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

Abstract

The application discloses a guidance control method based on a particle optimization algorithm and a differential game in a three-party game combat scene, which combines the efficient global search capability of the particle optimization algorithm and the real-time decision capability of the differential game, and provides a more accurate and reliable solution for the guidance control of a missile in the three-party game combat scene.The method comprises the following steps: S1, establishing a six-degree-of-freedom model of the missile; S2, solving an optimal guidance strategy for a three-party differential game problem; S3, introducing a particle optimization algorithm to iteratively update three-loop autopilot parameters according to a performance index formula to track the optimal guidance strategy; and S4, performing a missile strike simulation based on the guidance control method based on the particle optimization algorithm and the differential game in the three-party game combat scene.The method provides an efficient, reliable and accurate solution for the guidance control of the missile in the three-party game combat scene, and has important application value and prospect.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of aerospace, and particularly relates to a guidance control method based on a particle optimization algorithm and a differential game in a three-party game combat scenario. BACKGROUND

[0002] With the continuous progress of aerospace technology and the continuous improvement of the comprehensive performance of aerospace weapons, air combat intelligence has become an inevitable trend of future development. In the evolution process of air combat intelligence, various aircraft carrying anti-missile systems have emerged as key components of air power, which can effectively avoid missile strikes. In particular, in future battlefields, there may be a type of unmanned aerial vehicle with an anti-missile system, which can launch defense missiles to intercept our attack missiles to ensure the safety of the unmanned aerial vehicle. For this kind of advanced armed unmanned aerial vehicle with an anti-missile system, there is currently no good guidance control method to let the missile bypass the anti-missile system to effectively attack the armed unmanned aerial vehicle. Early application of game theory in the study of missile guidance problems mainly focuses on two-party combat scenarios. However, due to the small missiles carried on the anti-UAV missile system, they need to avoid the interception of the missiles launched by the UAV, so the overload of the missile changes dramatically, and the rapid response of the controller is also required. Therefore, it is of great research significance to extend the traditional game theory to the three-party game combat scenario and improve the rapid response capability of the missile controller in the three-party game combat scenario. SUMMARY

[0003] In order to overcome the shortcomings of the prior art, the application provides a guidance control method based on a particle optimization algorithm and a differential game in a three-party game combat scenario, which combines the high global search capability of the particle optimization algorithm and the real-time decision capability of the differential game, and provides a more accurate and reliable solution for the guidance control of the missile in the three-party game combat scenario. The method comprises the following steps: S1: building a six-degree-of-freedom model of the missile; S2: solving the optimal guidance strategy of the three-party differential game problem; S2: introducing a particle optimization algorithm to iteratively update the three-loop autopilot parameters according to the performance index formula in real time to track the optimal guidance strategy; S4: simulating the missile attack based on the guidance control method based on the particle optimization algorithm and the differential game in the three-party game combat scenario. The method provides an efficient, reliable and accurate solution for the guidance control of the missile in the three-party game combat scenario, and has important application value and prospect.

[0004] The technical solution adopted by the application to solve its technical problems is as follows:

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

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

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

[0008] In the case of STT missile control mode, the pitch control and yaw control are decoupled, and the particle optimization algorithm is added for parameter setting, and the roll control only needs to constrain the roll angle and roll angular velocity, without additional particle optimization algorithm;

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

[0010] Given the target, attack missile, and defense missile state parameters as inputs, and given the state information of unmanned aerial vehicles and enemy air targets as inputs, the guidance control process of the attack missile against the target is automatically completed by the guidance control method based on the particle optimization algorithm and the differential game in the three-party game combat scenario.

[0011] Further, the step 1 is specifically:

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

[0013]

[0014] In the formula, P is the thrust, X, Y, and Z are the aerodynamic forces, M x , M y , and M z are the aerodynamic moments, V, θ, and ψ V are the speed, trajectory inclination angle, and trajectory deflection angle of the missile, ω x , ω y , and ω z are the components of the body coordinate system rotation angular velocity ω along the body coordinate system axes, ψ, and γ are the pitch angle, yaw angle, and roll angle of the missile, x, y, and z are the position coordinates of the missile mass center, α, β, and γ V are the attack angle, side slip angle, and speed roll angle of the missile, m is the mass of the missile, δ x , δ y , δ z , and δ p are the three deflection angles and engine adjustment parameters of the missile; G represents the gravitational acceleration; J x , J y , and J z are the moments of inertia of the missile about the body coordinate system axes; m crepresents the mass consumption of the missile in unit time; ε1, ε2, ε3, ε4 represent errors of the guidance system respectively.

[0015] Further, the step 2 is specifically:

[0016] Step 2-1: establishing a combat kinematics model of the target, the defense missile and the attack missile in 0≤t≤t f ;

[0017] Step 2-2: considering the initial state of the dynamic system, constructing a Hamilton function and deriving partial derivatives to obtain necessary condition equations of the optimal solution;

[0018] Step 2-3: obtaining Riccati differential equations according to the necessary condition equations of the optimal solution, defining a state feedback gain matrix for the guidance instruction, and solving the Riccati differential equations to obtain an optimal guidance strategy.

[0019] Further, the combat kinematics model of the target, the defense missile and the attack missile in 0≤t≤t f established in the step 2-1 is as follows:

[0020]

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

[0022] Further, the necessary condition equations of the optimal solution in the step 2-2 are as follows:

[0023]

[0024] wherein P is a positive definite matrix, defining weights on respective guidance inputs; y 31 =(x 31 ,u 31 ) T is a relative state vector between the attack missile 3 and the target 1, y 23 =(x 23 ,u23 ) T is the relative state vector between the defense missile 2 and the attacking missile 3; G' is a (6x3) input coefficient matrix; P i is the analytical solution of Riccati differential equation, i = 1, 2.

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

[0026]

[0027] wherein F represents a (12x12) state coefficient matrix.

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

[0029] Further, the step 3 is specifically:

[0030] In the iterative updating mechanism of the performance index formula of the particle optimization algorithm, the speed of the new population is determined by three parts is the first part, which represents the influence of the speed of the corresponding last generation individual on the speed of the current generation individual; is the second part, which represents the influence of the optimal value of the last generation individual on the speed of the current individual; is the third part, which represents the influence of the optimal value of the last generation population on the speed of the current particle; the three parts are linearly added to determine the speed of the current individual, and the speed of the current individual and the position of the last generation individual are linearly added to determine the position of the current individual;

[0031] The coefficient ω of the first part in the iterative updating 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 particle individual on the position of the new generation population, and the coefficient representing the degree is called the learning factor, denoted by c1, and the other is a random variable uniformly distributed in the range of [0 1], denoted by r1; the coefficient of the third part also consists of two parts, one represents the degree of influence of the best position experienced by the particle swarm on the position of the new generation population, which is also called the learning factor, denoted by c2, and the other is a random variable uniformly distributed in the range of [0 1], denoted by r2;

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

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

[0034] Wherein, Ts is the regulation time, sigma is the overshoot, sigma1, sigma2 are the coefficients of the regulation time and the overshoot respectively.

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

[0036] The previous channel of the three-loop autopilot has an integral element, which is equivalent to adding an angular velocity feedback loop, forming three feedback loops, so that the autopilot becomes a full-state feedback system; the formula is shown as formula (6), wherein e(t) represents the control deviation, K A , K g , w i , K dc are the coefficients formed by the three coefficients and the deviation in the formula, and K A , K g and w i are used as gains to adjust the dynamic system performance, and K dc can be directly calculated from K A and the missile parameters, which is represented by the following formula:

[0037]

[0038] Further, the step 4 is specifically:

[0039] Step 4-1: The guidance module receives the target, defense missile and attack missile motion state information, and the guidance module obtains the optimal guidance strategy by solving the three-party differential game problem based on the three-party game combat scene information at this moment;

[0040] Step 4-2: The three-loop autopilot receives the optimal guidance strategy under the initial control parameters to generate the attack missile's maneuvering control quantity, and provides it to the motion module; the motion module updates the next moment state of the target, defense missile and attack missile by solving the kinematics and dynamics equations of the target, defense missile and attack missile; at the same time, the autopilot receives the optimal guidance strategy under the initial control parameters to generate the attack missile's maneuvering control quantity, and provides it to the control parameter setting module, which changes the next moment control parameters of the three-loop autopilot based on the performance index formula through the particle optimization algorithm; the updated state information is then provided to the guidance module, which calculates the optimal guidance strategy, and the process is repeated to complete the guidance control method based on the particle optimization algorithm and differential countermeasure for the missile attack process in the three-party game combat scene;

[0041] Step 4-3: Realize that the given target, defense missile and attack missile motion state information is input, and the guidance control method based on the particle optimization algorithm and differential countermeasure in the three-party game combat scene automatically completes the guidance control process of the attack missile attacking the target.

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

[0043] In order to solve the problem of missile attack on unmanned aerial vehicle with anti-missile system in a three-party game combat scenario, the present application proposes a guidance control method based on particle optimization algorithm and differential game in a three-party game combat scenario. Firstly, a three-party game combat scenario is proposed. The three-party game combat scenario includes an unmanned aerial vehicle target, which launches a defense missile to intercept the attack missile and performs an evasion action when it realizes that it is being tracked by an attack missile. 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 evading the defense missile and intercepting its main target - the unmanned aerial vehicle. Then, considering the initial state of the dynamic system, the Hamilton function is constructed and its partial derivative is obtained to get the necessary condition equation of the optimal solution. According to the necessary condition equation of the optimal solution, the Riccati differential equation is obtained, and the optimal control overload is solved. Finally, the particle optimization algorithm is introduced to adjust the controller parameters of the three-loop autopilot, and the controller parameters are optimized based on the performance index formula in the three-party game combat scenario, so as to realize the evasion of the attack missile from the defense missile and the interception of the main target - the unmanned aerial vehicle. The method of the present application provides an efficient, reliable and accurate solution for the guidance control of missiles in a three-party game combat scenario, and has important application value and prospect. BRIEF DESCRIPTION OF DRAWINGS

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

[0045] Figure 2 The structure diagram of the control method;

[0046] Figure 3 The open-loop diagram of the autopilot;

[0047] Figure 4 The flow chart of air combat;

[0048] Figure 5 The overshoot variation curve of the three-loop autopilot step response with iteration number;

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

[0050] Figure 7 The height-longitudinal range diagram of the target, the attack missile and the defense missile;

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

[0052] Figure 9Target, attacking projectile, and defense projectile lateral range-longitudinal range plot;

[0053] Figure 10 Target, attacking projectile, and defense projectile miss distance plot. DETAILED DESCRIPTION

[0054] The application is further illustrated below in conjunction with the accompanying drawings and examples.

[0055] The application discloses a guidance control method based on a particle optimization algorithm and a differential game in a three-party game combat scenario.

[0056] According to the guidance control method based on the particle optimization algorithm and the differential game in the three-party game combat scenario, the following steps are included:

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

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

[0059] Step S3: introduce a particle optimization algorithm to iteratively update three-loop autopilot parameters according to a performance index formula to track the optimal guidance strategy in real time; in the case where the missile control mode adopts STT, the pitch control and the yaw control are decoupled, and the particle optimization algorithm can be added for parameter setting, and on the roll control, only the roll angle and the roll angular velocity need to be constrained, and the particle optimization algorithm does not need to be additionally added;

[0060] Step S4: perform a missile attack process based on the guidance control method based on the particle optimization algorithm and the differential game in the three-party game combat scenario; given target, attacking projectile, and defense projectile state parameters as inputs, and given unmanned aerial vehicle and enemy aerial target state information as inputs, the guidance control method based on the particle optimization algorithm and the differential game in the three-party game combat scenario automatically completes a guidance control process of the attacking projectile attacking the target.

[0061] Specifically, in step S1, the missile six-degree-of-freedom model is built in a trajectory coordinate system and is represented by the following formula:

[0062]

[0063] Where P is the thrust force, X, Y, Z are the aerodynamic forces, M x ,M y ,M z are the aerodynamic moments, V, θ, ψ V are the velocity, the trajectory inclination angle, the trajectory deflection angle of the missile, ω x ,ω y ,ω z are the components of the rotation angular velocity ω of the missile body coordinate system along the axes of the missile body coordinate system ψ, γ are the pitch angle, the yaw angle, the roll angle of the missile, x, y, z are the position coordinates of the mass center of the missile, α, β, γ V are the attack angle, the side slip angle, the velocity roll angle, m is the mass of the missile, δ x ,δ y ,δ z ,δ p are the three deflection angles of the missile and the engine adjustment parameters.

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

[0065] S2.1. establishing the engagement kinematics model of the target, the defense missile and the attack missile at (0≤t≤t f );

[0066] S2.2. considering the initial state of the dynamic system, constructing the Hamilton function and taking the partial derivative to obtain the necessary condition equation of the optimal solution;

[0067] S2.3. obtaining the Riccati differential equation according to the necessary condition equation of the optimal solution, defining the state feedback gain matrix for the guidance instruction, and solving the Riccati differential equation to obtain the optimal guidance strategy.

[0068] The engagement kinematics model of the target, the defense missile and the attack missile at (0≤t≤t f ) established in step S2.1 is as follows:

[0069]

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

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

[0072]

[0073] wherein is a positive definite matrix which defines the weight on the respective guidance input; G is a (6x3) input coefficient matrix, P 31 = (x 31 , u 31 ) T is the relative state vector between the attacking missile 3 and the target 1, y 23 = (x 23 , u 23 ) T is the relative state vector between the defending missile 2 and the attacking missile 3; G is a (6x3) input coefficient matrix, P i is the analytical solution of Riccati differential equation.

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

[0075]

[0076] wherein is a positive definite matrix which defines the weight on the respective guidance input; G is a (6x3) input coefficient matrix, P i is the analytical solution of Riccati differential equation.

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

[0078] In step S3, the velocity of the new population in the iterative updating mechanism of the performance index formula of the particle optimization algorithm is determined by three parts is the first part, which represents the influence of the velocity of the corresponding last generation individual on the velocity of the current generation individual. is the second part, which represents the influence of the optimal value of the last generation individual on the velocity of the current individual, is the third part, which represents the influence of the optimal value of the last generation population on the velocity of the current particle. The three parts are jointly determined by linear addition to determine the velocity of the current individual, and the current position of the individual and the position of the last generation individual are linearly added to jointly determine the position of the current individual.

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

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

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

[0082] Where Ts is the regulation time, sigma is the overshoot, and σ1, σ2 are the coefficients of the regulation time and the overshoot, respectively.

[0083] In step S3, the autopilot open-loop diagram, which has an integral element in the front channel, is equivalent to adding an angular velocity feedback loop, forming three feedback loops, so that the autopilot becomes a full-state feedback system. Its formula is shown in formula (13), where K A , K g , w i , K dc are the coefficients composed of K A , K g and w i as gains to adjust the performance of the dynamic system. And K dc can be directly calculated from K A and missile parameters, which is represented by the following formula:

[0084]

[0085] In step S4, the guidance control method based on particle optimization algorithm and differential game in the three-party game combat scene is as follows:

[0086] First, the guidance module receives the target, defense missile and attack missile motion state information, and the guidance module obtains the optimal guidance strategy by solving the three-party differential game problem based on the three-party game combat scene information at this moment;

[0087] Subsequently, the three-loop autopilot receives the optimal guidance strategy under the initial control parameters to generate the attack missile's maneuvering control quantity and provides it to the motion module; the motion module updates the next time state of the target, defense missile and attack missile by solving the kinematics and dynamics equations of the target, defense missile and attack missile; at the same time, the autopilot receives the optimal guidance strategy under the initial control parameters to generate the attack missile's maneuvering control quantity and provides it to the control parameter setting module, and the control parameter setting module changes the next time control parameters of the three-loop autopilot based on the performance index 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, so as to complete the missile attack process based on the particle optimization algorithm and differential game in the three-party game combat scenario.

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

[0089] Embodiment:

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

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

[0092] Step 2: use a 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 according to the performance index formula to track the optimal guidance strategy in real time;

[0094] Step 4: perform the missile attack process based on the particle optimization algorithm and the differential game in the three-party game combat scenario.

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

[0096]

[0097] In the formula, P is the thrust, X, Y and Z are the aerodynamic forces, M x , M y , M z are the aerodynamic moments, V, θ and ψ V are the velocity, trajectory inclination angle and trajectory deflection angle of the missile, ω x , ω y , ω z are the components of the body coordinate system rotation angular velocity ω along the body coordinate system axes, respectively. ψ, γ are the pitch, yaw, and roll angles of the missile, x, y, z are the position coordinates of the missile's center of mass, α, β, γ V are 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 are the three deflection angles of the missile and the engine adjustment parameters.

[0098] In step 2, Figure 1 is the target, attack missile, and defense missile engagement geometry. The three-party game engagement kinematics model will be considered, and the definition of kinematics variables is given. The differential equations of position, velocity, and acceleration of vehicle i (in this mathematical model i = 1, 2, 3) 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] Simplify (16) to get its state space expression as follows:

[0102]

[0103] According to the above formula, the relative kinematics equation between vehicles i and j can be obtained

[0104]

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

[0106] For the current problem, assume that the target is labeled j = 1 and the attacking missile is labeled i = 3 when the two engage. 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 relative kinematic states of interest are:

[0107] 1. The state of the attacking missile 3 relative to the target 1 is (x 31 , u 31 ), with acceleration commands given by (a3, a1), respectively. Here a1 includes the evasion strategy performed by the target 1 a3 includes the pursuit strategy performed by the attacking missile 3

[0108] 2. The state of the defending missile 2 relative to the attacking missile 3 is (x 23 , u 23 ), with acceleration commands given by (a2, a3), respectively. Here a3 includes the evasion strategy performed by the attacking missile 3 a2 includes the pursuit strategy performed by the defending missile 2

[0109] Clearly, a1 includes only the evasion maneuver of the target 1 while a2 includes only the pursuit maneuver of the defending missile 2 to intercept the attacking missile 3 On the other hand, the attacking missile a3 is designed to avoid the defending missile 2 and to intercept the target 1, so a3 includes both and Thus

[0110] According to equation (18), the engagement kinematic models of the attacking missile 3 with the target 1 and the defending missile 2 with the attacking missile 3 at (0 < t < t f ) can be expressed in the following forms, respectively: (t f is the termination time of the engagement)

[0111]

[0112] which can be written in the following forms, respectively:

[0113]

[0114] where y 31 = (x 31 , u 31 ) T is the relative state vector between the attacking missile 3 and the target 1. y 23 = (x 23 , u 23 ) TThe relative state vector between the defense missile 2 and the attacking missile 3. F is the state coefficient matrix. G is the (6x3) input coefficient matrix.

[0115] In Step 2, the three-party differential game problem is solved. The initial state of the dynamic system is considered to be: 31 (t0) = y 31 (0), y 23 (t0) = y 23 (0), a scalar quadratic performance index (PI):

[0116]

[0117] Where [S1, S2] is a positive semi-definite matrix of the final state weight. [Q1, Q2] is a positive semi-definite matrix of the current state weight. is a positive definite matrix, which defines the weight on each guidance input.

[0118] To obtain its optimal solution, the Hamilton function is constructed as follows:

[0119]

[0120] The partial derivative of the Hamilton function is obtained, and the necessary condition for the optimal solution is obtained. 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 obtained as follows

[0123]

[0124] Consider the special case 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 obtained analytical solution is a function of the remaining time, as follows:

[0125]

[0126] Where:

[0127]

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

[0129]

[0130] wherein:

[0131]

[0132] In step 3, Figure 2 is the structure diagram of the control method. In the case of STT missile control mode, the pitch control and yaw control are decoupled, and the particle optimization algorithm can be added respectively for parameter tuning. The roll control only needs to constrain the roll angle and roll angular velocity, and does not need to add the particle optimization algorithm. In practical application, the three-loop autopilot algorithm loop should be used as the main loop, and the parameter tuner accepts the difference between the required overload and the actual overload, and this part of the difference is processed by the parameter tuner to become the corresponding evaluation parameter. Based on the corresponding evaluation parameter, the particle algorithm is optimized, and finally the tuned parameters are output.

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

[0134] Particle swarm optimization algorithm is a typical one in swarm intelligence optimization algorithm. Scholars have been inspired by the natural process of how birds hunt, and have developed it into an optimization algorithm. Each bird in the bird flock exchanges information with other birds in the group to update its flight speed and location, gradually approaching the vicinity of food to find the location of food. Researchers correspond the individuals in the bird flock to particles, the bird flock to particle swarm, and the rules in the bird flock to find food to the iterative evolution formula (29). Each particle in the bird flock corresponds to a feasible solution to the optimization problem. The initialized particle swarm is randomly generated within the specified feasible solution range. As can be seen from formula (29), in its iterative updating mechanism, the speed of the new population is determined by three parts The first part is the influence of the corresponding individual speed of the previous generation on the speed of the current generation. The second part is the influence of the optimal value of the previous generation on the speed of the current generation, The third part is the influence of the optimal value of the previous population on the speed of the current particle. The three parts are linearly added to determine the speed of the current individual, and the linear addition of the current speed of the individual and the position of the previous generation of individuals determines the position of the current individual.

[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, which is called the learning factor and is denoted by c1, and the other is a random variable uniformly distributed in the range of [0 1] and denoted by r1, the coefficient of the third part also consists of two parts, one represents the degree of influence of the best position experienced by the particle swarm on the position of the new generation population, which is also called the learning factor and is denoted by c2, and the other is a random variable uniformly distributed in the range of [0 1] and denoted by r2.

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

[0138] In addition to the basic settings of the particle optimization algorithm, the parameter tuner 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 regulation time are added to the performance indicator formula. The performance indicator formula is shown in formula (30).

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

[0140] Where Ts is the regulation time, sigma is the overshoot, and σ1, σ2 are the coefficients of the regulation time and the overshoot, respectively.

[0141] Figure 3 The mathematical model of the particle optimization algorithm is constructed for the open-loop diagram of the automatic pilot as follows:

[0142] It has an integral element in the front channel, which is equivalent to adding an angular velocity feedback loop, forming three feedback loops, so that the pilot becomes a full-state feedback system. The formula is shown in formula (31), where K A , K g , w i , K dc are the coefficients composed of them, and K A , K g and wi K is used as a gain to adjust the performance of the dynamic system. dc It can be made by K A The missile parameters are calculated directly.

[0143]

[0144] In step S4, Figure 4 This is a flowchart of the air combat process. The entire air combat process is divided into four parts: a motion module in a three-way game scenario, an autopilot control module, a guidance module based on differential game theory in a three-way game scenario, and a parameter tuning module based on particle optimization algorithm. First, the guidance module receives motion state information from the target, defensive missile, and attack missile. Using the information from the three-way game scenario at that moment, the guidance module solves a three-way differential game problem to obtain the optimal guidance strategy. Subsequently, the three-loop autopilot, under initial control parameters, receives the optimal guidance strategy to generate the maneuver control input for the attack missile and provides it to the motion module. The motion module updates the states of the target, defensive missile, and attack missile at the next moment by solving the kinematic and dynamic equations. Simultaneously, the autopilot, under initial control parameters, receives the optimal guidance strategy to generate the maneuver control input for the attack missile and provides it to the control parameter tuning module. The control parameter tuning module uses a particle optimization algorithm based on performance index formulas to change the control parameters of the three-loop autopilot at the next moment. 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 based on the guidance and control method of particle optimization algorithm and differential game in a three-way game scenario.

[0145] To better evaluate the proposed guidance and control method, simulation experiments were conducted on the proposed guidance and control method. Figure 5 The curve shows the overshoot of the step response of a three-loop autopilot as a function of the number of iterations. Figure 6 The graph shows the step response curve of the three-loop autopilot as a function of iterations. Through ten iterations of the particle optimization algorithm, the final steady-state value of the three-loop autopilot system under the calculated parameters is 1.0026, the system overshoot is 0%, there is no peak time, and the system settling time is 0.03 s. Where K... A The value is 694.9507, w i K is 21.0914. g The value is 909.7346.

[0146] Figure 7 Altitude-longitudinal range chart for target, attack missile, and defense missile. Figure 8 Altitude-lateral range chart for target, attack, and defense missiles. Figure 9Target, attacking projectile, and defending projectile lateral-range versus longitudinal-range plots, in which the trajectory of the target is shown as a "solid line", the trajectory of the attacking projectile is shown as a "dashed line", and the trajectory of the defending projectile is shown as a "dotted line". The (circles, asterisks) in the figure indicate the closest distance between the attacking projectile and the target, and the (boxes, asterisks) indicate the closest distance between the attacking projectile and the defending projectile.

[0147] From Figures 7-9 the characteristic behavior of the target (solid line trajectory), the attacking projectile (dashed line trajectory), and the defending projectile (dotted line trajectory) can be seen. The attacking projectile successfully evades the defending projectile launched by the UAV and successfully hits the UAV after flying for some time.

[0148] Figure 10 Miss distance plot for the target, attacking projectile, and defending projectile. Projected miss distances are shown as Figure 10 . Miss 31 is the miss distance between the attacking projectile and the target, and Miss 23 is the miss distance between the defending projectile and the attacking projectile. This figure shows that at 7.53 seconds, Miss 23 is 28.45 meters, which indicates that the attacking projectile successfully evades the defending projectile at the first encounter. The first miss distance between the attacking projectile and the target, 61 meters, occurs at 9.67 seconds. This indicates that the target has safely evaded the attacking projectile at the first encounter. The attacking projectile changes its pursuit trajectory in order to evade the defending projectile, and thus fails to successfully intercept the target. From Figure 10 it can be further seen that the attacking projectile approaches the target in subsequent engagements; however, the closest distance is 0.4 m, at which time the target is considered to be hit.

Claims

1. A guidance and control method based on particle optimization algorithm and differential game in a three-way game scenario, characterized in that, Includes the following steps: Step 1: Build a six-degree-of-freedom model of the missile; Step 2: Solve the three-party differential game problem using the Riccati differential equation to obtain the optimal guidance strategy; Step 2-1: Establish the target, defensive missiles, and offensive missiles in the condition 0≤t≤t f Engagement kinematics model; Step 2-2: Consider the initial state of the dynamic system, construct the Hamiltonian function and take its partial derivatives to obtain the necessary condition equation for the optimal solution; The necessary equation for the optimal solution is as follows: in It is a positive definite matrix, defining the weights on each guidance input; y 31 =(x 31 ,u 31 ) T Let y be the relative state vector between missile 3 and target 1. 23 =(x 23 ,u 23 ) T G is the relative state vector between defensive missile 2 and attack missile 3; G is the (6×3) input coefficient matrix; P i Let i be the analytical solution to the Riccati differential equation, i = 1, 2; Steps 2-3: 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. Step 3: Introduce the particle optimization algorithm to iteratively update the parameters of the three-loop autopilot in real time according to the performance index formula to track the optimal guidance strategy; When the missile control method adopts STT, pitch control and yaw control are decoupled and parameter tuning is performed by adding particle optimization algorithms. Roll control only needs to constrain its roll angle and roll angular velocity, and no additional particle optimization algorithm is needed. Overshoot and settling time are incorporated into the performance metric formula for the particle optimization algorithm, which is expressed by the following formula: itde=log(Ts / σ1)+log(sigma / σ2) (5) Where Ts is the settling time, sigma is the overshoot, and σ1 and σ2 are the coefficients of the settling time and the overshoot, respectively; Step 4: Conduct missile strike process based on particle optimization algorithm and differential game guidance control method in a three-way game scenario; Given the state parameters of the target, attack missile, and defense missile as input, and the state information of the UAV and enemy aerial targets as input, the guidance and control method based on particle optimization algorithm and differential game in a three-way game scenario automatically completes the guidance and control process of the attack missile striking the target.

2. The guidance and control method based on particle optimization algorithm and differential game in a three-way game scenario according to claim 1, characterized in that, Step 1 specifically involves: In the ground inertial coordinate system, the six-degree-of-freedom model of the missile can be represented by the following formula: In the formula, P is the thrust, X, Y, and Z are the aerodynamic forces, and M is the thrust. x M y M z These are the aerodynamic torques, V, θ, and ψ, respectively. V These are the missile's velocity, trajectory inclination angle, and trajectory deflection angle, respectively, ω x ,ω y ,ω z Let ω represent the components of the angular velocity ω along each axis of the missile's coordinate system, θ, ψ, and γ represent the missile's pitch, yaw, and roll angles, respectively, and x, y, and z represent the position coordinates of the missile's center of mass, α, β, and γ. V These represent the missile's angle of attack, sideslip angle, and roll angle, respectively, where m is the missile's mass, and δ is the missile's velocity roll angle. x ,δ y ,δ z ,δ p These represent the missile's three deflection angles and engine adjustment parameters; G represents gravitational acceleration; J... x J y J z These represent the moments of inertia of the missile about each axis of the missile's coordinate system; m c ε1 represents the mass loss of the missile per unit time; ε2, ε3, and ε4 represent the errors of the guidance system, respectively.

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

4. The guidance and control method based on particle optimization algorithm and differential game in a three-way game scenario according to claim 3, characterized in that, In steps 2-3, the Riccati differential equation is as follows: Where F represents a (12×12) state coefficient matrix.

5. The guidance and control method based on particle optimization algorithm and differential game in a three-way game scenario according to claim 4, characterized in that, The optimal guidance strategy is missile overload.

6. The guidance and control method based on particle optimization algorithm and differential game in a three-way game scenario according to claim 5, characterized in that, Step 3 specifically involves: In the iterative update mechanism of the particle optimization algorithm based on the performance index formula, the velocity of the new population is determined by three factors. The first part represents the influence of the speed of the previous generation on the speed of the current generation. The second part represents the impact of the previous generation's optimal value on the current individual's speed; The third part represents the influence of the previous generation's optimal value on the current particle's velocity; these three parts are linearly added together to determine the velocity of the current individual, and the current individual's velocity and the position of the previous generation's individual are linearly added together to determine the current individual's position. The particle optimization algorithm uses an iterative update mechanism based on the performance index formula. The coefficient ω in the first part is called the inertia weight value. The coefficient in the second part consists of two values. The first value 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 denoted by c1. The other value is a random variable that is randomly and uniformly distributed in the range of [0 1] and is denoted by r1. The coefficient in the third part also consists of two parts. One value represents the degree of influence of the best position experienced by the particle swarm on the position of the new generation population. This value is also called the learning factor and is denoted by c2. The other value is a random variable that is randomly and uniformly distributed in the range of [0 1] and is denoted by r2.

7. The guidance and control method based on particle optimization algorithm and differential game in a three-way game scenario according to claim 6, characterized in that, The three-loop autopilot specifically refers to: The front channel of the three-loop autopilot has an integral element, 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, and K A K g w i K dc The coefficients formed by these coefficients are used to compose K using the combination of the three coefficients and the deviation in the formula. A K g and w i K is used as a gain to adjust the performance of a dynamic system. dc It can be made by K A The missile parameters are directly calculated and expressed by the following formula:

8. The guidance and control method based on particle optimization algorithm and differential game in a three-way game scenario according to claim 7, characterized in that, Step 4 specifically involves: Step 4-1: The guidance module receives the motion status information of the target, defensive missile and attack missile. The guidance module uses the information of the three-party game battle scenario at this moment to solve the three-party differential game problem to obtain the optimal guidance strategy. Step 4-2: Under initial control parameters, the three-loop autopilot receives the optimal guidance strategy to generate the maneuver control input of the attack missile and provides it to the motion module. The motion module updates the state of the target, the defensive missile, and the attack missile at the next moment by solving the kinematic and dynamic equations. Simultaneously, under initial control parameters, the autopilot receives the optimal guidance strategy to generate the maneuver control input of the attack missile and provides it to the control parameter tuning module. The control parameter tuning module changes the control parameters of the three-loop autopilot at the next moment based on the performance index formula using a particle optimization algorithm. The updated state information is then provided to the guidance module, which calculates the optimal guidance strategy. This process is repeated to complete the missile strike process based on the guidance control method of particle optimization algorithm and differential game in a three-way game scenario. Step 4-3: Given the motion state information of the target, defensive missile, and attack missile, the guidance and control method based on particle optimization algorithm and differential game in a three-way game scenario automatically completes the guidance and control process of the attack missile striking the target.

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