Guidance control method based on particle optimization algorithm and differential game in tripartite game scene

Abstract

The invention discloses a guidance control method based on a particle optimization algorithm and a differential game in a tripartite game scene, which is based on the particle optimization algorithm and the differential game and combines the efficient global search capability of the particle optimization algorithm and the real-time decision capability of the differential game. And a more accurate and reliable solution is provided for guided missile guidance control in a tripartite game combat scene. Comprising the following steps: S1, building a missile six-degree-of-freedom model; s2, solving an optimal guidance strategy by a tripartite differential game problem; s2, introducing a particle optimization algorithm to iteratively update parameters of the three-loop autopilot in real time according to a performance index formula so as to track an optimal guidance strategy; and S4, missile strike simulation is carried out based on a particle optimization algorithm and a differential game guidance control method in a tripartite game combat scene. The method provides an efficient, reliable and accurate solution for guided missile guidance control in a tripartite game combat scene, and has important application value and prospect.

Description

Technical Field

[0001] The present invention belongs to the field of aerospace technology, and specifically relates to a guidance and control method based on a particle optimization algorithm and differential countermeasures in a three-party game combat scenario. Background Art

[0002] With the continuous advancement of aerospace technology and the continuous improvement of the comprehensive performance of aerospace weapons, intelligent air combat has become an inevitable trend of future development. In the evolution of intelligent air combat, various aircraft carrying anti-missile systems have emerged as key components of air power. This type of aircraft can effectively avoid missile strikes. In particular, on the battlefield of the future, there is likely to be a type of drone with an anti-missile system, which can launch defensive missiles to intercept our attack missiles to ensure the safety of the drone. For this kind of advanced armed drone with an anti-missile system, there is currently no good guidance and control method to allow missiles to bypass the anti-missile system and effectively attack armed drones. Early research on the application of game theory to missile guidance problems mainly focused on combat scenarios involving both parties. However, since the small missiles carried on the anti-UAV missile system need to avoid the interceptor missiles launched by the drone, the overload of the missile changes dramatically, which puts high demands on the rapid response of the controller. Therefore, it is of great research significance to address the fact that traditional game theory cannot be extended to three-party game combat scenarios and to improve the rapid response capability of missile controllers in three-party game combat scenarios. Summary of the invention

[0003] In order to overcome the shortcomings of the prior art, the present invention provides a guidance and control method based on particle optimization algorithm and differential countermeasures in a three-party game engagement scenario. Based on particle optimization algorithm and differential countermeasures, it combines the efficient global search capability of particle optimization algorithm and the real-time decision-making capability of differential countermeasures, and provides a more accurate and reliable solution for the guidance and control of missiles in a three-party game engagement scenario. The method includes the following steps: S1: building a six-degree-of-freedom model of a missile; S2: solving the optimal guidance strategy for a three-party differential game problem; S2: introducing a particle optimization algorithm to iteratively update the parameters of a three-loop autopilot in real time according to the performance indicator formula to track the optimal guidance strategy; S4: performing missile strike simulation based on the guidance and control method based on particle optimization algorithm and differential countermeasures in a three-party game engagement scenario. This method provides an efficient, reliable and accurate solution for the guidance and control of missiles in a three-party game engagement scenario, and has important application value and prospects.

[0004] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0005] Step 1: Build a six-degree-of-freedom model of the missile;

[0006] Step 2: Use the Riccati differential equation to solve the three-party differential game problem to obtain the optimal guidance strategy;

[0007] Step 3: Introduce a particle optimization algorithm to iteratively update the three-loop autopilot parameters in real time according to the performance indicator formula to track the optimal guidance strategy;

[0008] When the missile control method adopts STT, the pitch control and yaw control are decoupled, and the particle optimization algorithm is added to each for parameter adjustment. The roll control only needs to constrain its roll angle and roll angular velocity, and no additional particle optimization algorithm is needed.

[0009] Step 4: Conduct missile strike process based on particle optimization algorithm and differential game guidance and control method in a three-party game combat scenario;

[0010] Given the state parameters of the target, attack missile, and defense missile as input, and the state information of the UAV and the enemy's aerial target as input, the guidance and control method based on the particle optimization algorithm and differential countermeasures in the three-party game combat scenario automatically completes the guidance and control process of the attack missile hitting the target.

[0011] Furthermore, the step 1 is specifically as follows:

[0012] In the ground inertial coordinate system, the six-degree-of-freedom model of the missile is expressed by the following formula:

[0013]

[0014] (1) Where P is thrust, X, Y, and Z are aerodynamic forces, and M x ,M y ,M z are the aerodynamic moments, V, θ, ψ V are respectively the missile's speed, ballistic inclination, and ballistic deviation, ω x ,ω y ,ω z are the components of the angular velocity ω of the projectile coordinate system along each axis of the projectile coordinate system, ψ,γ are the missile's pitch angle, yaw angle, and roll angle, respectively; x, y, z are the position coordinates of the missile's center of mass, respectively; α, β, γ V are the missile’s attack angle, sideslip angle, and velocity roll angle, m is the missile’s mass, δ x ,δ y ,δ z ,δ p They are the three deflection angles of the missile and the engine adjustment parameters; G represents the acceleration of gravity; J x , J y , J z Respectively represent the missile's moment of inertia about each axis of the missile body coordinate system; mc It represents the mass consumption of the missile per unit time; ε1, ε2, ε3, and ε4 represent the errors of the guidance system respectively.

[0015] Furthermore, the step 2 is specifically as follows:

[0016] Step 2-1: Establish the target, defense missile and attack missile at 0≤t≤t f Kinematic model of engagement during combat;

[0017] Step 2-2: Consider the initial state of the dynamic system, construct the Hamiltonian function and calculate its partial derivative to obtain the necessary condition equation for the optimal solution;

[0018] Step 2-3: Obtain the Riccati differential equation based on the optimal solution necessary condition equation, define the state feedback gain matrix for the guidance command, and solve the Riccati differential equation to obtain the optimal guidance strategy.

[0019] Furthermore, in step 2-1, the target, the defense projectile and the attack projectile are established in the range of 0≤t≤t f The kinematic model of the engagement is as follows:

[0020]

[0021] where x i =(x i ,y i ,z i ) T is the position vector of vehicle i in the fixed axis; u i =(u i ,v i ,w i ) T is the velocity vector of vehicle i in the fixed axis; a i =(a xi ,a yi ,a zi ) T is the acceleration vector of vehicle i in the fixed axis.

[0022] Furthermore, in step 2-2, the necessary condition equation for the optimal solution is as follows:

[0023]

[0024] in is a positive definite matrix that defines the weights on the respective guidance inputs; y 31 =(x 31 ,u 31 ) T is the relative state vector between the attack missile 3 and the target 1, y 23 =(x 23,u 23 ) T is the relative state vector between the defense missile 2 and the attack missile 3; G' is the (6×3) input coefficient matrix; P i is the analytical solution of the Riccati differential equation, i=1,2.

[0025] Furthermore, in step 2-3, the Ricatti differential equation is as follows:

[0026]

[0027] Wherein, F represents the (12×12) state coefficient matrix.

[0028] Furthermore, the optimal guidance strategy is missile overload.

[0029] Furthermore, the step 3 is specifically as follows:

[0030] In the iterative update mechanism of the particle optimization algorithm based on the performance indicator formula, the speed of the new group is determined by three parts: The first part represents the influence of the speed of the corresponding previous generation on the speed of the current generation. The second part represents the influence of the optimal value of the previous generation of individuals on the current individual speed; The third part represents the influence of the optimal value of the previous generation group on the current particle speed. These three parts jointly determine the speed of the contemporary individual through linear addition, and the contemporary speed of the individual and the position of the previous generation of individuals are linearly added to jointly determine the contemporary individual position.

[0031] The coefficient ω of the first part of the iterative update mechanism of the particle optimization algorithm according to the performance index formula is called the inertia weight value; the coefficient of the second part consists of two values. The first one represents the degree of influence of the best position experienced by the individual particle on the position of the new generation population. This coefficient representing the degree is called the learning factor and is represented by c1, and the other is a random variable randomly and uniformly distributed in the range of [0 1] and is represented by r1; the coefficient composition of the third part is also composed of two parts, one represents the degree of influence of the best position experienced by the particle group on the position of the new generation population, which is also called the learning factor and is represented by c2, and the other is a random variable randomly and uniformly distributed in the range of [0 1] and is represented by r2;

[0032] The overshoot and adjustment time are added to the performance index formula of the particle optimization algorithm, and the performance index formula is expressed by the following formula:

[0033] itde=log(Ts / σ1)+log(sigma / σ2) (5)

[0034] Among them, Ts is the adjustment time, sigma is the overshoot, σ1 and σ2 are the coefficients of the adjustment time and overshoot respectively.

[0035] Furthermore, the three-loop autopilot is specifically:

[0036] The three-loop autopilot has an integral link in the front channel, which is equivalent to adding an angular velocity feedback loop, forming three feedback loops, thus making the autopilot a full-state feedback system; its formula is shown in equation (6), where e(t) represents the control deviation, K A , K g 、w i , K dc As the coefficient composed of it, K is converted into A , K g and w i As a gain to adjust the dynamic system performance, K dc Can be K A And the missile parameters are directly calculated, which is expressed by the following formula:

[0037]

[0038] Furthermore, the step 4 is specifically as follows:

[0039] Step 4-1: The guidance module receives the motion state information of the target, the defensive missile and the attack missile. The guidance module uses the three-party game combat scene information at that moment to solve the three-party differential game problem to obtain the optimal guidance strategy;

[0040] Step 4-2: The three-loop autopilot accepts the optimal guidance strategy under the initial control parameters to generate the maneuver control quantity of the attack missile, and provides it to the motion module; the motion module updates the state of the target, the defense missile and the attack missile at the next moment by solving the kinematic and dynamic equations of the target, the defense missile and the attack missile; at the same time, the autopilot accepts the optimal guidance strategy under the initial control parameters to generate the maneuver control quantity of the attack missile, and provides it to the control parameter setting module, and the control parameter setting module changes the control parameters of the three-loop autopilot at the next moment based on the performance indicator formula through the particle optimization algorithm; the updated state information is then provided to the guidance module, and the guidance module calculates the optimal guidance strategy, and this process is repeated to complete the missile strike process based on the guidance control method of the particle optimization algorithm and differential countermeasures in the three-party game battle scenario;

[0041] Step 4-3: Given the target, defense missile and attack missile motion state information as input, the guidance and control method based on particle optimization algorithm and differential countermeasures in the three-party game combat scenario automatically completes the guidance and control process of the attack missile hitting the target.

[0042] The beneficial effects of the present invention are as follows:

[0043] In order to solve the problem of guidance control of missiles attacking unmanned aerial vehicles carrying anti-missile systems in a three-party game engagement scenario, the present invention proposes a guidance control method based on particle optimization algorithm and differential countermeasures in a three-party game engagement scenario. First, a three-party game engagement scenario will be proposed. The three-party game engagement scenario includes a drone target, and when it realizes that it is being tracked by an attack missile, it launches a defense missile to intercept the attack missile and perform evasive actions. The role of the defense missile is only to intercept the incoming missile; on the other hand, the attack missile must perform a dual role, including avoiding the defense missile and intercepting its main target, namely the drone. Then consider the initial state of the dynamic system, construct the Hamiltonian function and take partial derivatives of it, and obtain the optimal solution necessary condition equation. According to the optimal solution necessary condition equation, the Riccati differential equation is obtained, and the Riccati differential equation is solved to obtain the optimal control overload. Finally, the particle optimization algorithm is introduced to adjust the controller parameters of the three-loop autopilot, and the controller parameters are optimized by the performance indicator formula based on the three-party game engagement scenario, and finally the attack missile in the three-party game engagement scenario can avoid the defense missile and intercept its main target, namely the drone. The method of the invention provides an efficient, reliable and accurate solution for the guidance and control of missiles in the three-party game engagement scenario, which has important application value and prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 The geometric relationship between the target, attack missile and defense missile;

[0045] Figure 2 is a structural diagram of the control method;

[0046] Figure 3 This is the open loop diagram for the autopilot;

[0047] Figure 4 It is a flowchart of air operations;

[0048] Figure 5 The overshoot of the step response of the three-loop autopilot changes with the number of iterations;

[0049] Figure 6 The step response curve of the three-loop autopilot changes with the number of iterations;

[0050] Figure 7 It is the altitude-longitudinal range diagram of the target, attack missile and defense missile;

[0051] Figure 8 It is the height-lateral range diagram of the target, attack missile and defense missile;

[0052] Fig. 9It is the horizontal range-vertical range diagram of the target, attack missile and defense missile;

[0053] Fig.10 It is a graph of the miss amount of the target, attack missile and defense missile. DETAILED DESCRIPTION

[0054] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0055] The present invention discloses a guidance and control method based on a particle optimization algorithm and a differential strategy in a three-party game scenario. The guidance and control method is based on the particle optimization algorithm and the differential strategy, and combines the efficient global search capability of the particle optimization algorithm and the real-time decision-making capability of the differential strategy, providing a more accurate and reliable solution for the guidance and control of missiles in a three-party game scenario. The guidance and control system realizes the rapid setting of the parameters of the three-loop autopilot through the particle optimization algorithm. At the same time, the introduction of the differential strategy enables the guidance and control system to have a stronger real-time decision-making capability.

[0056] According to the present invention, a guidance and control method based on a particle optimization algorithm and differential countermeasures in a three-party game battle scenario includes the following steps:

[0057] Step S1: build a missile six-degree-of-freedom model;

[0058] Step S2: Solve the optimal guidance strategy for the three-party differential game problem; the problem is solved using the Riccati differential equation;

[0059] Step S3: Introduce the particle optimization algorithm to iteratively update the three-loop autopilot parameters in real time according to the performance indicator formula to track the optimal guidance strategy; when the missile control method adopts STT, the pitch control and yaw control are decoupled, and the particle optimization algorithm can be added to each for parameter adjustment. For roll control, only the roll angle and roll angular velocity need to be constrained, and no additional particle optimization algorithm is needed;

[0060] Step S4: In a three-party game combat scenario, the guidance and control method based on the particle optimization algorithm and differential countermeasures is used to carry out the missile strike process; given the state parameters of the target, the attack missile, and the defense missile as input, and given the state information of the UAV and the enemy's air target as input, the guidance and control method based on the particle optimization algorithm and differential countermeasures in the three-party game combat scenario automatically completes the guidance and control process of the attack missile striking the target.

[0061] Specifically, in step S1, in the ballistic coordinate system, the missile six-degree-of-freedom model is constructed as represented by the following formula:

[0062]

[0063] Where P is thrust, X, Y, Z are aerodynamic forces, M x ,M y ,M z are the aerodynamic moments, V, θ, ψ V are respectively the missile's speed, ballistic inclination, and ballistic deviation, ω x ,ω y ,ω z They are the components of the angular velocity ω of the projectile coordinate system along each axis of the projectile coordinate system. ψ,γ are the missile's pitch angle, yaw angle, and roll angle, respectively; x, y, z are the position coordinates of the missile's center of mass, respectively; α, β, γ V They are respectively the angle of attack, sideslip angle, and velocity roll angle, m is the mass of the missile, δ x ,δ y ,δ z ,δ p They are the three deflection angles of the missile and the engine adjustment parameters.

[0064] In step S2, solving the optimal overload of the three-party differential game problem specifically includes:

[0065] S2.1. Establish the target, defense missile and attack missile in (0≤t≤t f ) when the combat kinematic model;

[0066] S2.2. Consider the initial state of the dynamic system, construct the Hamiltonian function and take its partial derivative to obtain the necessary condition equation for the optimal solution;

[0067] S2.3. Obtain the Riccati differential equation based on the necessary condition equation for the optimal solution, define the state feedback gain matrix for the guidance command, and solve the Riccati differential equation to obtain the optimal guidance strategy.

[0068] In step S2.1, the target, defense missile and attack missile are established in (0≤t≤t f ) is as follows:

[0069]

[0070] where x i =(x i ,y i ,z i ) T is the position vector of vehicle i in the fixed axis; u i =(u i ,v i ,w i ) T is the velocity vector of vehicle i in the fixed axis; a i =(a xi ,a yi,a zi ) T is the acceleration vector of vehicle i in the fixed axis.

[0071] In step S2.2, the necessary condition equation for the optimal solution is as follows:

[0072]

[0073] in is a positive definite matrix that defines the weights on the respective guidance inputs; y 31 =(x 31 ,u 31 ) T is the relative state vector between the attack missile 3 and the target 1, y 23 =(x 23 ,u 23 ) T is the relative state vector between the defense missile 2 and the attack missile 3; G is the (6×3) input coefficient matrix, P i Analytical solution to the Riccati differential equation.

[0074] In step S2.3, the Riccati differential equation is as follows:

[0075]

[0076] in is a positive definite matrix that defines the weights on the respective guidance inputs; G is a (6×3) input coefficient matrix, P i Analytical solution to the Riccati differential equation.

[0077] In step S2.3, the optimal guidance strategy is missile overload.

[0078] In the iterative update mechanism of the particle optimization algorithm in step S3 according to the performance indicator formula, the speed of the new group is determined by three parts: The first part represents the influence of the speed of the corresponding previous generation on the speed of the current generation. The second part represents the influence of the optimal value of the previous generation on the current individual speed. The third part represents the influence of the optimal value of the previous generation group on the current particle speed. These three parts jointly determine the speed of the contemporary individual through linear addition, and the contemporary speed of the individual and the position of the previous generation of individuals linearly add to determine the contemporary individual position.

[0079] First, the coefficient ω of the first part of the iterative update mechanism of the performance index formula of the particle optimization algorithm is called the inertia weight value. The coefficient of the second part consists of two values. The first one represents the degree of influence of the best position experienced by the individual particle on the position of the new generation population. This coefficient representing the degree is called the learning factor and is represented by c1. The other is a random variable randomly and uniformly distributed in the range of [0 1] and is represented by r1. The coefficient composition of the third part is also composed of two parts. One represents the degree of influence of the best position experienced by the particle group on the position of the new generation population. It is also called the learning factor and is represented by c2. The other is a random variable randomly and uniformly distributed in the range of [0 1] and is represented by r2.

[0080] Secondly, the overshoot and adjustment time are added to the performance index formula of the particle optimization algorithm. The performance index formula is expressed by the following formula:

[0081] itde=log(Ts / σ1)+log(sigma / σ2) (12)

[0082] Among them, Ts is the adjustment time, sigma is the overshoot, σ1 and σ2 are the coefficients of the adjustment time and overshoot respectively.

[0083] In step S3, the open-loop diagram of the autopilot has an integral link in the front channel, which is equivalent to adding an angular velocity feedback loop, forming three feedback loops, thus making the autopilot a full-state feedback system. Its formula is shown in formula (13), where K A , K g 、w i , K dc As the coefficient composed of it, K is converted into A , K g and w i As a gain, it is used to adjust the dynamic system performance. dc Can be K A And the missile parameters are directly calculated, which is expressed by the following formula:

[0084]

[0085] In step S4, the missile strike process based on the particle optimization algorithm and the guidance and control method of differential game in the three-party game battle scenario is as follows:

[0086] First, the guidance module receives the motion status information of the target, the defensive missile and the attack missile. The guidance module uses the information of the three-party game battle scene at that moment to solve the three-party differential game problem to obtain the optimal guidance strategy.

[0087] Subsequently, the three-loop autopilot accepts the optimal guidance strategy under the initial control parameters to generate the maneuver control quantity of the attack missile, and provides it to the motion module; the motion module updates the state of the target, the defense missile and the attack missile at the next moment by solving the kinematic and dynamic equations of the target, the defense missile and the attack missile; at the same time, the autopilot accepts the optimal guidance strategy under the initial control parameters to generate the maneuver control quantity of the attack missile, and provides it to the control parameter setting module, which changes the control parameters of the three-loop autopilot at the next moment based on the performance indicator formula through the particle optimization algorithm; the updated state information is then provided to the guidance module, and the guidance module calculates the optimal guidance strategy, and this process is repeated to complete the missile strike process based on the guidance and control method of the particle optimization algorithm and differential countermeasures in the three-party game combat scenario;

[0088] Finally, given the target, defense missile and attack missile motion state information as input, the guidance and control method based on particle optimization algorithm and differential countermeasures in the three-party game combat scenario automatically completes the guidance and control process of the attack missile hitting the target.

[0089] Example:

[0090] A guidance and control method based on particle optimization algorithm and differential game in a three-party game scenario:

[0091] Step 1: Build a six-degree-of-freedom model of the missile;

[0092] Step 2: Use the three-party differential game problem to solve the optimal guidance strategy;

[0093] Step 3: Introduce a particle optimization algorithm to iteratively update the three-loop autopilot parameters in real time according to the performance indicator formula to track the optimal guidance strategy;

[0094] Step 4: In the three-party game scenario, the missile strike process is carried out based on the guidance and control method of particle optimization algorithm and differential game.

[0095] In step 1, in the ground inertial coordinate system, the six-degree-of-freedom model of the missile is expressed by the following formula:

[0096]

[0097] Where P is thrust, X, Y, and Z are aerodynamic forces, and M is x ,M y ,M z are the aerodynamic moments, V, θ, ψ V are respectively the missile's speed, ballistic inclination, and ballistic deviation, ω x ,ω y ,ω z are the components of the angular velocity ω of the projectile coordinate system along each axis of the projectile coordinate system, ψ,γ are the missile's pitch angle, yaw angle, and roll angle, respectively; x, y, z are the position coordinates of the missile's center of mass, respectively; α, β, γ V They are respectively the angle of attack, sideslip angle, and velocity roll angle, m is the mass of the missile, δ x ,δ y ,δ z ,δ p They are the three deflection angles of the missile and the engine adjustment parameters.

[0098] In step 2, Figure 1 The geometric relationship between the target, the attack missile and the defense missile is given. The kinematic model of the three-party game engagement is considered and the definition of the kinematic variables is given. The differential equations of the position, velocity and acceleration of the aircraft i (i = 1, 2, 3 in this mathematical model) can be written as:

[0099]

[0100] where x i =(x i ,y i ,z i ) T is the position vector of vehicle i in the fixed axis; u i =(u i ,v i ,w i ) T is the velocity vector of vehicle i in the fixed axis; a i =(a xi ,a yi ,a zi ) T is the acceleration vector of vehicle i in the fixed axis.

[0101] Simplifying (16), we get the state space expression as follows:

[0102]

[0103] According to the above formula, the relative kinematic equation between aircraft i and j can be obtained:

[0104]

[0105] where x ij =x i -x j is the relative position vector of aircraft i and j. ij =u i -u j is the relative velocity vector of aircraft i and j. I is the (3×3) identity matrix; and i≠j.

[0106] For the current problem, assume that when the attacking missile engages the target, the target is labeled j = 1 and the attacking missile is labeled i = 3. For the engagement between the attacking missile and the defending missile, the attacking missile is labeled j = 3 and the defending missile is labeled i = 2. In this case, the following relative kinematic states are of interest:

[0107] 1, the state of attack missile 3 relative to target 1 is (x 31 ,u 31 ), the acceleration instructions are given by (a3, a1) respectively. Here a1 includes the escape strategy executed by target 1 a3 includes the pursuit strategy executed by attacker 3

[0108] 2, the states of defense bullet 2 relative to attack bullet 3 are (x 23 ,u 23 ), the acceleration instructions are (a2, a3). Here a3 includes the evasion strategy executed by attacker 3 a2 includes the pursuit strategy executed by defender 2

[0109] Obviously, a1 only includes the evasive maneuver of target 1 A2 only includes the pursuit maneuver of defense missile 2 to intercept attack missile 3 On the other hand, the attack missile a3 is designed to avoid defender 2 and intercept target 1, so a3 includes and therefore

[0110] According to formula (3.3), attack missile 3 and target 1, defense missile 2 and attack missile 3 are in (0≤t≤t f ) can be expressed as follows: f The end time of the battle)

[0111]

[0112] Write them in the following forms:

[0113]

[0114] where y 31 =(x 31 ,u 31 ) T is the relative state vector between the attack missile 3 and the target 1. 23 =(x 23 ,u 23 ) Tis the relative state vector between the defense missile 2 and the attack missile 3. F is the state coefficient matrix. G is the (6×3) input coefficient matrix.

[0115] In step 2, the three-party differential game problem is solved. Consider the initial state of the dynamic system as: y 31 (t0) = y 31 (0),y 23 (t0) = y 23 (0), a scalar quadratic performance indicator (PI):

[0116]

[0117] Where [S1,S2] is the semi-positive definite matrix of the final state weights. [Q1,Q2] is the semi-positive definite matrix of the current state weights. is a positive definite matrix that defines the weights on the respective guidance inputs.

[0118] In order to obtain the optimal solution, the Hamiltonian function is constructed as follows:

[0119]

[0120] Taking partial derivatives of the Hamiltonian function, we can obtain the necessary conditions for the optimal solution, and the solution can be expressed as:

[0121]

[0122] In step 2, the Riccati differential equation is solved. According to the above equation, the Riccati differential equation is as follows

[0123]

[0124] Consider its characteristics Q i =0;S i =diag[s,s,s,0,0,0], where i=1,2 and R 31 =r 31 I; R 23 =r 23 I; the analytical solution obtained is the remaining time function, as shown below:

[0125]

[0126] in:

[0127]

[0128] It is found in formula (23) that the given optimal guidance input consists of state feedback, that is, it contains the state (y 31 ,y 23 ), the state feedback gain matrix is ​​defined for the guidance command as follows:

[0129]

[0130] in:

[0131]

[0132] In step 3, Figure 2 The structure diagram of the control method. When the missile control method adopts STT, the pitch control and yaw control are decoupled, and the particle optimization algorithm can be added to each for parameter tuning. For roll control, only the roll angle and roll angular velocity need to be constrained, and no additional particle optimization algorithm is needed. In practical applications, the three-loop autopilot algorithm loop should be used as the main loop, and the parameter setter accepts the difference between the required overload and the actual overload, and this part of the difference is processed by the parameter setter to become the corresponding evaluation parameter. Based on the corresponding evaluation parameters, the particle algorithm is used to optimize, and finally the adjusted parameters are output.

[0133] The mathematical model for constructing the particle optimization algorithm is as follows:

[0134] The particle swarm optimization algorithm is a typical one among the swarm intelligence optimization algorithms. Scholars were inspired by the natural process of how birds hunt, and thus evolved it into an optimization algorithm. Each bird in the flock communicates with other birds in the group to exchange information to update its flight speed and location, gradually approaching the vicinity of food to find the location of food. Researchers corresponded individuals in the flock to particles, bird groups to particle groups, the law of the bird flock's search for food to iterative evolution formula (29), and each particle in the bird flock's search for food to a feasible solution to the problem to be optimized. The initialized particle group is randomly generated within the range of the specified feasible solution. It can be seen from formula (29) that in its iterative update mechanism, the speed of the new group is jointly determined by three parts: The first part represents the influence of the speed of the corresponding previous generation on the speed of the current generation. The second part represents the influence of the optimal value of the previous generation on the current individual speed. The third part represents the influence of the optimal value of the previous generation group on the current particle speed. These three parts jointly determine the speed of the contemporary individual through linear addition, and the contemporary speed of the individual and the position of the previous generation of individuals linearly add to determine the contemporary individual position.

[0135]

[0136] The coefficient ω of the first part in formula (29) is called the inertia weight value. The coefficient of the second part consists of two values. The first one represents the degree of influence of the best position experienced by the individual particle on the position of the new generation population. This coefficient representing the degree is called the learning factor and is represented by c1. The other is a random variable randomly and uniformly distributed in the range of [0 1] and is represented by r1. The coefficient composition of the third part also consists of two parts. One represents the degree of influence of the best position experienced by the particle group on the position of the new generation population. It is also called the learning factor and is represented by c2. The other is a random variable randomly and uniformly distributed in the range of [0 1] and is represented by r2.

[0137] In the iterative update mechanism of the PSO algorithm, it can be seen that the speed of the new generation of population is jointly affected by three parts. The position of the new generation of population is composed of the linear addition of the position of the previous generation of population and the speed of the new generation of population. Therefore, the most important thing in its iterative update mechanism is to determine the speed of the new generation of population, and the influence of the three parts of the speed is determined by their respective coefficients. Among them, the learning factor plays a greater role in multi-dimensional problems. In low-dimensional problems, it is usually set to a fixed value according to the experimental results of predecessors. Therefore, the parameter setter designed in this paper sets the inertia weight value to 1, c1, c2 are both 2, and v i The initial value is 0.

[0138] In addition to the basic settings for the particle optimization algorithm, the parameter setter also needs to select appropriate performance indicators to ensure the optimization quality, which comes from the main technical indicators determined when designing the controller. Therefore, overshoot and adjustment time are added to the performance indicator formula. The performance indicator formula is shown in (4.3).

[0139] itde=log(Ts / σ1)+log(sigma / σ2) (30)

[0140] Among them, Ts is the adjustment time, sigma is the overshoot, σ1 and σ2 are the coefficients of the adjustment time and overshoot respectively.

[0141] Figure 3 For the open-loop diagram of the autopilot, the mathematical model of the particle optimization algorithm is constructed as follows:

[0142] Its front channel has an integral link, which is equivalent to adding an angular velocity feedback loop, forming three feedback loops, thus making the autopilot a full-state feedback system. Its formula is shown in formula (31), where K A , K g 、w i , K dc As the coefficient composed of it, K is converted into A , K g and wi As a gain, it is used to adjust the dynamic system performance. dc Can be K A And the missile parameters are calculated directly.

[0143]

[0144] In step S4, Figure 4 The figure is a flowchart of air combat. The whole air combat process is divided into four parts: the motion module under the three-party game engagement scenario, the autopilot control module, the guidance module based on differential game under the three-party game engagement scenario, and the parameter setting module based on particle optimization algorithm. First, the guidance module receives the motion state information of the target, the defense missile and the attack missile. The guidance module uses the three-party game engagement scenario information at this moment to solve the three-party differential game problem to obtain the optimal guidance strategy. Subsequently, the three-loop autopilot accepts the optimal guidance strategy under the initial control parameters to generate the maneuver control quantity of the attack missile and provides it to the motion module. The motion module updates the state of the target, the defense missile and the attack missile at the next moment by solving the kinematic and dynamic equations of the target, the defense missile and the attack missile. At the same time, the autopilot accepts the optimal guidance strategy under the initial control parameters to generate the maneuver control quantity of the attack missile and provides it to the control parameter setting module. The control parameter setting module changes the control parameters of the three-loop autopilot at the next moment based on the performance indicator formula through the particle optimization algorithm. The updated status information is then provided to the guidance module, which calculates the optimal guidance strategy. This process is repeated to complete the missile strike process in a three-party game scenario using a guidance and control method based on a particle optimization algorithm and differential countermeasures.

[0145] In order to better evaluate the proposed guidance and control method, a simulation experiment was carried out on the guidance and control method proposed in this paper. Figure 5 This is the curve showing the overshoot of the step response of the three-loop autopilot changing with the number of iterations. Figure 6 The step response curve of the three-loop autopilot changes with the number of iterations. After ten iterations of particle optimization algorithm, the final system steady-state value under the three-loop autopilot parameters is 1.0026, the system overshoot is 0%, the system does not have peak time, and the system adjustment time is 0.03s. A is 694.9507, w i is 21.0914, K g It is 909.7346.

[0146] Figure 7 It is the height-longitudinal range diagram of the target, attack missile and defense missile. Figure 8 It is the height-lateral range diagram of the target, attack missile and defense missile. Fig. 9The horizontal range-longitudinal range diagram of the target, attack missile, and defense missile. In these diagrams, the trajectory of the target is displayed as a "solid line", the trajectory of the attack missile is displayed as a "dotted line", and the trajectory of the defense missile is displayed as a "dotted line". The (circle, asterisk) in the diagram represents the closest distance between the attack missile and the target, and the (square, asterisk) represents the closest distance between the attack missile and the defense missile.

[0147] from Figure 7-Figure 9 The characteristic behaviors of the target (solid line trajectory), the attack missile (dashed line trajectory) and the defense missile (dotted line trajectory) can be seen in the figure. After flying for a period of time, the attack missile successfully avoided the defense missile launched by the drone and successfully hit the drone.

[0148] Fig.10 It is the miss distance diagram of the target, attack missile and defense missile. Fig.10 As shown. Among them, Miss31 is the miss distance between the attacking missile and the target, and Miss23 is the miss distance between the defensive missile and the attacking missile. The figure shows that at 7.53 seconds, Miss23 is 28.45 meters, which indicates that the attacking missile successfully avoided the defensive missile when it first encountered the defensive missile. The first miss distance of 61 meters between the attacking missile and the target occurred at 9.67 seconds. This shows that the target has safely avoided the attacking missile in the first encounter. In order to avoid the defensive missile, the attacker changed his tracking trajectory and therefore failed to successfully intercept the target. From Fig.10 It can be further seen in Figure 1 that the attack projectile approached the target in the subsequent engagement; however, the closest distance was 0.4m, at which point it was considered to have hit the target.

Claims

1. A guidance and control method based on particle optimization algorithm and differential game in a three-party game scenario, characterized in that: The steps include: Step 1: Build a six-degree-of-freedom model of the missile; Step 2: Use the Riccati differential equation to solve the three-party differential game problem to obtain the optimal guidance strategy; Step 3: Introduce a particle optimization algorithm to iteratively update the three-loop autopilot parameters in real time according to the performance indicator formula to track the optimal guidance strategy; When the missile control method adopts STT, the pitch control and yaw control are decoupled, and the particle optimization algorithm is added to each for parameter adjustment. The roll control only needs to constrain its roll angle and roll angular velocity, and no additional particle optimization algorithm is needed. Step 4: Conduct missile strike process based on particle optimization algorithm and differential game guidance and control method in a three-party game combat scenario; Given the state parameters of the target, attack missile, and defense missile as input, and the state information of the UAV and the enemy's aerial target as input, the guidance and control method based on the particle optimization algorithm and differential countermeasures in the three-party game combat scenario automatically completes the guidance and control process of the attack missile hitting the target.

2. According to claim 1, a guidance and control method based on particle optimization algorithm and differential game in a three-party game battle scenario is characterized in that: The step 1 is specifically as follows: In the ground inertial coordinate system, the six-degree-of-freedom model of the missile is expressed by the following formula: Where P is thrust, X, Y, Z are aerodynamic forces, M x ,M y ,M z are the aerodynamic moments, V, θ, ψ V are respectively the missile's speed, ballistic inclination, and ballistic deviation, ω x ,ω y ,ω z are the components of the angular velocity ω of the projectile coordinate system along each axis of the projectile coordinate system, are the missile's pitch angle, yaw angle, and roll angle, respectively; x, y, and z are the position coordinates of the missile's center of mass, α, β, and γ are V are the missile’s attack angle, sideslip angle, and velocity roll angle, m is the missile’s mass, δ x ,δ y ,δ z ,δ p They are the three deflection angles of the missile and the engine adjustment parameters; G represents the acceleration of gravity; J x , J y , J z Respectively represent the missile's moment of inertia about each axis of the missile body coordinate system; m c It represents the mass consumption of the missile per unit time; ε1, ε2, ε3, and ε4 represent the errors of the guidance system respectively.

3. According to claim 2, the guidance and control method based on particle optimization algorithm and differential game in a three-party game battle scenario is characterized in that: The step 2 is specifically as follows: Step 2-1: Establish the target, defense missile and attack missile at 0≤t≤t f Kinematic model of engagement during combat; Step 2-2: Consider the initial state of the dynamic system, construct the Hamiltonian function and calculate its partial derivative to obtain the necessary condition equation for the optimal solution; Step 2-3: Obtain the Riccati differential equation based on the optimal solution necessary condition equation, define the state feedback gain matrix for the guidance command, and solve the Riccati differential equation to obtain the optimal guidance strategy.

4. According to claim 3, the guidance and control method based on particle optimization algorithm and differential game in a three-party game battle scenario is characterized in that: In step 2-1, the target, defense missile and attack missile are established at 0≤t≤t f The kinematic model of the engagement is as follows: where x i =(x i ,y i ,z i ) T is the position vector of vehicle i in the fixed axis; u i =(u i ,v i ,w i ) T is the velocity vector of aircraft i in the fixed axis; a i =(a xi ,a yi ,a zi ) T is the acceleration vector of vehicle i in the fixed axis.

5. According to claim 4, the guidance and control method based on particle optimization algorithm and differential game in a three-party game battle scenario is characterized in that: In step 2-2, the necessary condition equation for the optimal solution is as follows: in is a positive definite matrix that defines the weights on the respective guidance inputs; y 31 =(x 31 ,u 31 ) T is the relative state vector between the attack missile 3 and the target 1, y 23 =(x 23 ,u 23 ) T is the relative state vector between the defense missile 2 and the attack missile 3; G' is the (6×3) input coefficient matrix; P i is the analytical solution of the Riccati differential equation, i=1,2.

6. According to claim 5, a guidance and control method based on particle optimization algorithm and differential game in a three-party game battle scenario is characterized in that: In step 2-3, the Riccati differential equation is as follows: Wherein, F represents the (12×12) state coefficient matrix.

7. The guidance and control method based on particle optimization algorithm and differential game in a three-party game battle scenario according to claim 6 is characterized in that: The optimal guidance strategy is missile overload.

8. The guidance and control method based on particle optimization algorithm and differential game in a three-party game battle scenario according to claim 7 is characterized in that: The step 3 is specifically as follows: In the iterative update mechanism of the particle optimization algorithm based on the performance indicator formula, the speed of the new group is determined by three parts: The first part represents the influence of the speed of the corresponding previous generation on the speed of the current generation. The second part represents the influence of the optimal value of the previous generation of individuals on the current individual speed; The third part represents the influence of the optimal value of the previous generation group on the current particle speed. These three parts jointly determine the speed of the contemporary individual through linear addition, and the contemporary speed of the individual and the position of the previous generation of individuals are linearly added to jointly determine the contemporary individual position. The coefficient ω of the first part of the iterative update mechanism of the particle optimization algorithm according to the performance index formula is called the inertia weight value; the coefficient of the second part consists of two values. The first one represents the degree of influence of the best position experienced by the individual particle on the position of the new generation population. This coefficient representing the degree is called the learning factor and is represented by c1, and the other is a random variable randomly and uniformly distributed in the range of [0 1] and is represented by r1; the coefficient composition of the third part is also composed of two parts, one represents the degree of influence of the best position experienced by the particle group on the position of the new generation population, which is also called the learning factor and is represented by c2, and the other is a random variable randomly and uniformly distributed in the range of [0 1] and is represented by r2; The overshoot and adjustment time are added to the performance index formula of the particle optimization algorithm, and the performance index formula is expressed by the following formula: itde=log(Ts / σ1)+log(sigma / σ2) (5) Among them, Ts is the adjustment time, sigma is the overshoot, σ1 and σ2 are the coefficients of the adjustment time and overshoot respectively.

9. The guidance and control method based on particle optimization algorithm and differential game in a three-party game battle scenario according to claim 8 is characterized in that: The three-loop autopilot is specifically: The front channel of the three-loop autopilot has an integral link, which is equivalent to adding an angular velocity feedback loop, forming three feedback loops, thus making the autopilot a full-state feedback system; The formula is shown in formula (6), where e(t) represents the control deviation, K A , K g 、w i , K dc As the coefficient composed of it, K is converted into A , K g and w i As a gain to adjust the dynamic system performance, K dc Can be K A And the missile parameters are directly calculated, which is expressed by the following formula:

10. The guidance and control method based on particle optimization algorithm and differential game in a three-party game battle scenario according to claim 9 is characterized in that: The step 4 is specifically as follows: Step 4-1: The guidance module receives the motion state information of the target, the defensive missile and the attack missile. The guidance module uses the three-party game combat scene information at that moment to solve the three-party differential game problem to obtain the optimal guidance strategy; Step 4-2: The three-loop autopilot accepts the optimal guidance strategy under the initial control parameters to generate the maneuver control quantity of the attack missile, and provides it to the motion module; the motion module updates the state of the target, the defense missile and the attack missile at the next moment by solving the kinematic and dynamic equations of the target, the defense missile and the attack missile; at the same time, the autopilot accepts the optimal guidance strategy under the initial control parameters to generate the maneuver control quantity of the attack missile, and provides it to the control parameter setting module, and the control parameter setting module changes the control parameters of the three-loop autopilot at the next moment based on the performance indicator formula through the particle optimization algorithm; the updated state information is then provided to the guidance module, and the guidance module calculates the optimal guidance strategy, and this process is repeated to complete the missile strike process based on the guidance control method of the particle optimization algorithm and differential countermeasures in the three-party game battle scenario; Step 4-3: Given the target, defense missile and attack missile motion state information as input, the guidance and control method based on particle optimization algorithm and differential countermeasures in the three-party game combat scenario automatically completes the guidance and control process of the attack missile hitting the target.

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