Decentralization cooperative guidance method based on strategy fusion and differential game

Abstract

The invention discloses a strategy fusion and differential game-based decentration cooperative guidance method, which comprises the following steps of: aiming at the problem of cluster system collapse caused by missed missile leading, combining the differential game with a consistency formation theory to enable missiles to approach a target in a predetermined formation so as to realize decentration; aiming at the problem that an HJI equation coupled by a nonlinear system is difficult to solve, constructing a neural network by utilizing a self-adaptive dynamic programming technology to carry out online solving on an optimal control strategy of pursuit and escape parties; for the dilemma that multiple escape strategies are difficult to select due to the fact that pursuit control strategies always appear in pairs, an interest value function is introduced, and a strategy fusion mechanism is provided; for the problem of a local minimum value possibly occurring in an artificial potential field method, a dynamic adjustment factor is introduced, and collision avoidance among intelligent agents of the whole cluster system is achieved.

Description

Technical Field

[0001] The present invention relates to the field of aircraft guidance, and in particular to a decentralized collaborative guidance method based on strategy fusion and differential game. Background Art

[0002] As modern warfare presents increasingly stronger characteristics such as non-contact, precision, informationization, and systematization, precision-guided weapons, as the main equipment for achieving modern battlefield target strikes, have attracted great attention from countries around the world in terms of the development of related technologies and equipment. They are booming at an unprecedented speed and playing an irreplaceable role. Among them, aviation-guided bombs are the most numerous air-to-ground weapons among the world's airborne high-precision weapons. The main features of aviation-guided bombs are simple structure, easy use, long range, high hit accuracy, low cost, and high cost-effectiveness. In-depth research on the development and application of aviation-guided bomb clusters is an effective means to change the single combat mode in the future and enhance the overall combat effectiveness of the system. It is the premise and guarantee for winning the initiative on the future battlefield and winning future wars.

[0003] The performance of a traditional single missile can no longer meet the strike requirements of the current complex air combat system. In the 1970s, the United States proposed the concept of missile group coordinated operations, which has important military significance. Multi-missile cluster coordinated guidance can significantly improve the attack and defense performance of missiles under high confrontation conditions, achieve penetration of enemy missile interception systems and saturation attacks on targets, ensure the successful destruction of key targets on the battlefield, and improve combat effectiveness. Considering that the existing guidance methods, whether coordinated guidance based on proportional guidance method, or optimal coordinated guidance, adaptive coordinated guidance, sliding mode coordinated guidance, etc., all use the residual time consistency characteristics to ensure that multiple missiles attack static or small maneuvering targets at the same time. Therefore, the above-mentioned coordinated guidance design methods all need to obtain the relevant maneuvering information of the attack target in advance, but do not consider the dynamic game characteristics between the missile and the target. The designed guidance law is difficult to meet the needs of countering high-speed and highly maneuverable intelligent targets.

[0004] Therefore, in order to address the uncertain dynamic characteristics between missile groups and between missiles and targets in the process of multi-missile coordinated guidance under non-ideal confrontation conditions, it is necessary to study a new coordinated guidance method with low requirements for inter-missile communication and excellent reliability, anti-destruction and robustness to meet the requirements of missile cluster combat in a high-intensity confrontation environment.

[0005] In addition, many scholars at home and abroad have tried to linearize the system to solve the problem of solving the HJI equation in optimal control, but it is often difficult to achieve in actual situations. For complex nonlinear systems, it is inevitable to solve coupled nonlinear partial differential equations in the design process of differential game cooperative guidance laws. In recent years, adaptive dynamic programming (ADP) technology has attracted the attention of many scholars as an effective tool to solve the optimal control problem of nonlinear systems. Its basic principle is to use function approximation structures (such as neural networks, etc.) to approximate the performance index function, and then update the parameters of the function approximation structure according to the Bellman optimality principle to obtain the optimal performance index function and the optimal control strategy. However, so far, there are few application results of ADP technology in the field of aerospace, especially it is rarely used in the design of nonlinear differential game guidance laws. In addition, in existing studies, the problem of collision avoidance between missiles is not considered. When the target can actively identify the incoming missile to avoid it, the collision probability of the multi-missile cluster increases, and the strike effect is significantly reduced. Therefore, it is necessary to break through the existing collaborative guidance design framework for complex nonlinear collaborative guidance systems and carry out research on the theory and method of collaborative collision avoidance guidance based on differential games. Summary of the invention

[0006] The purpose of the present invention is to propose a decentralized collaborative guidance method based on strategy fusion and differential game. Aiming at the problems of limited control by our side, target identifiable attack and avoidance, large cluster calculation and easy collision between missiles in the multi-to-one pursuit and escape system of missiles, the distributed collision avoidance collaborative guidance law based on strategy fusion and differential game is studied. The present invention first proposes a new decentralized scheme, which represents the cost function by integrating consensus and forming distance. Considering the limitation of control input and unknown target maneuverability, a differential game guidance law is designed, combined with adaptive dynamic programming technology, to solve the optimal control strategy of both parties of pursuit and escape online; then, the dynamic weight strategy fusion technology is introduced to solve the dilemma of multiple escape strategies caused by the appearance of pursuit control strategy and escape control strategy in pairs. Finally, in view of the collision problem caused by coordinating the relative distance between missiles and targets and the easy collision between missiles, an improved artificial potential field method is proposed, which introduces a dynamic adjustment factor, solves the local minimum problem at the same time, and realizes the collision avoidance between the intelligent agents of the entire cluster system.

[0007] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0008] A decentralized collaborative guidance method based on strategy fusion and differential game, the missile distributed collaborative guidance method comprising the following steps:

[0009] S1: Establish a relative motion model of the projectile and the target, select the relative distance between the projectile and the target as the state variable, and obtain the nonlinear multi-agent system as follows:

[0010]

[0011] in, is the state variable of the i-th missile, is x i The derivative of x i,1 is the relative distance between the projectile and the target, x i,2 is the rate of change of the relative distance between the projectile and the target, n is the dimension of the system state variable, α i is the track angle of the i-th missile, θ i is the sight angle of the i-th missile, β is the track angle of the target, u i and T are the normal control inputs perpendicular to the velocity direction of the i-th missile and the target, respectively, and are used to generate the lateral acceleration of the missile and the target in the autopilot. is the derivative of the sight angle;

[0012] S2: For a single missile and target, the consistent formation error and the miss amount are selected as performance indicators, and the performance indicator function of both parties in the game is constructed. According to the necessary conditions of the Nash-Pontryagin maximum and minimum principle, the optimal control strategy is obtained, and then the time-varying HJI equation is obtained:

[0013]

[0014] Among them, J i * (x i ) is x i The optimal cost function, J i * (x i )About x i The partial differential Q(x i ) is a positive definite function, R s is a symmetric positive definite matrix, γ represents the restriction on the missile control input;

[0015] S3, using ADP technology to approximate the optimal cost function online, the network weight update law is obtained as:

[0016]

[0017] in, is the derivative of the ideal weight estimate, is the estimated value of the ideal weight, e c is the error function, is the partial derivative of the activation function σ(x) with respect to x, η is the learning rate, F1 and F2 are adjustment parameters greater than 0, J s is a smooth, radially unbounded differentiable function that satisfies To increase stability;

[0018] S4, for the target, proposes a strategy fusion solution, and combines the target escape strategy v1,v1,…,v N The optimal escape strategy of the target obtained by vector fusion is:

[0019]

[0020] Among them, the correction weight coefficient ψ i (t) is the interest value of the target at time t for missile i, satisfying the relationship 0≤Ψ i (t)≤1 and N is the number of missiles;

[0021] S5: The artificial potential field method is used to deal with the collision problem. The relative distance between the missile and the target is used as the coordination variable to obtain the command acceleration u of the i-th missile. i "for:

[0022] u″ i (t) = u i (t)+u′ i (t)

[0023] Among them, u i (t) is the command acceleration of the ith missile to achieve coordination, u' i (t) is the command acceleration of missile i to avoid collision.

[0024] Furthermore, in step S1, the process of obtaining the nonlinear multi-agent system includes the following steps:

[0025] S11: Assume that the missile and the target are both point masses, and the velocity of the i-th missile is V i , the target speed is V T , is the derivative of the sight angle of the ith missile, r i and are the relative distance between the missile and the target and the derivative of the relative distance between the missile and the target respectively. Then the relative kinematic equation between the ith missile and the target is:

[0026]

[0027] S12: Select state variables The state equation of the guidance system is:

[0028]

[0029] The feasible domain of the system is N is the number of missiles, is x i1 The derivative of is x i2 The derivative of

[0030] S13: The state equation of the nonlinear system in step S12 is further described as a nonlinear multi-agent system: in u i and v T are the normal control inputs perpendicular to the velocity directions of the i-th missile and the target, respectively.

[0031] Furthermore, in step S2, the process of obtaining the time-varying HJI equation includes the following steps:

[0032] S21: For missiles, construct a continuous-time nonlinear differential game system:

[0033]

[0034] Among them, x i ∈R n is the state variable of the ith missile, u i ∈R m and v T ∈R Z are the control inputs of both parties in the game, f(x i )∈R n ,g(x i )∈R n×m and k(x i )∈R n×Z is a locally Lipschitz continuous nonlinear function with f(0)=0, n, m, Z are the dimensions of the variables;

[0035] Three missiles form a triangle formation to pursue, and the distance between the missiles is r ij It can be expressed as:

[0036]

[0037] The local consistency error of the missile δ i It can be expressed as:

[0038]

[0039] Where h(t) is the expected distance between missiles, a ij is the weight value of the communication between missiles, N i ={j:(i,j)∈E}, E represents the communication set;

[0040] Taking the consistency formation error and the miss amount as performance indicators, the performance indicator function J is selected i :

[0041]

[0042] Among them, λ1 and λ2 represent weight values, satisfying λ1+λ2=1, Q 1i (x i )=δ i T Q1δ i , Q 2i (x i )=x i T Q2 i , Q1 and Q2 are both positive definite functions, R v is a symmetric positive definite matrix, γ represents the restriction on our missile control input;

[0043] S22: Find the Nash equilibrium solution (u,v T ), so that the performance indicators meet:

[0044] J(u * ,v T )≤J(u * ,v T * )≤J(u,v T * )

[0045] Among them, u * ,v T * It represents the optimal control input of our missile and target;

[0046] The Hamiltonian function is defined as:

[0047]

[0048] in That is J i (x i ) for variable x i Find partial derivatives;

[0049] In the infinite time domain, the derivative of the optimal performance index with respect to time is 0, that is,

[0050] S23, according to the necessary conditions of the Nash-Pontryagin maximum-minimum principle and The optimal control strategy is obtained:

[0051]

[0052] in, u i * (x i ,t),v T * (x i ,t) represents the optimal control input perpendicular to the missile, i.e., the acceleration command;

[0053] Substituting the control strategy into the Hamiltonian function in step S22, the time-varying HJI equation is obtained:

[0054]

[0055] Furthermore, in step S3, the process of using the ADP technology to online approximate the optimal cost function includes the following steps:

[0056] S31, using neural network to approximate the optimal cost function J online i * (x i ):

[0057]

[0058] Among them, W c ∈R L is the ideal weight vector of the neural network, σ(x i )∈R L is the activation function, ε(x i ) is the approximation error of the neural network;

[0059] Taking partial derivative of the optimal cost function, we get:

[0060]

[0061] in, Denotes the activation function and the approximation error x i The partial derivative of

[0062] Substitute the partial derivative of the optimal cost function into the optimal control strategy shown in the optimal control strategy of step S23:

[0063]

[0064] The time-varying HJI equation is obtained:

[0065]

[0066] The residual error caused by the neural network approximation is obtained by sorting:

[0067]

[0068] S32, estimate the ideal weights based on the output of the neural network:

[0069]

[0070] in, and are the estimates of the optimal cost function and the ideal weights, respectively;

[0071] right Taking partial derivatives we get:

[0072]

[0073] Substituting the optimal control strategy into the optimal control strategy, the estimate of the optimal control strategy is:

[0074]

[0075] in, The FA represents an estimate of the optimal control input perpendicular to the missile, i.e., the acceleration command;

[0076] Substituting the estimate of the optimal control strategy into the time-varying HJI equation in step S31, we obtain:

[0077]

[0078] S33, design neural network weight update law to optimize actual weights Let it infinitely approach the ideal weight W c , define the error function as:

[0079]

[0080] in, is the Hamiltonian function whose control input is the estimate of the optimal policy, is the Hamiltonian function whose control input is the optimal strategy;

[0081] The loss function is defined as:

[0082]

[0083] The weight coefficient of the network is corrected using the gradient descent method:

[0084]

[0085] Among them, η>0 is the learning rate of the neural network;

[0086] Substituting into the error function we get:

[0087]

[0088] S34, assume that there exists a continuously differentiable radially unbounded Lyapunov function J s (x):

[0089]

[0090] in, Indicates J s The partial derivative of (x) with respect to x, there exists a positive definite function Λ(x) that satisfies and So that the following inequality holds:

[0091]

[0092] Assume that the closed-loop system is bounded under the differential game control strategy and the bounding function is an expression about the variable x:

[0093]

[0094] Where c is a positive constant and c>0;

[0095] Add two items to the formula (*) and propose the network weight update law as follows:

[0096]

[0097] in, is a stabilizing term, defined as:

[0098]

[0099] When the system is stable, at this time The stabilization item does not work. When the system is unstable, The stabilization item comes into play to maintain the stability of the system.

[0100] Furthermore, in step S4, a strategy fusion scheme is proposed for the target, and the process of obtaining the optimal escape strategy for the target includes the following steps:

[0101] S41, regard the strategy fusion scheme as the target escape strategy v1,v1,...,v N The resultant vector is expressed as:

[0102]

[0103] Among them, the modified weight coefficient ψ i (t) represents the missile's interest in the target, satisfying 0≤ψ i (t)≤1 and N is the number of missiles;

[0104] S42, define ψ i 1 (t) is the distance interest function S r and the speed interest function S V The sum is expressed as:

[0105] ψ i 1 (t) = S r +S v

[0106] in, r i is the relative distance between the projectile and the target, r c is the escape radius of the target, V i is the speed of the ith missile, V T The speed of the target;

[0107] S43, get the weight coefficient ψ i Specific representation of (t):

[0108]

[0109] Furthermore, in step S5, the collision problem is processed by the artificial potential field method, and the relative distance between the missile and the target is used as the coordination variable. The process of obtaining the command acceleration of the i-th missile includes the following steps:

[0110] S51, assuming that the artificial potential field function is represented by U(x, y), and for each position in space, U(x, y) is differentiable, the force acting on the missile is the control force F(x, y) in the negative gradient direction of the artificial potential field function, expressed as:

[0111]

[0112] Among them, (x, y) represents the coordinates of the missile in the two-dimensional plane, Represents the gradient of U(x,y) at (x,y), and its direction is the direction of the maximum rate of change of the potential field at the coordinate (x,y);

[0113] The artificial potential field function between missile i and missile j is U ij , which satisfies:

[0114]

[0115] Among them, r ij represents the distance between missiles, n represents the number of missiles involved in the coordinated operation, It means that missile i is controlled by the artificial potential field of missile j. It means that missile j is controlled by the artificial potential field of missile i, U iIt represents the sum of the artificial potential field control forces exerted on missile i by other missiles;

[0116] S52, artificial potential field function U determined by the relative distance between projectiles ij (r ij )for:

[0117]

[0118] Among them, the coefficient K r Adjust the potential field strength, r min is the minimum safety radius between missile i and missile j, r s is the anti-collision threshold, when r ij >r s When there is no artificial potential field between the bullets, when r ij →r min When U ij →∞;

[0119] Combined with the artificial potential field control force, the control force F exerted on missile i in the potential field of missile j is ij (x i ,y i )for:

[0120]

[0121] Among them, (x i ,y i ) represents the coordinates of missile i in the two-dimensional plane.

[0122] The control force on missile i and F i (x i ,y i )for:

[0123]

[0124] S53, control force F i The command acceleration u′ caused by i for:

[0125]

[0126] Among them, m i is the mass of the missile, F ia is the control force F i Normal projection in velocity;

[0127] Combined with the cooperative guidance law, the command acceleration of the missile is obtained as:

[0128] u″ i =u i +u′ i

[0129] Among them, u i is the normal control input perpendicular to the velocity direction of the i-th missile. min <r ij ≤r s When the missile is at u i and u i 'When flying under the simultaneous action of the two commands, when the two commands are equal in size but opposite in direction at a certain moment, the missile will fall into a local minimum state;

[0130] S54, design a dynamic adjustment factor k based on the distance between bullets d To prevent the missile from falling into the local minimum:

[0131]

[0132] in, r dom is a random number, satisfying 0≤r dom ≤1, is the gain factor, and at the same time, -1<α d <1;

[0133] After the improvement, the control force on missile i is:

[0134]

[0135] When in r min <r ij ≤r s When the missile is at u i and u i 'Flying under the action of i +u′ i = 0, k d Start dynamically adjusting u′ i The value of r ij ≤r min When the potential force is infinite, the command u i It doesn't work. The missile is mainly used for collision avoidance.

[0136] Compared with the prior art, the present invention has the following beneficial effects:

[0137] First, the decentralized collaborative guidance method based on strategy fusion and differential game of the present invention takes into account the scenario where our control is limited, the target maneuver is unknown, and the incoming air-guided bombs (missiles) can be actively identified for evasion. A differential game guidance law based on ADP is designed to predict the target maneuver.

[0138] Second, the decentralized collaborative guidance method based on strategy fusion and differential game of the present invention uses neural network to approximate the solution of HJI equation online. Different from the traditional evaluation network-execution network structure, this paper adopts a single evaluation network to approximate the optimal cost function online, which simplifies the approximate structure of the neural network.

[0139] Third, the decentralized collaborative guidance method based on strategy fusion and differential game of the present invention aims at the problem of limited control input and unknown target maneuverability, proposes a control method based on differential game method to make missiles attack targets in a predetermined formation, and proposes a cost function to achieve decentralization by combining differential game and consistency formation theory. It does not need to estimate the remaining time of the moving target, and has the characteristics of simple structure, good real-time performance, small communication volume, and good scalability.

[0140] Fourth, the decentralized collaborative guidance method based on strategy fusion and differential game of the present invention uses an improved artificial potential field method to introduce a dynamic adjustment factor to solve the local minimum problem when coordinating the relative distance between the missile and the target, thereby achieving collision avoidance between the intelligent agents of the entire cluster system. BRIEF DESCRIPTION OF THE DRAWINGS

[0141] Figure 1 This is an overall flow chart of a decentralized collaborative guidance method based on strategy fusion and differential game.

[0142] Figure 2 This is a system structure block diagram based on the artificial potential field method.

[0143] Figure 3 Schematic diagram of the relative motion model between projectile and target.

[0144] Figure 4 This is a schematic diagram of the cluster system formation. DETAILED DESCRIPTION

[0145] The embodiments of the present invention are further described in detail below in conjunction with the accompanying drawings.

[0146] See also Figure 1 and Figure 2 The present invention discloses a decentralized collaborative guidance method based on strategy fusion and differential game, comprising the following steps:

[0147] Step 1: Establish a relative motion model between projectile and target, select the relative distance between projectile and target as the state variable, and obtain a nonlinear multi-agent system;

[0148] Consider the problem of coordinated pursuit of a maneuvering target by N missiles in a two-dimensional plane, where the missiles seek the optimal control strategy to pursue the maneuvering target T, while the target T tries to seek the optimal control strategy to avoid the attack. The N missiles achieve coordination through formation, such as Figure 3 , Figure 4 shown.

[0149] The research of this method is based on the final guidance stage, when the missile speed remains unchanged, and the direction of motion is changed by changing the magnitude of the normal acceleration. Assume that the missile and the target are both point masses, and the speed of the i-th missile is V i , the track angle is α i , the sight angle is θ i The target speed is V T , the track angle is β. i and T are the normal control inputs perpendicular to the missile and target velocity directions, respectively, used to generate the lateral acceleration of the missile and target in the autopilot, r i and is the relative distance between the missile and the target and its derivative. Then the relative kinematic equation between the ith missile and the target is:

[0150]

[0151] Selecting state variables Therefore, the state equation of the guidance system is:

[0152]

[0153] Among them, |α i -θ i |=0 and |β-θ|=0, the system is uncontrollable, which is the point that causes the system to be unstable. i →0, the state equation tends to infinity and the guidance process is destroyed. Therefore, the feasible domain of the system is But in reality, in the final stage of terminal guidance, the missile continues to move only by inertia. i If the radius is smaller than the capture radius, it is considered a successful capture. Therefore, it does not affect the pursuit accuracy and escape effect of both parties.

[0154] Formula (2) can be further described as a nonlinear multi-agent system in the following form:

[0155]

[0156] in u i and v T is the control input of the system.

[0157] Step 2: For missiles and targets, select the consistency formation error and miss distance as performance indicators, and construct the performance indicator function of both parties in the game. According to the necessary conditions of the Nash-Pontryagin maximum and minimum principle, the optimal control strategy is obtained, and then the time-varying HJI equation is obtained;

[0158] For missiles, a continuous-time nonlinear differential game system is constructed:

[0159]

[0160] Among them, x i ∈R n is the state variable, u i ∈R m and v T ∈R Z is the control input of both parties in the game, f(x i )∈R n ,g(x i )∈R n×m and k(x i )∈R n×Z is a locally Lipschitz continuous nonlinear function, n, m, z are the dimensions of the variables, and f(0) = 0. Obviously, the system (4) is controllable, and x = 0 is the equilibrium point of the system.

[0161] Three missiles form a triangle formation for pursuit. The distance between the missiles can be expressed as:

[0162]

[0163] The local consistency error of the missile can be expressed as:

[0164]

[0165] Where h(t) is the expected distance between missiles, a ij is the weight value of the communication between missiles, N i ={j:(i,j)∈E}, where E represents the communication set.

[0166] Taking the consistency formation error and the miss amount as performance indicators, the performance indicator function is selected as:

[0167]

[0168] Among them, λ1 and λ2 represent weight values, satisfying λ1+λ2=1, Q 1i (x i )=δ i T Q1δ i , Q 2i (x i )=x i T Q2 i , Q1 and Q2 are both positive definite functions, R v is a symmetric positive definite matrix, γ represents the restriction on our missile control input;

[0169] Since our control strategy u hopes to minimize the amount of misses, the enemy's control strategy v T In order to maximize the miss distance, a zero-sum differential game is formed. In the end, both the pursuer and the fugitive need to find a Nash equilibrium solution (u,v T ),make:

[0170] J(u * ,v T )≤J(u * ,v T * )≤J(u,v T * ) Formula (8)

[0171] The Hamiltonian function is defined as:

[0172]

[0173] in That is J i (x i ) for variable x i Find the partial derivative; in the infinite time domain, the derivative of the optimal performance index with respect to time is 0, that is, Combined with the boundary conditions, we can get:

[0174]

[0175] According to the necessary conditions of the Nash-Pontryagin maximum-minimum principle and The optimal control strategy is obtained as:

[0176]

[0177] in,

[0178] Substituting the control strategy (11) into (9), we get the time-varying HJI equation:

[0179]

[0180] in By solving the HJI equation, we obtain that since nonlinear partial differential equations are difficult to solve, the ADP technology is used to approximate the optimal cost function online.

[0181] Step 3: Since nonlinear partial differential equations are difficult to solve, the ADP technology is used to approximate the optimal cost function online. In order to minimize the square of the error and make the signal bounded during the closed-loop system learning process, a simplified network weight update law is proposed on this basis;

[0182] Assumption 1 Considering the affine nonlinear system (4) and the given performance index function (7), under the differential game control strategy (11), it is assumed that there exists a continuously differentiable radially unbounded Lyapunov function J s (x), so that the inequality Established. Among them, Indicates J s (x) with respect to x. Now we can determine that there is a positive definite function Λ(x) that satisfies and So that the following inequality holds:

[0183]

[0184] In addition, it is assumed that the closed-loop system is bounded under the differential game control strategy and the bounding function is an expression about the variable x:

[0185]

[0186] Among them, c>0 is a normal number.

[0187] Using neural network to approximate the optimal cost function J online * (x):

[0188]

[0189] Among them, W c ∈R L is the ideal weight vector of the neural network, σ(x i )∈R L is the activation function, ε(x i ) is the approximation error of the neural network.

[0190] Taking partial derivative of formula (15), we get:

[0191]

[0192] in, represents the partial derivative of the activation function with respect to x.

[0193] Substituting equation (16) into equation (11), the optimal control strategy is:

[0194]

[0195] Substituting equation (16) into equation (12), we get the HJI equation:

[0196]

[0197] The residual error caused by the neural network approximation is obtained by sorting:

[0198]

[0199] Since the ideal weights are unknown, the output of CNN will be used to estimate the ideal weights. The specific expression is as follows:

[0200]

[0201] in, and Represents an estimate of the optimal cost function and ideal weights.

[0202] Taking partial derivative of formula (20) we get:

[0203]

[0204] Substituting into equation (11), we get the estimate of the optimal control strategy:

[0205]

[0206] Substituting equation (22) into equation (12), we get the HJI equation:

[0207]

[0208] It is necessary to design a CNN weight update law to optimize the actual weights Let it infinitely approach the ideal weight W c Since the ideal weights are unknown, the error function is defined as:

[0209]

[0210] Define the loss function:

[0211]

[0212] Using the gradient descent method to correct the network weight coefficients, we have

[0213]

[0214] Among them, η>0 represents the learning rate of CNN.

[0215] Substituting equation (24) into equation (26), we can obtain

[0216]

[0217] Due to the actual weight The stability of the nonlinear system cannot be guaranteed, so a simplified network weight update law is proposed, which can not only minimize the square of the error, but also ensure that the signal is bounded during the closed-loop system learning process. Two terms are added to the basis of formula (27) to reduce the approximation error of the neural network and ensure the stability of the system, and we get

[0218]

[0219] in, F1 and F2 are adjustment parameters greater than 0; It has been given in hypothesis 1; is defined as follows:

[0220]

[0221] When the system (4) is stable, at this time The stabilization item does not work. When the system is unstable, The stabilization item comes into play to maintain the stability of the system.

[0222] Defining CNN weight estimation error According to (18), we can get:

[0223]

[0224] Combining equations (24), (28) and (30), the dynamics of CNN weight estimation error can be expressed as:

[0225]

[0226] Step 4: Propose a strategy fusion solution for the target. The process of obtaining the optimal escape strategy for the target includes the following steps:

[0227] The strategy fusion scheme can be regarded as the target escape strategy v1,v1,...,v N The resultant vector is expressed as:

[0228]

[0229] Where N is the number of missiles, and the corrected weight coefficient ψ i (t) represents the missile's interest in the target, satisfying 0≤ψ i (t)≤1 and:

[0230]

[0231] Define ψ i 1 (t) is the distance interest function S r and the speed interest function S VThe sum is expressed as:

[0232] ψ i 1 (t) = S r +S v Formula (34)

[0233] in, r c is the escape radius of the target;

[0234] Get the weight coefficient ψ i The specific expression of (t) is:

[0235]

[0236] Step 5: Use the artificial potential field method to deal with the problem of missile collision when the relative distance between missile and target is used as the coordination variable in the distributed coordination process. Obtain the command acceleration of the missile;

[0237] Assumption 2 The artificial potential field function is represented by U(x,y), and for every position in space, U(x,y) must be differentiable.

[0238] The artificial potential field method determines the direction and speed of the missile by searching for the direction in which the potential field value decreases. Therefore, the force acting on the missile is the control force in the negative gradient direction of the artificial potential field function, expressed as:

[0239]

[0240] in, Represents the gradient of U(x,y) at (x,y), which is a vector whose direction is the direction of the maximum rate of change of the potential field at position (x,y).

[0241] The artificial potential field function between missile i and missile j in the system is U ij , which has the following properties:

[0242] <1> The potential field function has symmetry, namely:

[0243]

[0244] <2> During the flight, missile i may be in the potential field of multiple missiles around it, so the total potential field U i It can be expressed as:

[0245]

[0246] In the formula, r ij represents the distance between missiles, and n represents the number of missiles involved in the coordinated combat.

[0247] like Figure 2 This is a system structure block diagram based on the artificial potential field method.

[0248] The artificial potential field function determined by the relative distance between projectiles is defined as:

[0249]

[0250] Among them, the coefficient K r Adjust the potential field strength, r min is the minimum safety radius between missile i and missile j, r s is the anti-collision threshold. When r ij →r min When U ij →∞.

[0251] Therefore, combined with equation (36), the control force on missile i in the potential field of missile j is:

[0252]

[0253] Furthermore, according to formula (38), the control force on missile i is:

[0254]

[0255] Control force F i The resulting command acceleration is:

[0256]

[0257] Among them, m i is the mass of the missile, F ia is the control force F i In the normal projection of the velocity, the missile's velocity heading angle is changed by the normal control input, thereby changing its direction of movement without changing the magnitude of the velocity.

[0258] Combining the consistency control algorithm and artificial potential field collision avoidance algorithm in the previous section, the command acceleration of the missile can be obtained as:

[0259] u i ”=u i +u i ' Formula (43)

[0260] When in r min <r ij ≤r s When the missile is at u i and u i 'When flying under the simultaneous action of two commands, when the two commands are equal in size but opposite in direction at a certain moment, the missile will fall into a local minimum state.

[0261] Design a dynamic adjustment factor k based on the distance between bullets d To prevent the missile from falling into the local minimum:

[0262]

[0263] in, r dom is a random number, satisfying 0≤r dom ≤1, is the gain factor; at the same time, -1<α d <1.

[0264] After the improvement, the control force on missile i is:

[0265]

[0266] When in r min <r ij ≤r s When the missile is at u i and u i 'Flying under the action of i +u i When '=0, k d Start dynamic adjustment i ' value, when r ij ≤r min When the potential force is infinite, the command u i It doesn't work. The missile is mainly used for collision avoidance.

[0267] Those skilled in the art will appreciate that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of complete hardware embodiments, complete software embodiments, or embodiments in combination with software and hardware. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code. The scheme in the embodiments of the present application can be implemented in various computer languages, for example, object-oriented programming language Java and literal scripting language JavaScript, etc.

[0268] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0269] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0270] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0271] Although the preferred embodiments of the present application have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the present application.

[0272] Obviously, those skilled in the art can make various changes and modifications to the present application without departing from the spirit and scope of the present application. Thus, if these modifications and variations of the present application fall within the scope of the claims of the present application and their equivalents, the present application is also intended to include these modifications and variations.

Claims

1. A decentralized collaborative guidance method based on strategy fusion and differential game, characterized in that: The method comprises the following steps: S1: Establish a relative motion model of the projectile and the target, select the relative distance between the projectile and the target as the state variable, and obtain the nonlinear multi-agent system as follows: in, is the state variable of the i-th missile, is x i The derivative of x i,1 is the relative distance between the projectile and the target, x i,2 is the rate of change of the relative distance between the projectile and the target, n is the dimension of the system state variable, α i is the track angle of the i-th missile, θ i is the sight angle of the i-th missile, β is the track angle of the target, u i and v T are the normal control inputs perpendicular to the velocity direction of the i-th missile and the target, respectively, used to generate the lateral acceleration of the missile and the target in the autopilot, and θ is the derivative of the line of sight angle; S2: For a single missile and target, the consistent formation error and the miss amount are selected as performance indicators, and the performance indicator function of both parties in the game is constructed. According to the necessary conditions of the Nash-Pontryagin maximum and minimum principle, the optimal control strategy is obtained, and then the time-varying HJI equation is obtained: Among them, J i * (x i ) is x i The optimal cost function, J i * (x i )About x i The partial differential Q(x i ) is a positive definite function, R s is a symmetric positive definite matrix, γ represents the restriction on the missile control input; S3, using ADP technology to approximate the optimal cost function online, the network weight update law is obtained as: in, is the derivative of the ideal weight estimate, is the estimated value of the ideal weight, e c is the error function, is the partial derivative of the activation function σ(x) with respect to x, η is the learning rate, F1 and F2 are adjustment parameters greater than 0, J s is a smooth, radially unbounded differentiable function that satisfies To increase stability; S4: Propose a strategy fusion solution for the target, and transform the target escape strategy v1,v1,...,v N The optimal escape strategy of the target obtained by vector fusion is: Among them, the correction weight coefficient ψ i (t) is the interest value of the target at time t for missile i, satisfying the relationship 0≤Ψ i (t)≤1 and N is the number of missiles; S5: The artificial potential field method is used to deal with the collision problem. The relative distance between the missile and the target is used as the coordination variable to obtain the command acceleration u of the i-th missile. i "for: u i ”(t) = u i (t) + u i '(t) Equation (5) Among them, u i (t) is the command acceleration of the ith missile to achieve coordination, u i '(t) is the command acceleration of the i missiles to avoid collision.

2. A decentralized collaborative guidance method based on strategy fusion and differential game as claimed in claim 1, characterized in that: The step S1 comprises: S11: Assume that the missile and the target are both point masses, and the velocity of the i-th missile is V i , the target speed is V T , is the derivative of the sight angle of the ith missile, r i and are the relative distance between the missile and the target and the derivative of the relative distance between the missile and the target respectively. Then the relative kinematic equation between the ith missile and the target is: S12: Select state variables The state equation of the guidance system is: The feasible domain of the system is N is the number of missiles, is x i1 The derivative of is x i2 The derivative of S13: The state equation of the nonlinear system in step S12 is further described as a nonlinear multi-agent system: in u i and v T are the normal control inputs perpendicular to the velocity directions of the i-th missile and the target, respectively.

3. The decentralized collaborative guidance method based on strategy fusion and differential game as claimed in claim 1, characterized in that: The step S2 comprises: S21: For missiles, construct a continuous-time nonlinear differential game system: Among them, x i ∈R n is the state variable of the ith missile, u i ∈R m and v T ∈R Z are the control inputs of both parties in the game, f(x i )∈R n ,g(x i )∈R n×m and k(x i )∈R n×Z is a locally Lipschitz continuous nonlinear function with f(0)=0, n, m, Z are the dimensions of the variables; Three missiles form a triangle formation to pursue, and the distance between the missiles is r ij It can be expressed as: The local consistency error of the missile δ i It can be expressed as: Where h(t) is the expected distance between missiles, a ij is the weight value of the communication between missiles, N i ={j:(i,j)∈E}, E represents the communication set; Taking the consistency formation error and the miss amount as performance indicators, the performance indicator function J is selected i : Among them, λ1 and λ2 represent weight values, satisfying λ1+λ2=1, Q 1i (x i )=δ i T Q1δ i , Q 2i (x i )=x i T Q2 i , Q1 and Q2 are both positive definite functions, R v is a symmetric positive definite matrix, γ represents the restriction on our missile control input; S22: Find the Nash equilibrium solution (u,v T ), so that the performance indicators meet: J(u * , v T ) ≤ J(u * , v T * ) ≤ J(u, v T * ) Equation (12) Among them, u * ,v T * It represents the optimal control input of our missile and target; The Hamiltonian function is defined as: in That is J i (x i ) for variable x i Find partial derivatives; In the infinite time domain, the derivative of the optimal performance index with respect to time is 0, that is, S23, according to the necessary conditions of the Nash-Pontryagin maximum-minimum principle and The optimal control strategy is obtained: in, u i * (x i ,t),v T * (x i ,t) represents the optimal control input perpendicular to the missile, i.e., the acceleration command; Substituting the control strategy into the Hamiltonian function in step S22, the time-varying HJI equation is obtained:

4. The decentralized collaborative guidance method based on strategy fusion and differential game as claimed in claim 1, characterized in that: The step S3 comprises: S31, using neural network to approximate the optimal cost function J online i * (x i ): Among them, W c ∈R L is the ideal weight vector of the neural network, σ(x i )∈R L is the activation function, ε(x i ) is the approximation error of the neural network; Taking partial derivative of the optimal cost function, we get: in, Denotes the activation function and the approximation error x i The partial derivative of Substitute the partial derivative of the optimal cost function into the optimal control strategy shown in equation (14) of step S23: The time-varying HJI equation is obtained: The residual error caused by the neural network approximation is obtained by sorting: S32, estimate the ideal weights based on the output of the neural network: in, and are the estimates of the optimal cost function and the ideal weights, respectively; Taking partial derivatives of formula (21) we get: Substituting into equation (14), we can get the estimate of the optimal control strategy: in, The FA represents an estimate of the optimal control input perpendicular to the missile, i.e., the acceleration command; Substituting the estimate of the optimal control strategy into the time-varying HJI equation in step S31, we obtain: S33, design neural network weight update law to optimize actual weights Let it infinitely approach the ideal weight W c , define the error function as: in, is the Hamiltonian function whose control input is the estimate of the optimal policy, is the Hamiltonian function whose control input is the optimal strategy; The loss function is defined as: The weight coefficient of the network is corrected using the gradient descent method: Among them, η>0 is the learning rate of the neural network; Substituting into the error function we get: S34, assume that there exists a continuously differentiable radially unbounded Lyapunov function J s (x): in, Indicates J s The partial derivative of (x) with respect to x, there exists a positive definite function Λ(x) that satisfies and So that the following inequality holds: Assume that the closed-loop system is bounded under the differential game control strategy and the bounding function is an expression about the variable x: Where c is a positive constant and c>0; By adding two items to formula (28), the network weight update law is proposed as follows: in, is a stabilizing term, defined as: J(x) is the cost function. When the system is stable, at this time The stabilization item does not work. When the system is unstable, The stabilization item comes into play to maintain the stability of the system.

5. The decentralized collaborative guidance method based on strategy fusion and differential game as claimed in claim 1, characterized in that: The step S4 comprises: S41, regard the strategy fusion scheme as the target escape strategy v1,v1,…,v N The resultant vector is expressed as: Among them, the modified weight coefficient ψ i (t) represents the missile's interest in the target, satisfying 0≤ψ i (t)≤1 and N is the number of missiles; S42, Definition is the distance interest function S r and the speed interest function S V The sum is expressed as: ψ i 1 (t) = S r +S v Formula (35) in, r i is the relative distance between the projectile and the target, r c is the escape radius of the target, V i is the speed of the ith missile, V T The speed of the target; S43, get the weight coefficient ψ i Specific representation of (t):

6. The decentralized collaborative guidance method based on strategy fusion and differential game as claimed in claim 1, characterized in that: The step S5 comprises: S51, assuming that the artificial potential field function is represented by U(x, y), and for each position in space, U(x, y) is differentiable, the force acting on the missile is the control force F(x, y) in the negative gradient direction of the artificial potential field function, expressed as: Among them, (x, y) represents the coordinates of the missile in the two-dimensional plane, Represents the gradient of U(x,y) at (x,y), and its direction is the direction of the maximum rate of change of the potential field at the coordinate (x,y); The artificial potential field function between missile i and missile j is U ij , which satisfies: Among them, r ij represents the distance between missiles, n represents the number of missiles involved in the coordinated operation, It means that missile i is controlled by the artificial potential field of missile j. It means that missile j is controlled by the artificial potential field of missile i, U i It represents the sum of the artificial potential field control forces exerted on missile i by other missiles; S52, artificial potential field function U determined by the relative distance between projectiles ij (r ij )for: Among them, the coefficient K r Adjust the potential field strength, r min is the minimum safety radius between missile i and missile j, r s is the anti-collision threshold, when r ij >r s When there is no artificial potential field between the bullets, when r ij →r min When U ij →∞; Combined with the artificial potential field control force, the control force F exerted on missile i in the potential field of missile j is ij (x i ,y i )for: Among them, (x i ,y i ) represents the coordinates of missile i in the two-dimensional plane. The control force on missile i and F i (x i ,y i )for: S53, control force F i The command acceleration u caused i 'for: Among them, m i is the mass of the missile, F ia is the control force F i Normal projection in velocity; Combined with the cooperative guidance law, the command acceleration of the missile is obtained as: u i ” = u i + u i ' Equation (43) Among them, u i is the normal control input perpendicular to the velocity direction of the i-th missile. min <r ij ≤r s When the missile is at u i and u i 'When flying under the simultaneous action of the two commands, when the two commands are equal in size but opposite in direction at a certain moment, the missile will fall into a local minimum state; S54, design a dynamic adjustment factor k based on the distance between bullets d To prevent the missile from falling into the local minimum: in, r dom is a random number, satisfying 0≤r dom ≤1, is the gain factor, and at the same time, -1<α d <1; After the improvement, the control force on missile i is: When in r min <r ij ≤r s When the missile is at u i and u i 'Flying under the action of i +u i When '=0, k d Start dynamic adjustment i ' value, when r ij ≤r min When the potential force is infinite, the command u i It doesn't work. The missile focuses on collision avoidance.

Images