A method for breaking through the defense of a distance-controllable missile
By constructing a getaway distance proxy model based on optimal control theory and BP neural network, the problem of uncontrollable missile getaway distance in three-dimensional space was solved, and the attack missile was able to effectively hit the target and save energy in three-dimensional space.
Patent Information
- Application Number
- CN202310445998.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2023-04-23
- Publication Date
- 2025-11-18
- Estimated Expiration
- 2043-04-23
AI Technical Summary
Existing technology cannot effectively control the escape distance of missiles in three-dimensional space, which may cause the missile to fly too far or consume too much energy, thus failing to hit the target effectively.
By employing a method based on optimal control theory and BP neural network, a getaway distance proxy model is constructed. The guidance law is designed using the trained BP neural network model and optimal control theory to control the getaway distance of the attack missile in three-dimensional space. The guidance law is designed in combination with optimal control theory, and the key parameters of the guidance law are trained using BP neural network to achieve controllable getaway distance of the attack missile.
While conserving energy as much as possible, the distance at which the attack missile escapes in three-dimensional space is controlled, ensuring that the attack missile can successfully hit the target.
Smart Images
Figure CN116360500B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of guidance technology, specifically relating to a method for missile penetration with controllable distance. Background Technology
[0002] Anti-ship missiles typically employ various penetration methods, including electronic jamming, stealth technology, decoy techniques, and maneuver penetration. Among these, maneuver penetration is a crucial method. Traditional maneuver penetration methods primarily involve programmed maneuvers, such as square wave maneuvers, serpentine maneuvers, and spiral maneuvers. However, programmed maneuvers operate according to pre-set strategies and cannot adjust in real-time to the current battlefield environment, lacking sufficient intelligence. Actively detecting enemy defensive missiles and designing penetration guidance laws based on optimal control theory or differential game theory for active maneuvering has become an inevitable trend in penetration technology development, and some research achievements have been made in this direction. Prior technology [1] (see IMADO F, KURODAT. Engagement tactics for two missiles against an optimally maneuvering aircraft. Journal of Guidance, Control and Dynamics, 2011, 34(2): 574-582.) assumes that the defensive missile uses proportional guidance law to intercept the attacking missile through identification and other means, with the aim of maximizing the zero-control miss distance of the defensive missile. Based on the optimal control theory, the optimal evasion strategy of the attacking missile in the two-dimensional plane is studied, and three optimal maneuvering modes are solved by the steepest descent method. Prior technology [2] (see LIANG HZ, WANG JY, WANG YH, et al. Optimal guidance against active defense ballistic missiles via differential game strategies. Chinese Journal of Aeronautics, 2020, 33(03): 978-989.) also addresses the problem of intercepting defensive missiles using proportional guidance laws in response to attack missile penetration counterattacks. Based on the optimal penetration guidance law obtained by maximizing the miss distance, samples are generated, and neural networks and fuzzy control methods are introduced to train the real-time suboptimal guidance law, resulting in a penetration guidance law with real-time performance and strong robustness. Prior technology [3] (see VITALY S, SHIMA Tal. Cooperative differential games guidance laws for imposing a relative interceptangle. Journal of Guidance, Control, and Dynamics, 2017, 40(10): 2465-2480.) simultaneously considers the maximum zero-control miss distance, fuel cost, and control saturation problem of attack and defense missiles. Based on switching control and linear quadratic differential countermeasure strategy, a penetration guidance law that can simultaneously achieve penetration and attack is designed.The prior technology [4] (see LIU F, DONG XW, LI QD, et al. Cooperative differential games guidance laws for multiple attackers against an active defense target. Chinese Journal of Aeronautics, 2022, 35(5): 374-389.) uses differential game theory to study the active penetration problem of many against one. It designs a single game performance index considering the multiple missile misses, relative interception angle error and energy cost, so that two attack missiles chase the target from different directions while dodging the defense missile.
[0003] The idea behind penetration methods based on optimal control or differential game theory is to maximize the miss distance of the defensive missile to achieve penetration for the attacking missile. While a large miss distance is advantageous for missile penetration, the attacking missile must still strike the target after penetration; therefore, maximizing the miss distance is not always beneficial. A large miss distance means a large minimum distance (escape distance) between the attacking missile and the defensive missile. The attacking missile may detour significantly, resulting in insufficient overload to hit the target after penetration and excessive energy loss. If the attacking missile can evade the defensive missile's interception at a distance slightly larger than its damage radius, it can successfully penetrate without detouring too far and affecting the target. However, this requires quantitative control of the attacking missile's escape distance. Currently, research in this area is relatively limited. Prior technologies [6] (see Sun Qilong, Qi Naiming, Zhao Jun, et al. Differential game guidance law for attacking active defense aircraft. Journal of National University of Defense Technology, 2018, 40(03): 7-14.) and [7] (SUN QL, ZHANG CF, NING L W. et al. Guidance laws for attacking defended target. Chinese Journal of Aeronautics, 2019, 32(10): 2337-2353.) derived an improved differential game guidance law for attack missiles to evade interception in a two-dimensional plane under different initial sign values of the miss distance. Performance indicators considering the kill distance of the defense missile were designed, and the escape distance was greater than the kill distance of the defense missile. However, this guidance law is only applicable to planar confrontation and does not consider the control energy cost of the attack missile. When the attack and defense confrontation between the attack missile and the defense missile occurs in three-dimensional space, the longitudinal and lateral motions are interconnected, and the motion model is different from the two-dimensional plane model. At this time, the above-mentioned penetration guidance law is no longer applicable. Summary of the Invention
[0004] In view of this, the purpose of the present invention is to provide a missile penetration method with controllable escape distance, which can control the escape distance of the attacking missile during penetration in three-dimensional space while minimizing energy consumption.
[0005] A method for evading missile penetration at controllable distances includes:
[0006] Step 1: During the terminal guidance phase of the attack missile, the defensive missile is detected. When r MD <r safe When the attack missile enters the penetration state, r safe Given the distance between bullets at the start of the penetration;
[0007] Step 2: Call the trained get-away distance proxy model f(X,r) * According to the distance of escape Given the current state variable X, solve for the guidance law parameter r. * ;
[0008] Among them, the distance-based proxy model f(X,r) * The training process is as follows:
[0009] Construct a state vector X = [r, q] y ,η yM ,η zM ,η yD ,η zD ] and guidance law parameter r * The constructed vector serves as the input, and the output is the desired escape distance r. min BP proxy model f(X,r) * ); r represents the relative distance between the attacking and defensive missiles, q y Indicates the azimuth angle of the line of sight. This indicates the lead angle of the velocity vector of the attacking projectile. This indicates the lead angle of the velocity vector of the defensive missile;
[0010] Simulations were performed in typical offensive and defensive scenarios to obtain multiple training data points X′=[X,r * ,r min Used for training the proxy model;
[0011] Step 3: Begin the penetration using the penetration guidance law of formula (26):
[0012]
[0013] The process of establishing the penetration guidance law includes:
[0014] Step 2.1, the projection u of the acceleration of the attacking and defensive projectiles on the x-axis of the line-of-sight coordinate system in equation (3) rand v r With normal acceleration The relationship between them is:
[0015]
[0016]
[0017] Where: L(q) y ,q z The transition matrix between the ground coordinate system and the line-of-sight coordinate system; L(θ,ψ) V Let be the transformation matrix between the ground coordinate system and the ballistic coordinate system, then:
[0018]
[0019]
[0020] Assuming the defensive missile uses the classic proportional guidance law to intercept the attacking missile, then:
[0021]
[0022] In the formula, K D This is the proportional guidance coefficient;
[0023] Let the state variable be... control variables Then the writing state space form of formula (3) is:
[0024]
[0025] in, in:
[0026]
[0027] Introducing the zero-control miss quantity z(t) simplifies and reduces the order of the system, letting
[0028] z(t)=[1 0]Ω(t f ,t)x(t) (12)
[0029] In the formula: t0 and t f Ω(t) represents the initial and final moments of guidance. f (t) is the state transition matrix, which is obtained by solving the homogeneous equation. The expression is:
[0030]
[0031] In the formula: t go =t f-t represents the remaining flight time; according to the state transition matrix:
[0032]
[0033] Differentiate the zero-control miss quantity z(t) and use u r and v r Expressed as:
[0034]
[0035] The quadratic performance index function is set as follows:
[0036]
[0037] Where: a>0, b>0 are weighting coefficients; t f It is the moment when the distance between the defensive missile and the offensive missile is the smallest, and this moment is designated as the termination moment of guidance. For t f The zero-control miss distance z(t) at time r; * It is a normal number, that is, after the breakthrough. Expected value;
[0038] Step 2.2: Solving for the optimal penetration guidance command
[0039] This step uses the maximum principle to solve the optimal guidance problem for attack missile penetration established in step 2.1; the Hamiltonian function is established by equation (17):
[0040]
[0041] In the formula: λ is a costate variable, and its canonical equation is:
[0042]
[0043] λ at the final time t f The cross-section condition that is satisfied is:
[0044]
[0045] Then, by solving equations (18) and (19), the costate quantity λ is:
[0046]
[0047] The optimal conditions that need to be met are:
[0048]
[0049] Solving equations (17) and (21) simultaneously, we get:
[0050]
[0051] In the formula, The open-loop solution representing the control quantity of the attack missile still needs to be used to obtain the guidance command. Substituting the value of into equation (15), we get:
[0052]
[0053] Transform equation (23) from t to t f Integral result:
[0054]
[0055]
[0056] In the formula:
[0057] The penetration guidance law command for the attacking missile is then solved as follows:
[0058]
[0059] Step 4: After the penetration was completed, the attack missiles were redirected to strike the target.
[0060] Preferably, in Step 2, the guidance law parameter r is solved. * The methods include:
[0061] After the proxy model in step 3.1 is trained, when the attacking missile detects the defensive missile and decides to initiate penetration, the proxy model f(X,r) is invoked. * Based on f(X,r) * ) and the expectation of getting rid of distance The key parameter r of the guidance law required for inverse kinematics * The parameter design problem is transformed into solving equations:
[0062]
[0063] The procedure for solving equation (30) using the secant method is as follows:
[0064] 1) Given And state variables X, g(r) * ), maximum allowed number of iterations N, convergence index ε;
[0065] 2) Set the initial guess solution
[0066] 3) Calculate g0 = g(c0), g1 = g(c1), n = 1;
[0067] 4) Calculation
[0068]
[0069]
[0070] 5) If |g(c)| < ε, output r * = c, stop iteration; otherwise go to 6;
[0071] 6) If n < N, set go to 4; otherwise output r * = c, stop iteration.
[0072] Preferably, the surrogate model f(X, r * ) is implemented by a BP neural network.
[0073] Preferably, the structure of the BP neural network includes an input layer, one or more hidden layers, and an output layer.
[0074] The present invention has the following beneficial effects:
[0075] Aiming at the penetration problem of the attacking missile in three-dimensional space, considering the requirements of both penetration and energy conservation, a penetration guidance law with controllable breakaway distance for the attacking missile is designed based on the optimal control theory;
[0076] The present invention constructs a BP neural network surrogate model, and based on this, gives the key parameters of the guidance law under different penetration initial postures and breakaway distance requirements.
[0077] By using the method of the present invention, the control of the breakaway distance during the penetration process of the attacking missile in three-dimensional space can be achieved on the premise of minimizing the control energy. BRIEF DESCRIPTION OF THE DRAWINGS
[0078] Figure 1 is a relative motion relationship diagram of the attacking missile - target - defensive missile;
[0079] Figure 2 is a structure diagram of the BP neural network surrogate model;
[0080] Figure 3 is a penetration process flow chart of the present invention;
[0081] Figure 4 is a ballistic diagram of the attacking missile and the defensive missile;
[0082] Figure 5(a) is a longitudinal acceleration diagram of the attacking missile;
[0083] Figure 5(b) is a lateral acceleration diagram of the attacking missile. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0084] The present invention will be described in detail below with reference to the accompanying drawings and by way of examples.
[0085] Step 1: Mathematical Modeling of Attacking and Defending Aircraft
[0086] Suppose an attack missile strikes a fixed, high-value target, and the target launches a defensive missile to intercept the attack missile. The relative motion relationship between the three is as follows: Figure 1 As shown in the figure. OX I Y I Z I Let T be a ground coordinate system with the target T as the origin, and M and D be the attack missile and the defense missile, respectively. MT and r MD These represent the distances between the attacking missile and the target, and between the attacking missile and the defensive missile, respectively. θ q ψ These are the elevation and yaw line-of-sight angles of the attack missile, respectively, q y q z These represent the elevation and yaw line-of-sight angles of the defensive missile, respectively. (q in the diagram) ψ and q y The direction is positive, q q and q z The direction is negative. and The figures show the velocity, trajectory inclination angle, and trajectory deviation angle of the attack and defense missiles, respectively, with θ in the figure. D and The direction is positive, θ M and The direction is negative. From Figure 1 The equations of motion between the defensive and offensive missiles can be obtained as follows:
[0087]
[0088] Similarly, the equations of relative motion between the attack missile and the target can be obtained as follows:
[0089]
[0090] Since it is necessary to design the penetration guidance law of the attack missile relative to the defensive missile, therefore, in equation (1) Differentiating, we get:
[0091]
[0092] Where: u r v r These are the projections of the accelerations of the defensive and offensive projectiles onto the x-axis of the line-of-sight coordinate system, respectively.
[0093] The motion models of attack and defense missiles are as follows:
[0094]
[0095] In the formula: (x i ,y i,z i () indicates the aircraft's position; and These are the vertical and horizontal normal accelerations, respectively, perpendicular to the aircraft's velocity vector; when the subscripts i = M and D, they represent attack missiles and defensive missiles, respectively.
[0096] Step 2: Design of a three-dimensional optimal penetration guidance law with controllable sway distance, specifically including:
[0097] Step 2.1: Establishing the optimal control model for the penetration problem.
[0098] In equation (3), the projection u of the acceleration of the attacking and defensive projectiles onto the x-axis of the line-of-sight coordinate system is... r and v r With normal acceleration The relationship between them is:
[0099]
[0100]
[0101] Where: L(q) y ,q z The transition matrix between the ground coordinate system and the line-of-sight coordinate system; L(θ,ψ) V Let be the transformation matrix between the ground coordinate system and the ballistic coordinate system, then:
[0102]
[0103]
[0104] Assuming the defensive missile uses the classic proportional guidance law to intercept the attacking missile, then:
[0105]
[0106] In the formula, K D This is the proportional guidance coefficient.
[0107] Let the state variable be... control variables Equation (3) can be written in state-space form as follows:
[0108]
[0109] in, in:
[0110]
[0111] During flight Since all the quantities are changing, equation (10) is a linear non-stationary system. However, at each moment, A, B, and C are determined. For ease of study, equation (10) can be regarded as determined at a certain moment, that is, it can be regarded as a linear stationary system for designing penetration guidance laws.
[0112] Introducing the zero-control miss quantity z(t) simplifies and reduces the order of the system, letting
[0113] z(t)=[1 0]Ω(t f ,t)x(t) (12)
[0114] In the formula: t0 and t f Ω(t) represents the initial and final moments of guidance. f (t) is the state transition matrix, which can be solved by solving the homogeneous equation. The expression is:
[0115]
[0116] In the formula: t go =t f -t represents the remaining flight time. According to the properties of the state transition matrix:
[0117]
[0118] Differentiating the zero-control miss quantity z(t) with respect to the zero control miss quantity, for simplicity, we use u r and v r Expressed as:
[0119]
[0120] Considering that when an attacking missile penetrates a defense, the minimum distance between it and the defensive missile (escape distance) must be greater than the defensive missile's kill radius, but it's not always better to have a larger escape distance. A larger escape distance may result in the missile circling around the defense, potentially missing its target. Therefore, an ideal escape distance r can be set. * Slightly larger than the kill radius of the defensive missile. If the attack missile uses a penetration guidance law that allows it to escape after penetration to a distance close to r. * This allows for penetration without requiring excessive flight distance to avoid affecting the target. Simultaneously, considering minimizing energy expenditure during penetration, the quadratic performance index function is set as follows:
[0121]
[0122] Where: a>0, b>0 are weighting coefficients; t f It is the moment when the distance between the defensive and offensive missiles is the smallest, and this moment is designated as the termination moment of guidance. For tf The zero-control miss distance z(t) at time r; * It is a normal number, that is, after the breakthrough. The expected value.
[0123] Step 2.2: Solving for the optimal penetration guidance command
[0124] This step uses the maximum principle to solve the optimal guidance problem for attack missile penetration established in step 2.1. The Hamiltonian function is established from equation (17):
[0125]
[0126] In the formula: λ is a costate variable, and its canonical equation is:
[0127]
[0128] λ at the final time t f The cross-section condition that is satisfied is:
[0129]
[0130] Then, from equations (18) and (19), the costate quantity λ can be obtained as:
[0131]
[0132] The optimal conditions that need to be met are:
[0133]
[0134] Solving equations (17) and (21) simultaneously yields:
[0135]
[0136] In the formula, The open-loop solution representing the control quantity of the attack missile still needs to be used to obtain the guidance command. Substituting equation (22) into equation (15) yields the value of .
[0137]
[0138] Transform equation (23) from t to t f The integral yields:
[0139]
[0140]
[0141] In the formula:
[0142] Substituting equation (25) into equation (22), the penetration guidance law command for the attack missile is obtained as follows:
[0143]
[0144] In the formula, z(t) is calculated by equation (12). Thus, the optimal guidance command for the attack missile's penetration is obtained.
[0145] Step 3: Design of Key Parameters for Guidance Law Based on BP Neural Network
[0146] In the guidance law command formula (26), the guidance law parameters that need to be set are a, b, and t. f and r * If high penetration accuracy is required, then 'a' needs to be set very large; if minimizing control energy consumption during penetration is desired, then 'b' needs to be set very large. For the terminal time 't' at the end of the penetration... f The following typical method is used for prediction:
[0147]
[0148] In the formula: t is the current time; t go This represents the estimated remaining flight time.
[0149] r * The setting is very important. For example, the design of the performance index function for the penetration problem, as shown in equation (16), is to make the zero-control miss distance within t f The value at time is z(t) f ) should be equal to r * The direct indicator of whether an attack missile can successfully penetrate a defense is the time difference between the attack missile and the defensive missile. f The distance at any given moment, i.e., the escape distance r min And getting rid of the distance and zero-control miss distance They are not equal. Furthermore, when t... f When fixed, the guidance law shown in equation (26) enables the attack missile to... equal to the set value r * However, for the penetration problem, the estimated remaining flight time in equation (27) is constantly changing, therefore t f It is also constantly changing; at this moment, at t f Timely It is not strictly equal to r * The difference between the two and t go The accuracy of the estimation is related to the motion of both the attacking and defensive missiles. In summary, the guidance law parameter r... * Distance r from getting away min The relationship is very complex and cannot be represented by an analytical expression. Therefore, it is necessary to study how to make the escape distance r minGuidance law parameter r * The setting method.
[0150] Considering typical combat scenarios for offensive and defensive missiles, simulations are used to obtain r. * and r min The data is then processed using a backpropagation neural network to learn r. * and r min The relationship between them is then discussed, and subsequently, in actual combat, guidance law parameters r are given based on the current combat environment and the trained neural network. * .
[0151] Step 3.1: Establishing a distance-based agent model based on a BP neural network
[0152] In a typical combat scenario, assuming the target is fixed, the initial position and guidance law of the defensive missile launched from the target are determined, and the velocities of the attacking and defensive missiles are fixed, then the factors affecting the penetration effectiveness of the attacking missile include the relative positions and velocities of the attacking and defensive missiles relative to the line of sight at the start of the penetration, as well as the penetration guidance law used by the attacking missile. Let the longitudinal velocity lead angle of the defensive missile be... and lateral velocity lead angle for:
[0153]
[0154] Similarly, the attack missile relative to the line r connecting M and D MD line of sight azimuth Define the attack projectile relative to r MD Longitudinal and lateral velocity lead angles:
[0155]
[0156] The above analysis shows that at the start of the penetration, the relative distance r between the attacking missile and the defensive missile, and the line-of-sight azimuth angle q... y The velocity vector lead angle of the attack projectile The velocity vector lead angle of the defensive missile and guidance law parameter r * Together they determined r min Therefore, construct a system starting from the initial state. and guidance law parameter r * The constructed vector serves as input and output as r. min BP neural network surrogate model f(X,r) * ).
[0157] Extensive simulations were conducted in typical offensive and defensive scenarios to obtain training data X′=[X i ,r i * ,r min,iThe normalized values (i = 1 to n) are used to train the BP neural network surrogate model. Based on the trained surrogate model, it can quickly determine the appropriate actions (r) given an initial state X. * time r min The value can be determined based on the desired escape distance. To select the guidance law parameter r * .
[0158] During sampling, the samples should cover typical adversarial scenarios as much as possible. This will make the trained network more applicable. In other words, the data of the attack missile in flight should be within the range of the sample data. Only then can the output accuracy of the network be guaranteed, making the parameter design of the guidance law more precise.
[0159] BP neural network structure as follows Figure 2 As shown. The BP neural network structure consists of an input layer, one or more hidden layers, and an output layer. The input quantity [X, r]... * The number of nodes in the input layer is determined to be m = 7, and the output quantity r is... min The number of nodes in the output layer is determined to be k=1, and the number of hidden layers and neurons L are to be determined. Neurons in adjacent layers are fully connected, while neurons in the same layer are not connected.
[0160] Step 3.2: Solving for the parameters of the penetration guidance law based on the surrogate model.
[0161] After the proxy model in step 3.1 is trained, when the attacking missile detects the defensive missile and decides to initiate penetration, the proxy model f(X,r) is invoked. * Based on f(X,r) * ) and the expectation of getting rid of distance The key parameter r of the guidance law required for inverse kinematics * The parameter design problem is transformed into solving equations:
[0162]
[0163] Obviously, equation (30) is a nonlinear equation. The process of solving equation (30) using the secant method is as follows.
[0164] 1) Given And state variables X, g(r) * ), maximum allowed number of iterations N, convergence index ε;
[0165] 2) Set the initial guess solution
[0166] 3) Calculate g0 = g(c0), g1 = g(c1), n = 1;
[0167] 4) Calculation
[0168]
[0169]
[0170] 5) If |g(c)| < ε, output r * = c, stop iteration; otherwise go to 6;
[0171] 6) If n < N, set go to 4; otherwise output r * = c, stop iteration.
[0172] After solving the guidance law parameters, the penetration guidance law is determined.
[0173] Assume that the attacking missile uses the guidance law of this invention to penetrate, and the proportional navigation law is used to attack the target before and after penetration.
[0174] In summary, the process of the attacking missile using the optimal penetration guidance law with controllable breakaway distance based on the neural network surrogate model for penetration is summarized as follows:
[0175] Step1: When the attacking missile detects the defensive missile during the process of attacking the target in the terminal guidance section, when r MD < r safe the attacking missile enters the penetration state, and r safe is the given missile-to-missile distance at the start of penetration;
[0176] Step2: Call f(X, r * ), and use the secant method to solve r according to * and the current state quantity X;
[0177] Step3: Start penetration using the guidance law of equation (26);
[0178] Step4: The penetration ends, and the attacking missile turns to attack the target.
[0179] The flow chart showing the above penetration process is as Figure 3 shown.
[0180] The following is the verification of the penetration method with controllable breakaway distance based on the neural network surrogate model and the optimal control principle.
[0181] Taking an attacking missile using a proportional navigation law with a proportional coefficient of K M = 3 to attack a high-value fixed target, and the target launches a defensive missile to intercept the attacking missile as an example, the defensive missile uses a proportional navigation law as shown in equation (9) with K D = 4 to intercept the attacking missile. During the process of the attacking missile attacking the target, it is assumed that the defensive missile is detected at a distance of 8 km from the defensive missile, and then the optimal penetration guidance law of this invention is used for penetration, and the penetration guidance law parameter a = 10 4b = 1.44 The attack missile successfully penetrated the defenses. The missile then continues to attack the target according to the proportional guidance law. Considering the missile's overload limitations, both the tangential and normal overloads do not exceed 8. At the start of the penetration, X = [8, 31.84, 8.1, -2.11, 8.09, 1.90], which is then substituted into the trained neural network surrogate model f(X, r * The guidance law parameter r is obtained by iterating twice using the secant method. * =32.36m, the escape distance r of the attack missile after adopting this guidance law is obtained. min =50.37m, which is consistent with the set expected value. The differences are minimal, achieving high-precision control over the escape distance. The ballistics, as well as the accelerations of the attacking and defensive projectiles, are as follows: Figure 4 As shown in -5.
[0182] In summary, the above are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.
Claims
1. A method for escaping missile penetration with controllable distance, characterized in that, include: Step 1: During the terminal guidance phase of the attack missile, the defensive missile is detected. When r MD <r safe When the attack missile enters the penetration state, r safe Given the distance between bullets at the start of the penetration; Step 2: Call the trained get-away distance proxy model f(X,r) * According to the distance of escape Given the current state variable X, solve for the guidance law parameter r. * ; Among them, the distance-based proxy model f(X,r) * The training process is as follows: Construct a state vector and guidance law parameter r * The constructed vector serves as the input, and the output is the desired escape distance r. min BP proxy model f(X,r) * ); r represents the relative distance between the attacking and defensive missiles, q y Indicates the azimuth angle of the line of sight. This indicates the lead angle of the velocity vector of the attacking projectile. This indicates the lead angle of the velocity vector of the defensive missile; Simulations were performed in typical offensive and defensive scenarios to obtain multiple training data points X′=[X,r * ,r min Used for training the proxy model; Step 3: Begin the penetration using the penetration guidance law of formula (26): The process of establishing the penetration guidance law includes: Step 2.1, the projection u of the acceleration of the attacking and defensive projectiles on the x-axis of the line-of-sight coordinate system in equation (3) r and v r With normal acceleration The relationship between them is: Where: L(q) y ,q z The transition matrix between the ground coordinate system and the line-of-sight coordinate system; L(θ,ψ) V Let be the transformation matrix between the ground coordinate system and the ballistic coordinate system, then: Assuming the defensive missile uses the classic proportional guidance law to intercept the attacking missile, then: In the formula, K D This is the proportional guidance coefficient; Let the state variable be... control variables Then the writing state space form of formula (3) is: in, in: Introducing the zero-control miss quantity z(t) simplifies and reduces the order of the system, letting z(t)=[1 0]Ω(t f ,t)x(t) (12) In the formula: t0 and t f Ω(t) represents the initial and final moments of guidance. f (t) is the state transition matrix, which is obtained by solving the homogeneous equation. The expression is: In the formula: t go =t f -t represents the remaining flight time; according to the state transition matrix: Differentiate the zero-control miss quantity z(t) and use u r and v r Expressed as: The quadratic performance index function is set as follows: Where: a>0, b>0 are weighting coefficients; t f It is the moment when the distance between the defensive and offensive missiles is the smallest, and this moment is designated as the termination moment of guidance. For t f The zero-control miss distance z(t) at time r; * It is a normal number, that is, after the breakthrough. Expected value; Step 2.2: Solving for the optimal penetration guidance command This step uses the maximum principle to solve the optimal guidance problem for attack missile penetration established in step 2.1; the Hamiltonian function is established by equation (17): In the formula: λ is a costate variable, and its canonical equation is: λ at the final time t f The cross-section condition that is satisfied is: Then, by solving equations (18) and (19), the costate quantity λ is: The optimal conditions that need to be met are: Solving equations (17) and (21) simultaneously, we get: In the formula, The open-loop solution representing the control quantity of the attack missile still needs to be used to obtain the guidance command. Substituting the value of into equation (15), we get: Transform equation (23) from t to t f Integral result: The penetration guidance law command for the attacking missile is then solved as follows: Step 4: After the penetration was completed, the attack missiles were redirected to strike the target.
2. The method for escaping missile penetration with controllable distance as described in claim 1, characterized in that, Step 2 involves solving for the guidance law parameter r. * The methods include: After the proxy model in step 3.1 is trained, when the attacking missile detects the defensive missile and decides to initiate penetration, the proxy model f(X,r) is invoked. * Based on f(X,r) * ) and the expectation of getting rid of distance The key parameter r of the guidance law required for inverse kinematics * The parameter design problem is transformed into solving equations: The procedure for solving equation (30) using the secant method is as follows: 1) Given And state variables X, g(r) * ), maximum allowed number of iterations N, convergence index ε; 2) Set the initial guess solution 3) Calculate g0 = g(c0), g1 = g(c1), n = 1; 4) Calculation 5) If |g(c)| < ε, output r * =c, stop iteration; otherwise go to step 6; 6) If n < N, set Go to 4; otherwise output r * = c and stop the iteration.
3. The method for escaping missile penetration with controllable distance as described in claim 1, characterized in that, The proxy model f(X,r) * It is implemented using a BP neural network.
4. The method for escaping missile penetration with controllable distance as described in claim 3, characterized in that, The BP neural network structure includes an input layer, one or more hidden layers, and an output layer.