designed. This method fully explores the tactical mechanism of the game confrontation between the parties in the air combat, overcomes the calculation error caused by the assumed target maneuvering state, and effectively improves the solution accuracy of the air combat decision-making quantitative model. Since the dynamic tactical control domain is the key node information for confrontation exercises in the beyond-visual-range air combat simulation environment, it is an important reference standard for the operator to execute the corresponding tactics in the air combat simulation confrontation environment. The dynamic tactical control domain solution method based on the three-party game in the air combat simulation environment proposed in the embodiment of the present invention has an excellent situational expression form, can meet the demand for decision-making information support in a highly dynamic and strong real-time simulation environment, effectively make up for the lack of air combat node information, and is of great significance for improving the beyond-visual-range air combat effectiveness of fighter jets in air combat confrontation games and air combat simulation systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 A schematic diagram illustrating the understanding of the dynamic tactical control domain in an embodiment of the invention;

[0054] Figure 2 A flow chart of a method for solving a dynamic tactical control domain based on a three-party game in an air combat simulation environment provided by an embodiment of the present invention;

[0055] Figure 3 A geometric battle relationship diagram of the three parties in the game according to an embodiment of the present invention;

[0056] Figure 4 A schematic diagram of a flow chart of searching for an outer boundary dynamic tactical control distance value using an advance and retreat method for a set of simulation data in an embodiment of the invention;

[0057] Figure 5 A schematic diagram of a process for searching for an inner boundary dynamic tactical control distance value using a binary search method for a set of simulation data in an embodiment of the invention;

[0058] Figure 6 A schematic diagram of the process of obtaining dynamic tactical control domains from different sets of simulation data in an embodiment of the invention;

[0059] Figure 7 A schematic diagram of the algorithm structure of a dynamic tactical control domain solution method based on a three-party game in an air combat simulation environment provided by an embodiment of the invention;

[0060] Figure 8 This is a trajectory diagram of a three-party game simulation confrontation in a simulation experiment of an embodiment of the invention;

[0061] Figure 9 This is a curve diagram of the relative distance change of the three-party game simulation confrontation in the simulation experiment of the embodiment of the invention;

[0062] Figure 10 This is a diagram showing the solution results of the dynamic tactical control domain in the simulation experiment of the embodiment of the invention. DETAILED DESCRIPTION

[0063] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0064] To facilitate understanding of the solution of the embodiment of the present invention, firstly, the relevant concepts of the dynamic tactical control domain proposed in the embodiment of the present invention are briefly described.

[0065] like Figure 1 As shown in Figure 1, the dynamic tactical control domain is a spatial region with inner and outer boundaries. If a user aircraft (hereinafter referred to as the user aircraft) launches a missile to attack a target within this region, it has a high probability of hitting the target. Even if the target launches a defensive missile at this time, the user aircraft can still break through the defensive missile's interception and hit the target. If the user aircraft launches a missile outside this region, it will not hit the target.

[0066] The boundary of the dynamic tactical control region is defined by the dynamic tactical control range (DTCR), which is defined as the relative distance between a point on the boundary of the dynamic tactical control region and the target. It should be noted that in the embodiment of the present invention, the maximum dynamic tactical control distance (the value of which is expressed as The outer boundary of the dynamic tactical control domain is represented by the minimum dynamic tactical control distance (the value of which is represented by The dynamic tactical control domain (DTC) corresponds to the inner boundary of the dynamic tactical control domain. The DTC is one of the most important maneuvering criteria in air combat simulations. Users can use its instructions to accurately judge the air combat situation and adjust offensive and defensive tactics in a timely manner.

[0067] To overcome the existing research deficiencies in quantitative reference information for air combat attack and defense in scenarios where aircraft launch defensive missiles, an embodiment of the present invention provides a dynamic tactical control zone (DTCZ) solution method based on a three-party game in an air combat simulation environment, which is applied to a beyond-visual-range air combat simulation environment under active defense tactics.

[0068] It should be noted that the execution entity of the method for solving a dynamic tactical control domain based on a three-party game in an air combat simulation environment provided by the embodiments of the present invention may be a device for solving a dynamic tactical control domain based on a three-party game in an air combat simulation environment, which may be run on an electronic device. The electronic device may be a server or a terminal device, but is not limited thereto.

[0069] like Figure 2 As shown, a method for solving a dynamic tactical control domain based on a three-party game in an air combat simulation environment provided by an embodiment of the present invention may include the following steps S1 to S4:

[0070] S1. Based on differential game theory, a three-party game system model is established to characterize the game confrontation relationship between the three aircraft. The three-party game system model is solved to obtain the control vectors of each aircraft to represent the solved optimal pursuit and escape guidance strategy.

[0071] Among them, the three aircraft are the target aircraft, the defense missile and the attack missile; the control vector is the acceleration vector of the aircraft.

[0072] In an optional embodiment, a three-party game system model is established based on differential game theory to characterize the three-party aircraft game confrontation relationship, which may include steps A1 to A3:

[0073] A1, establish the motion equations of the three aircraft in the inertial coordinate system;

[0074] In the embodiment of the present invention, the target aircraft implements active defense tactics, that is, it intercepts the incoming attack missiles by launching defense missiles to protect its own safety; the attack missile needs to take into account its own safety and mission completion in the process of attacking the target aircraft, that is, it needs to hit the target aircraft under the premise of avoiding interception by the defense missile. The target aircraft, defense missile and attack missile are the three warring aircraft, and the geometric engagement relationship between the three parties is as follows: Figure 3 shown.

[0075] In the embodiment of the present invention, T, D, and A represent a target aircraft, a defense missile, and an attack missile, respectively. and are the position components of the aircraft i (i = T, D, A, the same below) in the x, y, and z directions in the inertial system g, is the position vector of aircraft i in the inertial system; u i is the velocity vector of aircraft i in the inertial system; a i is the acceleration vector of aircraft i in the inertial system, used to represent the control strategy. ij (ij=AT, DA, the same below) is the relative position vector between aircraft i and j.

[0076] According to the geometric relationship of the engagement, the motion equations of the three aircraft in the inertial coordinate system are determined as follows:

[0077]

[0078] Among them, the relative position vector x ij =x i -x j ; Relative velocity vector u ij =u i -u j ; I is the identity matrix.

[0079] A2, rewrite the equation of motion into a state space equation to obtain the differential game model;

[0080] Specifically, according to formula (1), let y ij =(x ij ,u ij ) T is the state vector; acceleration vector a i 、a j is the control vector. Let the state coefficient matrix Input coefficient matrix Then formula (1) can be rewritten as the state space equation shown in formula (2), thus obtaining the differential game model.

[0081]

[0082] In the air combat game confrontation process of the embodiment of the present invention, the attacking missile A needs to minimize the distance between it and the target aircraft T, while maximizing the distance between it and the defending missile D. Therefore, the control strategy a of A A It can be divided into two parts: escape control strategy and pursuit control strategies In the process of A and D's confrontation, A's escape control strategy Need to maximize the distance between A and D; in the process of confrontation between A and T, A's pursuit control strategy The distance from T needs to be minimized.

[0083] Through A1 and A2, the process of establishing the dynamic model of aircraft engagement in beyond-visual-range air combat was completed.

[0084] A3 sets a performance indicator function for the differential game model, transforms the maximum-minimum optimization problem for solving the optimal pursuit-escape guidance strategy into a minimization problem, and makes assumptions about the solution of the differential game model to obtain a three-party game system model.

[0085] In the embodiment of the present invention, the solution of the differential game model is to find the optimal evasion-pursuit guidance law (OEGL), that is, to find the optimal (a i ,a j ), the formulaic representation is to obtain the optimal value of the performance index Among them, J ij represents the performance index of the pursuit and escape guidance strategy problem, J ij * Indicates J ij The optimal solution of .

[0086] For the above differential game model, the embodiment of the present invention designs a quadratic performance index function as follows:

[0087]

[0088] Among them, J AT represents the performance index function between A and T; J DA Represents the performance index function between D and A; represents the weighted norm of the vector; t0 is the starting time; t f1 is the confrontation terminal time between A and T, t f2 is the confrontation terminal time between D and A; S∈R 6×6 is the semi-positive definite terminal performance weight matrix (R l×l represents an l×l real number matrix); is the positive definite control performance weight matrix; They represent A’s escape control strategy, A’s pursuit control strategy, T’s escape control strategy, and D’s pursuit control strategy respectively. Formula (3) is obtained by making The sign in front is negative, which transforms the maximum and minimum optimization problem into a minimization problem, that is,

[0089] After setting the performance indicator function, it is necessary to solve the differential game model to obtain the optimal pursuit and escape control strategy. Before solving the differential game model, the embodiment of the present invention first makes the following assumptions:

[0090] (1) Since the attack and defense game mainly focuses on the control state of the terminal at the moment, the semi-positive terminal performance weight matrix S = diag(sss 0 0 0), s>0 is taken;

[0091] (2) To ensure the existence of the model solution, the positive definite control performance weight matrix is set to satisfy:

[0092] Parameters must meet:

[0093] (3) The air combat scene is transparent, that is, T, D, and A can obtain the parameter information of the other two parties.

[0094] Through the above processing, a three-party game system model can be obtained.

[0095] In an optional embodiment, solving the three-party game system model to obtain the control vectors of each party's aircraft to represent the solved optimal pursuit and escape guidance strategy may include steps B1 to B2:

[0096] B1, solve the three-party game system model using Hamiltonian function and matrix Riccati differential equations to obtain the optimal pursuit and escape guidance strategy in the form of state feedback gain;

[0097] This step will use the Hamiltonian function to solve the model based on the energy index function and the model's solution assumptions, with the aim of obtaining the optimal pursuit and escape control strategy for the three parties in the air combat.

[0098] First, construct the Hamiltonian function as follows:

[0099]

[0100] Among them, H AT and H DA Represent the Hamiltonian functions between A and T, and between D and A respectively; and denote the positive definite control performance weight matrix parameters respectively; represents the Lagrange multiplier vector in the optimal control problem between ATs; represents the Lagrange multiplier vector in the optimal control problem between DAs. The Lagrange multiplier vector is also called the adjoint variable or the co-state variable.

[0101] The necessary conditions that formula (4) must satisfy to achieve the optimal solution are:

[0102]

[0103] in, and The points on the AT and λ DA Find the derivative.

[0104] The 5th and 6th equations in formula (5) are the co-state equations of the Hamiltonian function, and the following assumptions are made for the co-state equations:

[0105]

[0106] Among them, P ij ∈R 6×6 is a Riccati matrix, which can be solved using the matrix Riccati differential equations:

[0107]

[0108] in, Right now: Substituting formulas (6) and (7) into formula (5), we can obtain the optimal pursuit guidance strategy in the form of state feedback gain:

[0109]

[0110] B2, impose control system constraints on the optimal pursuit and escape guidance strategy in the form of state feedback gain, and obtain the control vectors of each party's aircraft to represent the solved optimal pursuit and escape guidance strategy.

[0111] The guidance strategy derived from formula (8) is optimal, but when applied to actual aircraft control, it is also subject to the constraints of the control system. Therefore, the constraints of the control system are applied on it, and the optimal pursuit and escape guidance strategy is obtained as follows:

[0112]

[0113] in: is the upper limit of the guidance command of aircraft i.

[0114] Therefore, through the above solution, we can get a T 、a D and a A It represents the optimal pursuit and escape guidance strategy solved by all parties.

[0115] S2, constructing the motion model of the three aircrafts and setting the simulation constraints to obtain the simulation model;

[0116] In an optional embodiment, constructing a motion model of three aircraft includes:

[0117] The motion models of three-party aircraft are constructed by constructing the three-degree-of-freedom motion model of the aircraft and the three-degree-of-freedom motion model of the missile.

[0118] Specifically, first, for the target aircraft, its three-degree-of-freedom motion model is established as follows:

[0119]

[0120] Among them, (x, y, z) are the three coordinate components of the target aircraft's position in the inertial system; are the target aircraft's speed (scalar), track inclination and track deviation respectively; (a x ,a y ,a z ) are the guidance strategies a of the target aircraft respectively T The three coordinate components in the track system. It can be understood that a T Obtained through S1.

[0121] Secondly, both the defensive missile and the attacking missile are air-to-air missiles. The three-degree-of-freedom motion model of the air-to-air missile is established as follows:

[0122]

[0123] Among them, (x m ,y m ,z m ) are the three coordinate components of the position of missile m (m = D, A, the same below) in the inertial system; are respectively the missile speed (scalar), ballistic inclination and ballistic deviation; (a my ,a mz ) are the coordinate components of the missile guidance strategy in the y and z directions in the track system obtained by S1; T m 、D m is the thrust and resistance of the missile, t≤t push Time T m =T mmax , t>t push Time T m =0,t push is the thrust action time, T mmax is the maximum thrust of the missile; m m is the mass of the missile, g represents the acceleration due to gravity, and its value is 9.8m / s 2 Unlike aircraft, the change in missile speed is no longer determined by guidance strategy, but by thrust and drag.

[0124] Through the above processing, a motion model of the three aircraft can be constructed.

[0125] In an optional implementation manner, the simulation restriction conditions include:

[0126] ① If the missile-target distance is less than the missile's maximum damage radius and neither the time limit nor the speed limit is triggered, the missile is deemed to have successfully hit the target; otherwise, the missile attack is deemed to have failed.

[0127] ② The time limit condition is: when the missile flight time is greater than the missile controllable flight time, the missile energy is exhausted and cannot hit the target.

[0128] ③ Speed limit condition: when the missile speed is less than the minimum flight speed of the missile, the missile's maneuverability decreases and it cannot hit the target.

[0129] Among them, missiles include defense missiles and attack missiles; in the simulation constraints, the target is the object attacked by the missile; the target attacked by the defense missile is the attack missile, and the target attacked by the attack missile is the target aircraft. The missile-target distance is represented by r; the maximum damage radius of the missile is represented by R HIT The missile flight time is expressed as t; the missile controllable flight time is expressed as t max Indicates the missile speed in v m Indicates the minimum flight speed of the missile in v min express.

[0130] It's understandable that after building the motion model of the three aircraft and setting the simulation constraints, the simulation parameters must be set to complete the model. These parameters include the upper limit of missile guidance commands, missile thrust duration, minimum missile flight speed, maximum missile damage radius, missile mass, and maximum missile thrust. Specific values can be found in the experimental section and are not detailed here.

[0131] The simulation model of the embodiment of the present invention is used as a simulation environment to calculate the outer boundary and the inner boundary of the DTCZ.

[0132] S3, for each set of simulation data obtained, based on the implementation of the optimal pursuit and escape guidance strategy by all three parties in the air combat, the boundary of the dynamic tactical control domain is searched using the simulation data, simulation model, and improved advance and retreat method to obtain the outer boundary dynamic tactical control distance value and the inner boundary dynamic tactical control distance value corresponding to the simulation data;

[0133] Among them, any set of simulation data represents the motion state of the three parties' aircraft, including the altitude, speed, initial position, initial heading angle, target azimuth, target entry angle and maneuvering overload of the three parties in the air combat.

[0134] The embodiment of the present invention can obtain multiple sets of simulation data in advance. The multiple sets of simulation data belong to the same air combat simulation environment. Each set of simulation data corresponds to a situation. The situation is mainly based on the target entry angle q m It is reflected that the situation of multiple sets of simulation data is continuous.

[0135] In the embodiment of the present invention, the process of acquiring multiple sets of simulation data may be to determine a set of previous simulation data and sequentially change the target entry angle in the set of simulation data with a preset step size, thereby obtaining multiple sets of simulation data with only different target entry angles.

[0136] In a set of prior simulation data, the value of each parameter can be set to a specific value according to the situation, or determined by using a corresponding parameter search range. The parameter search range corresponding to each parameter is determined based on an empirical value obtained from actual measured data.

[0137] In the embodiment of the present invention, the initial positions of the three air combat parties can be specifically set according to the air combat simulation scene; the initial heading angles of the three air combat parties represent the speed directions of the three air combat parties, and can also be specifically set according to the air combat simulation scene.

[0138] The remaining parameters can be determined using corresponding parameter search ranges. For example, the altitude of the three air combat parties can have the same parameter search range, such as 2000-20000 meters, or 1500-15000 meters. The speed of the three air combat parties can have the same parameter search range, such as 150-450 m / s, or 100-500 m / s. The target azimuth angle can have a parameter search range of -45° to 45°, for example. The target approach angle can have a parameter search range of 0° to 360°, for example. The maneuvering overload of the three parties can have a parameter search range of 0-9g, for example, expressed in units of gravitational acceleration. Based on a set of prior simulation data, the above parameters can be randomly selected within the corresponding parameter search range.

[0139] The only difference between the target entry angles in each set of simulation data obtained sequentially is the change in a preset step size, which can be, for example, 1°, 5°, or 10°, and can be selected as needed.

[0140] S3 is to perform DTCZ boundary search. Specifically, taking a set of simulation data as an example, the specific process of obtaining the outer boundary dynamic tactical control distance value and the inner boundary dynamic tactical control distance value corresponding to the set of simulation data is explained.

[0141] In an optional implementation, S3 may include:

[0142] S31, for each set of obtained simulation data, based on the execution of the optimal pursuit-and-escape guidance strategy by all three parties in the air combat, using the set of simulation data, the simulation model, and the advance-and-retreat method, searching for the outer boundary of the dynamic tactical control domain, and obtaining the outer boundary dynamic tactical control distance value corresponding to the set of simulation data;

[0143] S32 , searching the inner boundary of the dynamic tactical control domain using the outer boundary dynamic tactical control distance value corresponding to the set of simulation data and a dichotomy method to obtain the inner boundary dynamic tactical control distance value corresponding to the set of simulation data.

[0144] Specifically, the embodiment of the present invention searches for the DTCZ boundary by improving the advance-retreat method on the basis of all three parties in the air combat executing the optimal pursuit-escape guidance strategy. The idea of improving the advance-retreat method to solve the DTCZ is: use the advance-retreat method to solve the outer boundary of the DTCZ, that is, Then, based on the obtained outer boundary value, the inner boundary of DTCZ is solved using the bisection method, that is,

[0145] S31 and S32 are described below respectively.

[0146] In an optional implementation manner, S31 may include the following steps:

[0147] S311, for each set of simulation data obtained, on the basis of all three parties in the air combat executing the optimal pursuit-and-escape guidance strategy, using the simulation model to conduct an air combat confrontation simulation under the corresponding situation based on the set of simulation data and the obtained initial distance between the attacking missile and the target aircraft, to obtain an initial miss distance simulation result between the attacking missile and the target aircraft; and setting an initial outer boundary search point based on the initial miss distance simulation result;

[0148] Among them, the initial distance between the attack missile and the target aircraft can be set to R0. On the basis of all three parties in the air combat implementing the optimal pursuit and escape guidance strategy, according to this set of simulation data and R0, the simulation model is input to perform air combat confrontation simulation under the corresponding situation. The simulation result of the initial miss distance between the attack missile and the target aircraft will be output, expressed as MD0, and the initial outer boundary search point R1 = R0-0.5MD0 is set with MD0.

[0149] S312, performing an air combat confrontation simulation using the outer boundary search points used in the current iteration, and outputting a simulation result of the miss distance of the current iteration;

[0150] Specifically, in the kth iteration, the outer boundary search point R used in the current iteration is used k Perform air combat simulation and output the current iteration's miss distance simulation result MD k The simulation model has already completed the simulation parameter settings, and the simulation process is subject to simulation constraints. After the simulation process is completed, a value will be output as the miss distance simulation result.

[0151] The outer boundary search point used in the first iteration is the initial outer boundary search point. In other words, the outer boundary search point used in the first iteration of the advance-retreat method is R1.

[0152] S313, based on the numerical comparison relationship between the miss amount simulation result of the current iteration and the lower limit value and the upper limit value in the preset outer boundary search point range, the outer boundary search point used in the next iteration is obtained, and when the miss amount simulation result of the current iteration does not fall within the outer boundary search point range, the air combat confrontation simulation is continued according to the outer boundary search point used in the next iteration until the miss amount simulation result falls within the outer boundary search point range, the iteration is stopped and the outer boundary search point used in the next iteration corresponding to the obtained outer boundary dynamic tactical control distance value corresponding to the group of simulation data.

[0153] The processing idea of S313 is: when the miss distance simulation result MD k Search point range not outside the boundary [R HIT ,R E ], the outer boundary reverse search is performed with a certain step size, that is, the miss amount simulation result MD of the current iteration k The outer boundary search point R used in the k+1th iteration k+1 The update condition is then simulated again under the new outer boundary search point; when the miss distance simulation result MD k In R HIT ,R E ], it is considered that the solution has been obtained under this situation. Finally, the miss distance simulation result MD at this time k The corresponding outer boundary search point R used in the next iteration k+1 As the outer boundary dynamic tactical control distance value.

[0154] It can be understood that the embodiment of the present invention searches for the outer boundary dynamic tactical control distance value corresponding to the set of simulation data by continuously adjusting the outer boundary search point used in the iteration during the simulation iteration.

[0155] Among them, the lower limit value R in the preset outer boundary search point range HIT The maximum damage radius of the missile, the upper limit R E The expected value of the outer boundary search error is set based on experience.

[0156] In an optional embodiment, the outer boundary search point used in the next iteration is obtained based on the numerical comparison relationship between the miss distance simulation result of the current iteration and the lower limit value and the upper limit value in the preset outer boundary search point range, including:

[0157] Determine whether the miss distance simulation result of the current iteration is less than the lower limit value in the outer boundary search point range; if so, use the first formula to determine the outer boundary search point used in the next iteration.

[0158] If not, determine whether the miss distance simulation result of the current iteration is greater than or equal to the upper limit value in the outer boundary search point range. If so, use the second formula to determine the outer boundary search point used in the next iteration; if not, use the third formula to determine the outer boundary search point used in the next iteration.

[0159] Among them, the first formula is R k+1 =R k +d-0.5MD k :The second formula is R k+1 =R k -d-0.5MD k :The third formula is R k+1 =R k -0.5MD k ; R k Indicates the outer boundary search point used in the kth iteration; MD k is the k-th miss distance simulation result; d is the preset reverse boundary search step; k is a natural number greater than 0.

[0160] It is understandable that if the iteration can be stopped, the R k According to the third formula, R k+1 , that is, to get the corresponding situation It is used as the outer boundary dynamic tactical control distance value corresponding to this group of simulation data.

[0161] Please combine the outer boundary dynamic tactical control distance value search process with the advance and retreat method Figure 4 Understand that, compared to the above text part, Figure 4 The description of the steps has been simplified accordingly and will not be described in detail here.

[0162] In an optional implementation manner, S32 may include the following steps:

[0163] S321, calculating the binary segmentation point according to the inner boundary search point range used in the current iteration;

[0164] Specifically, in the embodiment of the present invention, each iteration is implemented using a corresponding inner boundary search point range. When the inner boundary search point range changes, the iteration number also changes accordingly.

[0165] For ease of understanding, the iterative process of the inner boundary search is represented by q, where q is a natural number greater than 0. For the current iteration as the qth iteration, the inner boundary search point range used in the current iteration can be expressed as [R n,q ,R f,q ].

[0166] The lower limit of the inner boundary search point range used in the first iteration is 0, and the upper limit is the inner boundary dynamic tactical control distance value corresponding to the set of simulation data. That is, for q = 1, [R n,1 ,R f,1 ] n,1 =0km; R f,1 The inner boundary dynamic tactical control distance value corresponding to the set of simulation data solved by S31.

[0167] The inner boundary search point range used in the qth iteration [R n,q ,R f,q The calculated dichotomy split point can be used with R g,q The calculation formula is as follows:

[0168]

[0169] S322, performing a three-party game confrontation simulation using a simulation model based on the dichotomy split point corresponding to the current iteration and the set of simulation data to obtain a simulated value of the miss distance;

[0170] Specifically, R g,q This data is then fed into a simulation model to simulate a three-way game between an attacking missile, a defending missile, and a target aircraft. The simulation model has already been configured with simulation parameters and is subject to simulation constraints. After the simulation is complete, a simulated miss distance value is output.

[0171] S323, determining whether the miss distance simulation value indicates that the target aircraft was not hit by the attack missile, and narrowing the inner boundary search point range used in the current iteration accordingly based on different determination results;

[0172] The method for determining whether the miss distance simulation value indicates that the target aircraft is not hit by the attack missile may be:

[0173] The miss distance simulation value is a first preset value, indicating that the target aircraft is not hit by the attack missile; the miss distance simulation value is a second preset value, indicating that the target aircraft is hit by the attack missile.

[0174] For example, the first preset value and the second preset value may be 0 and 1 respectively, and of course other numbers may be used to distinguish whether the target aircraft is not hit by the attack missile.

[0175] In the embodiment of the present invention, whether the target aircraft is hit by the attack missile or not, the inner boundary search point range used in the current iteration will be narrowed down eventually, but the narrowing methods of the two are different. It can be understood that the embodiment of the present invention searches for the inner boundary dynamic tactical control distance value corresponding to the set of simulation data by continuously narrowing the inner boundary search point range in the simulation iteration.

[0176] Specifically, based on different judgment results, the inner boundary search point range used in the current iteration is narrowed down accordingly, including the following steps:

[0177] ① If the miss distance simulation value indicates that the target aircraft is hit by the attack missile, the upper limit value of the inner boundary search point range used in the current iteration is replaced with the dichotomy split point corresponding to the current iteration;

[0178] For the qth iteration, if the output miss distance simulation value after the simulation process is completed indicates that the target aircraft is hit by the attack missile, the inner boundary search point range used in the current iteration can be directly reduced in a corresponding manner. The reduced inner boundary search point range obtained in this way is [R n,q ,R g,q ].

[0179] ②, if the miss distance simulation value indicates that the target aircraft is not hit by the attack missile, determining whether at least one of a time limit condition and a speed limit condition is satisfied;

[0180] For the qth iteration, if after the simulation process is completed, the output miss distance simulation value indicates that the target aircraft was not hit by the attack missile, it is necessary to further determine the reason why the target aircraft was not hit by the attack missile to determine whether the inner boundary search point range used in the current iteration can be directly narrowed down accordingly.

[0181] At this time, it is necessary to determine whether at least one of the time constraint and the speed constraint is met. The time constraint and the speed constraint are the contents of the simulation constraint. Please understand them in conjunction with the previous text and will not be explained in detail here.

[0182] ③If it is not satisfied, return to the dichotomy split point corresponding to the current iteration and the set of simulation data, and use the simulation model to perform the three-party game confrontation simulation step and re-simulate with the original input data;

[0183] If neither the time limit nor the speed limit is met, the reason the target aircraft was not hit by the attacking missile was not due to the attacking missile's energy exhaustion or reduced dynamic performance. This could be due to some data delay or other factors. Therefore, it is necessary to re-simulate using the original simulation input data and output the miss distance simulation value again. Determine whether the outputted miss distance simulation value indicates that the target aircraft was not hit by the attacking missile. If the target aircraft is again determined to have been hit by the attacking missile, execute step 1. If the target aircraft is again determined to have not been hit, execute step 2.

[0184] ④ If satisfied, replace the lower limit value in the inner boundary search point range used in the current iteration with the binary split point corresponding to the current iteration.

[0185] If the time limit condition or the speed limit condition is met, that is, the reason why the target aircraft was not hit by the attack missile is due to the attack missile's energy exhaustion or the decline in dynamic performance, then there is no need to simulate again. The inner boundary search point range used in the current iteration can be directly reduced in a corresponding manner. The reduced inner boundary search point range obtained in this way is [R g,q ,R f,q ].

[0186] Through the above steps, after the simulation model outputs a miss distance simulation value for the binary split point corresponding to the current iteration of the input and the set of simulation data, no matter what the miss distance simulation value is for judging whether the target aircraft is not hit by the attack missile, or whether it is re-simulated, a narrowed inner boundary search point range will be obtained in the end, which is [R n,q ,R g,q ] or [R g,q ,R f,q ].

[0187] At the same time, it should be emphasized that in the above process, even if re-simulation occurs, it still belongs to the same iteration because the same inner boundary search point range is used as the simulation input data.

[0188] S324, determining whether the reduced inner boundary search point range meets a preset error requirement;

[0189] Regardless of whether the inner boundary search point range after reduction is [R n,q ,R g,q ] or [R g,q ,R f,q ], it is necessary to further judge whether it meets the preset error requirements.

[0190] In an optional implementation manner, determining whether the narrowed inner boundary search point range meets a preset error requirement includes:

[0191] It is determined whether the reduced inner boundary search point range satisfies the condition that the absolute value of the difference between the upper and lower limits is less than a preset inner boundary precision constant.

[0192] That is to say, for [R n,q ,R g,q ], to determine whether there is |R n,q -R g,q |<ε;For [R g,q ,R f,q ], to determine whether there is |R g,q -R f,q |<ε. ε represents a preset inner boundary accuracy constant, which is determined based on experience, such as 500 meters, 1000 meters, etc.

[0193] If not, executing S325, using the narrowed inner boundary search point range as the inner boundary search point range used in the next iteration, and returning to the step of calculating the binary segmentation point based on the inner boundary search point range used in the current iteration;

[0194] If the reduced inner boundary search point range does not meet the preset error requirement, the iteration cannot be stopped, and the reduced inner boundary search point range is used as the inner boundary search point range for the next iteration, and the process returns to S321 to continue the iteration.

[0195] That is to say, if the narrowed inner boundary search point range is [R n,q ,R g,q ], determine [R n,q+1 ,R f,q+1 ]=[R n,q ,R g,q ] and return to S321.

[0196] If the narrowed inner boundary search point range is [R g,q ,R f,q ], determine [R n,q+1 ,R f,q+1 ]=[R g,q ,R f,q ] and return to S321.

[0197] If yes, execute S326 to calculate the binary division point of the narrowed inner boundary search point range as the inner boundary dynamic tactical control distance value corresponding to the group of simulation data.

[0198] Specifically, if the narrowed inner boundary search point range meets the preset error requirement, the iteration is stopped, and the binary division point of the narrowed inner boundary search point range is calculated according to formula (12), and the calculated binary division point is determined as the inner boundary dynamic tactical control distance value corresponding to the group of simulation data, that is, the inner boundary dynamic tactical control distance value under the corresponding situation.

[0199] For a set of simulation data, the inner boundary dynamic tactical control distance value search process based on dichotomy is combined with Figure 5 Compared with the above text, Figure 5 The description of the steps has been simplified accordingly and will not be described in detail here.

[0200] It should be noted that, for the current iteration, if the simulation value of the miss distance output by the simulation model indicates that the target aircraft was not hit by the attack missile, and it is determined that both the time limit condition and the speed limit condition are not met, t=t+dt means adding a simulation cycle, and using the original input data to perform a re-simulation of the current iteration means that the binary split point corresponding to the current iteration and the set of simulation data are input into the simulation model again for simulation, but the iteration number remains unchanged during the re-simulation.

[0201] It can be understood that, through the DTCZ boundary search in step S3, each set of simulation data can obtain the corresponding outer boundary dynamic tactical control distance value and inner boundary dynamic tactical control distance value.

[0202] S4, sequentially connecting the same dynamic tactical control distance values obtained from each set of simulation data under the same air combat simulation environment and with continuous situations to obtain the inner and outer boundaries of the dynamic tactical control domain, and the area enclosed by the inner and outer boundaries constitutes the dynamic tactical control domain;

[0203] As before, each set of simulation data under the same air combat simulation environment and with continuous situations differs only in the target entry angle, and is used to represent different situations.

[0204] It is understood that S3 uses a set of simulation data to obtain the corresponding outer boundary dynamic tactical control distance values and inner boundary dynamic tactical control distance values, and therefore only outputs a set of dynamic tactical control distances under a fixed situation. Embodiments of the present invention can utilize multiple sets of simulation data with different situations to obtain outer boundary dynamic tactical control distance values and inner boundary dynamic tactical control distance values under different situations.

[0205] The outer boundary dynamic tactical control distance values obtained from each group of simulation data in the embodiment of the present invention are connected in sequence to obtain the outer boundary of the dynamic tactical control domain. The inner boundary dynamic tactical control distance values obtained from each group of simulation data in the embodiment of the present invention are connected in sequence to obtain the inner boundary of the dynamic tactical control domain. The area enclosed by the inner and outer boundaries is determined as the dynamic tactical control domain.

[0206] In the embodiment of the present invention, the target entry angle q m The range is usually selected as [0°, 360°]. The target entry angle in each set of simulation data changes with a preset step size. As mentioned above, each discrete target entry angle corresponds to a situation. By sequentially connecting the same dynamic tactical control distance values from 0° to 360° under the situation solved by the model, the boundary corresponding to the dynamic tactical control domain can be obtained, including the inner boundary or the outer boundary. Finally, the area enclosed by the inner boundary and the outer boundary is determined as the dynamic tactical control domain. Since the target entry angle q m The range is [0°, 360°], so the calculated dynamic tactical control domain is a closed annular area.

[0207] For the process of obtaining dynamic tactical control domains from different sets of simulation data, see Figure 6 Understood, no further details will be given here.

[0208] In summary, the embodiment of the present invention is based on differential game theory, designs a game confrontation mechanism for all parties in air combat, and abstracts the air combat problem into two sets of differential game models, namely a three-party game system model and a simulation model for boundary search. On the basis of air combat game confrontation, the embodiment of the present invention establishes a theoretical model of the dynamic tactical control domain and designs a corresponding solution method. The method proposed in the embodiment of the present invention is mainly divided into two parts: ① three-party game system modeling and solution; ② DTCZ solution based on the improved advance and retreat method, that is, DTCZ boundary search using a simulation model. The specific algorithm structure is as follows. Figure 7 shown.

[0209] The three-party game system model of the embodiment of the present invention proposes an optimal pursuit and escape guidance strategy for the three parties in an air combat based on differential game theory from the perspective of air combat behavior. The DTCZ solution model uses an improved advance and retreat method to quickly search the DTCZ boundary based on the implementation of the optimal pursuit and escape guidance strategy by all parties in the air combat, and can obtain the DTCZ under different situations.

[0210] Figure 7 The larger dotted box on the left side represents the three-party game system model, which is divided into two parts: model establishment and model solution, which specifically corresponds to the S1 step in the previous article. The optimal pursuit and escape guidance strategy solved is the guidance instruction. Figure 7The dotted box on the right side represents the simulation model used for boundary search, that is, the DTCZ solution model, which uses the guidance instructions output by the three-party game system model and multiple sets of simulation data obtained under different situations, and uses the improved advance and retreat method to search the boundary of the DTCZ, and obtain the outer boundary dynamic tactical control distance value and the inner boundary dynamic tactical control distance value corresponding to each set of simulation data, and then obtain the dynamic tactical control domain DTCZ. Among them, the construction process of the simulation model corresponds to the previous step S2, the search process of the outer boundary dynamic tactical control distance value and the inner boundary dynamic tactical control distance value corresponding to a set of simulation data corresponds to the previous step S3, and the process of obtaining the dynamic tactical control domain corresponds to the previous step S4. For specific content, please refer to Figure 7 As well as the understanding of the previous content, I will not repeat it here.

[0211] To address the issue of decision-making information support in beyond-visual-range air combat simulations, an embodiment of the present invention proposes a quantitative characterization scheme for the dynamic tactical control zone (DTCZ) with adaptive, timely, and high-precision features. First, a three-party game system model is established based on differential game theory to characterize the three-party aircraft game confrontation relationship. Based on this, the optimal pursuit and escape guidance strategy for the three parties in the air combat is calculated. Then, a simulation model for boundary search is constructed. Based on the optimal pursuit and escape guidance strategy executed by each party in the air combat, a real-time DTCZ solution method based on an improved advance-and-retreat method is designed. This method can obtain the corresponding outer and inner boundary dynamic tactical control distance values for each set of simulation data in different situations, thereby obtaining the dynamic tactical control zone. The simulation results can meet the decision-making information solution requirements in scenarios with drastic situation changes in the air combat simulation environment. The embodiment of the present invention fully considers the decision-making requirements of fighter jets in beyond-visual-range air combat simulations, balancing their own safety and mission completion. Based on air combat process analysis, a theoretical model of the dynamic tactical control zone is established, and a DTCZ solution method based on the three-party game is designed. This method fully explores the tactical mechanism of the game confrontation between the parties in the air combat, overcomes the calculation error caused by the assumed target maneuvering state, and effectively improves the solution accuracy of the air combat decision-making quantitative model. Since the dynamic tactical control domain is the key node information for confrontation exercises in the beyond-visual-range air combat simulation environment, it is an important reference standard for the operator to execute the corresponding tactics in the air combat simulation confrontation environment. The dynamic tactical control domain solution method based on the three-party game in the air combat simulation environment proposed in the embodiment of the present invention has an excellent situational expression form, can meet the demand for decision-making information support in a highly dynamic and strong real-time simulation environment, effectively make up for the lack of air combat node information, and is of great significance for improving the beyond-visual-range air combat effectiveness of fighter jets in air combat confrontation games and air combat simulation systems.

[0212] In order to verify the effectiveness of the dynamic tactical control domain solution method based on three-party game in the air combat simulation environment proposed in the embodiment of the present invention, the following is an explanation combined with experimental data.

[0213] In order to fully verify the model constructed by the embodiment of the present invention, the simulation part mainly includes two parts: the verification of the optimal pursuit and escape guidance strategy and the verification of the dynamic tactical control domain. The embodiment of the present invention selects the semi-positive definite terminal performance weight matrix S = diag (1 1 1 0 0 0), and the positive definite control performance weight matrix parameters The controllable flight times for the attack and defense missiles are 100 seconds and 50 seconds, respectively. In an air combat environment, the altitude difference between the enemy and friendly aircraft is relatively small, so the friendly aircraft launching the attack missile is assumed to be in the same plane as the target aircraft. Other simulation parameter settings for the missiles (attack and defense) are shown in Table 1.

[0214] Table 1 Missile simulation parameter setting table

[0215]

[0216] (1) Simulation analysis of the optimal pursuit and escape guidance strategy

[0217] Assume that at the beginning of the simulation, the altitude of the three air combat parties is 7000m, the speed is 300m / s, the initial position of the attacking missile is [80,0]km, the initial position of the target aircraft and the defense missile is [0,0]km, the initial heading angle of the attacking missile is 180°, and the initial heading angle of the target aircraft and the defense missile is 0°. Under these simulation conditions, the simulation results of the target-defense missile-attack missile three-party pursuit and escape confrontation based on differential game are as follows: Figure 8 and Figure 9 shown.

[0218] Figure 8 In the figure, the dashed line, dot-dash line, and solid line represent the maneuvering trajectories of the target aircraft, the defense missile, and the attack missile, respectively; Figure 9 In the figure, the solid line and the dotted line are the relative distance change curves between the defense missile and the attack missile, and between the attack missile and the target aircraft, respectively. Figure 8 The horizontal axis represents the X direction, and the vertical axis represents the Z direction. Figure 9 The horizontal axis represents time, and the vertical axis represents relative distance. Figure 8 、 Figure 9 It can be seen that under this situation, the attacking missile broke through the interception of the defensive missile and hit the target aircraft. Although the attacking missile successfully evaded the defensive missile (MD = 6603m), it was forced to change its trajectory to a certain extent, delaying the pursuit process and reducing the energy required for the final interception of the target aircraft. This also indirectly demonstrates the effectiveness of the tactic of launching defensive missiles in enhancing the survivability of the carrier aircraft.

[0219] (2) DTCZ simulation verification

[0220] The DTCZ must be calculated based on the control strategies of all parties involved in an air combat. Based on differential game theory, the maneuvering strategy adopted by the target aircraft or defending missile is the most disadvantageous for the attacking missile to track the target aircraft, but the most advantageous for the target aircraft to evade it. If the target aircraft or defending missile fails to implement this strategy, the attacking missile's tracking effect will only develop in a direction that is more favorable to the attacking missile. Therefore, calculating the DTCZ based on the optimal pursuit-and-escape guidance strategy has broader significance.

[0221] The target azimuth angle is set to 0°, the target entry angle range is [0,360]°, the target entry angle simulation step is 10°, and other simulation conditions are the same as (1). The DTCZ solution results based on the improved advance and retreat method under this simulation condition are as follows: Figure 10 shown.

[0222] Figure 10 In the figure, the dotted line and the solid line are the inner and outer boundaries of the DTCZ, respectively. The closed annular area enclosed by the inner and outer boundaries is the DTCZ. From the simulation results, we can see that:

[0223] (1) The DTCZ is wider in the head-on and tail-off regions and narrower on both sides. As the entry angle gradually increases, the inner and outer boundaries shrink toward the center. The outer boundary of the DTCZ in the head-on situation is larger, which is conducive to preemptive launch and quick disengagement, ensuring the safety of the carrier aircraft; the DTCZ in the tail-off situation is wider, which is conducive to the carrier aircraft attacking and occupying the position, creating launch conditions for attacking the target aircraft.

[0224] (2) The outer boundary of the DTCZ reaches its maximum at 96.39 km in the head-on situation and is shortest at 49.50 km in the tail-off situation. The outer boundary of the DTCZ is mainly related to the energy consumed during the confrontation. As the entry angle increases, the energy consumed during the tail-off maneuver decreases. The higher energy reserve after the turn allows the target aircraft to escape the threat of the attacking missile more quickly, thereby compressing the range of the DTCZ.

[0225] (3) The inner boundary of the DTCZ reaches its maximum length in the head-on situation, at 71.06 km, and is the shortest in the tailing situation, at 9.95 km. The inner boundary of the DTCZ is mainly related to defensive missiles. For attacking missiles coming from the front, defensive missiles have the best interception effect.

[0226] Overall, the boundary search strategy based on the improved advance and retreat method can achieve accurate and rapid solution of the boundary value of the dynamic tactical control domain according to the characteristics of the dynamic tactical control domain.

[0227] In summary, the dynamic tactical control domain solution method based on three-party game in the air combat simulation environment provided by the embodiment of the present invention fully considers the characteristics of high dynamics, strong real-time and uncertainty of the air combat simulation system, effectively makes up for the loopholes in the air combat confrontation situation information perception in the active defense scenario, thereby improving the combat effectiveness of fighter jets in the air combat confrontation simulation system, and has strong engineering practicality and effectiveness.

[0228] The above description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention are included in the scope of protection of the present invention.

Claims

1. A method for solving dynamic tactical control domain based on three-party game in an air combat simulation environment, characterized by: Applied to a beyond-visual-range air combat simulation environment under active defense tactics, the method includes: Based on differential game theory, a three-party game system model is established to characterize the game confrontation relationship between three aircraft. The three-party game system model is solved to obtain the control vectors of each aircraft to represent the solved optimal pursuit and escape guidance strategy. The three aircraft are the target aircraft, the defense missile, and the attack missile; the control vectors are the acceleration vectors of the aircraft. Construct the motion model of the three aircraft and set simulation constraints to obtain the simulation model; For each set of simulation data obtained, based on the implementation of the optimal pursuit-escape guidance strategy by all three parties in the air combat, the boundary of the dynamic tactical control domain is searched using the set of simulation data, the simulation model, and the improved advance-retreat method, to obtain the outer boundary dynamic tactical control distance value and the inner boundary dynamic tactical control distance value corresponding to the set of simulation data; The same dynamic tactical control distance values obtained from each set of simulation data with continuous situations in the same air combat simulation environment are connected in sequence to obtain the inner and outer boundaries of the dynamic tactical control domain, and the area enclosed by the inner and outer boundaries constitutes the dynamic tactical control domain; wherein, any set of simulation data represents the motion state of the three-party aircraft; the each set of simulation data with continuous situations in the same air combat simulation environment only has different target entry angles, which are used to represent different situations.

2. The method for solving the dynamic tactical control domain based on three-party game in an air combat simulation environment according to claim 1 is characterized in that: The three-party game system model based on differential game theory to characterize the three-party aircraft game confrontation relationship includes: Establishing the motion equations of the three aircraft in an inertial coordinate system; Rewriting the equation of motion into a state-space equation yields a differential game model; A performance index function for the differential game model is set, and the maximum and minimum optimization problem for solving the optimal pursuit and escape guidance strategy is transformed into a minimization problem. The solution assumption of the differential game model is made to obtain a three-party game system model.

3. The method for solving the dynamic tactical control domain based on three-party game in an air combat simulation environment according to claim 2 is characterized in that: Solving the three-party game system model to obtain the control vectors of each party's aircraft to represent the solved optimal pursuit and escape guidance strategy includes: The three-party game system model is solved using the Hamiltonian function and the matrix Riccati differential equations to obtain an optimal pursuit and escape guidance strategy in the form of state feedback gain; The constraints of the control system are imposed on the optimal pursuit and escape guidance strategy in the form of state feedback gain, and the control vectors of the aircraft of each party are obtained to represent the solved optimal pursuit and escape guidance strategy.

4. The method for solving the dynamic tactical control domain based on three-party game in an air combat simulation environment according to claim 1 or 3, characterized in that: The construction of the motion model of the three-party aircraft includes: The motion models of three-party aircraft are constructed by constructing the three-degree-of-freedom motion model of the aircraft and the three-degree-of-freedom motion model of the missile.

5. The method for solving the dynamic tactical control domain based on three-party game in an air combat simulation environment according to claim 4 is characterized in that: The simulation constraints include: If the missile-target distance is less than the missile's maximum damage radius and neither the time limit nor the speed limit is triggered, the missile is deemed to have successfully hit the target; otherwise, the missile attack is deemed to have failed. The time limit condition is: when the missile flight time is greater than the missile controllable flight time, the missile energy is exhausted and cannot hit the target; The speed limit condition is: when the missile speed is less than the minimum flight speed of the missile, the missile's maneuverability is reduced and it cannot hit the target; The missiles include the defense missiles and the attack missiles; the targets are objects attacked by the missiles; the objects attacked by the defense missiles are the attack missiles, and the objects attacked by the attack missiles are the target aircraft.

6. The method for solving the dynamic tactical control domain based on three-party game in an air combat simulation environment according to claim 5 is characterized in that: For each set of simulation data obtained, on the basis that all three parties in the air combat execute the optimal pursuit and escape guidance strategy, the boundary of the dynamic tactical control domain is searched using the set of simulation data, the simulation model, and the improved advance and retreat method, and the outer boundary dynamic tactical control distance value and the inner boundary dynamic tactical control distance value corresponding to the set of simulation data are obtained, including: For each set of simulation data obtained, based on the implementation of the optimal pursuit-and-escape guidance strategy by all three parties in the air combat, the outer boundary of the dynamic tactical control domain is searched using the set of simulation data, the simulation model, and the advance-and-retreat method to obtain the outer boundary dynamic tactical control distance value corresponding to the set of simulation data; The inner boundary of the dynamic tactical control domain is searched using the outer boundary dynamic tactical control distance value corresponding to the group of simulation data and the dichotomy method to obtain the inner boundary dynamic tactical control distance value corresponding to the group of simulation data.

7. The method for solving the dynamic tactical control domain based on three-party game in an air combat simulation environment according to claim 6 is characterized in that: For each set of simulation data obtained, on the basis that all three parties in the air combat execute the optimal pursuit and escape guidance strategy, the outer boundary of the dynamic tactical control domain is searched using the set of simulation data, the simulation model, and the advance and retreat method to obtain the outer boundary dynamic tactical control distance value corresponding to the set of simulation data, including: For each set of simulation data obtained, on the basis of all three parties in the air combat executing the optimal pursuit-and-escape guidance strategy, an air combat confrontation simulation under a corresponding situation is performed using the simulation model based on the set of simulation data and the obtained initial distance between the attacking missile and the target aircraft, to obtain an initial miss distance simulation result between the attacking missile and the target aircraft; and an initial outer boundary search point is set according to the initial miss distance simulation result; Perform an air combat confrontation simulation using the outer boundary search point used in the current iteration, and output a miss distance simulation result of the current iteration; wherein the outer boundary search point used in the first iteration is the initial outer boundary search point; Based on the numerical comparison relationship between the miss amount simulation result of the current iteration and the lower limit value and the upper limit value in the preset outer boundary search point range, the outer boundary search point used in the next iteration is obtained. When the miss amount simulation result of the current iteration does not fall within the outer boundary search point range, the air combat confrontation simulation is continued according to the outer boundary search point used in the next iteration until the miss amount simulation result falls within the outer boundary search point range. The iteration is stopped and the outer boundary search point used in the next iteration is used as the outer boundary dynamic tactical control distance value corresponding to the group of simulation data.

8. The method for solving the dynamic tactical control domain based on three-party game in an air combat simulation environment according to claim 7 is characterized in that: The outer boundary search point used in the next iteration is obtained based on the numerical comparison relationship between the miss distance simulation result of the current iteration and the lower limit value and the upper limit value in the preset outer boundary search point range, including: Determine whether the miss distance simulation result of the current iteration is less than the lower limit value in the outer boundary search point range; if so, determine the outer boundary search point used in the next iteration using the first formula; If not, determine whether the miss distance simulation result of the current iteration is greater than or equal to the upper limit value in the outer boundary search point range, and if so, use the second formula to determine the outer boundary search point used in the next iteration; if not, use the third formula to determine the outer boundary search point used in the next iteration; Among them, the first formula is R k+1 =R k +d-0.5MD k : The second formula is R k+1 =R k -d-0.5MD k : The third formula is R k+1 =R k -0.5MD k ; R k Indicates the outer boundary search point used in the kth iteration; MD k is the k-th miss distance simulation result; d is the preset reverse boundary search step; k is a natural number greater than 0.

9. The method for solving the dynamic tactical control domain based on three-party game in an air combat simulation environment according to claim 6, characterized in that: The method of searching the inner boundary of the dynamic tactical control domain using the outer boundary dynamic tactical control distance value corresponding to the set of simulation data and the dichotomy method to obtain the inner boundary dynamic tactical control distance value corresponding to the set of simulation data includes: Calculate the binary split point based on the inner boundary search point range used in the current iteration; the lower limit of the inner boundary search point range used in the first iteration is 0, and the upper limit is the outer boundary dynamic tactical control distance value corresponding to the set of simulation data; According to the dichotomy split point corresponding to the current iteration and the set of simulation data, a three-party game confrontation simulation is performed using the simulation model to obtain a simulation value of the miss amount; determining whether the miss distance simulation value indicates that the target aircraft is not hit by the attack missile, and narrowing the inner boundary search point range used in the current iteration accordingly based on different determination results; Determine whether the narrowed inner boundary search point range meets the preset error requirements; If not, using the narrowed inner boundary search point range as the inner boundary search point range used in the next iteration, and returning to the step of calculating the binary segmentation point based on the inner boundary search point range used in the current iteration; If so, the binary division point of the narrowed inner boundary search point range is calculated as the inner boundary dynamic tactical control distance value corresponding to the set of simulation data.

10. The method for solving the dynamic tactical control domain based on three-party game in an air combat simulation environment according to claim 9, characterized in that: The step of narrowing the inner boundary search point range used in the current iteration based on different judgment results includes: If the miss distance simulation value indicates that the target aircraft is hit by the attack missile, the upper limit value in the outer boundary search point range used in the current iteration is replaced by the dichotomy segmentation point corresponding to the current iteration; If the miss distance simulation value indicates that the target aircraft is not hit by the attack missile, determining whether at least one of the time limit condition and the speed limit condition is satisfied; If not satisfied, returning to the step of performing a three-party game confrontation simulation using the simulation model based on the dichotomy split point corresponding to the current iteration and the set of simulation data and re-simulating with the original input data; If satisfied, the lower limit value in the outer boundary search point range used in the current iteration is replaced with the binary segmentation point corresponding to the current iteration.

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