A space-time guidance-decision-making integrated control method and system based on distributed optimization

Abstract

This application discloses a distributed optimization-based space-time guidance-decision-making integrated control method and system, relating to the field of space-time guidance. The method includes establishing a dynamic model for each missile and determining the remaining flight time of each missile; determining a space-time-constrained distributed guidance law for each missile based on a preset convergence time coordinated by the dynamic model, the remaining flight time, and the missile group time; determining a distributed optimization problem for determining the expected terminal line-of-sight angle based on the remaining flight time; determining an angle decision protocol for each missile based on the preset convergence time of the angle decision, the distributed optimization problem for the expected terminal line-of-sight angle, the remaining flight time, and the expected terminal line-of-sight angle; determining a space-time guidance decision-making integrated control protocol for each missile based on the angle decision protocol and the space-time-constrained distributed guidance law, and controlling the normal acceleration and expected terminal line-of-sight angle of each missile based on the control protocol. This application improves the attack effectiveness of the missile group.

Description

Technical Field

[0001] The present application relates to the field of space-time guidance, and in particular to a space-time guidance-decision-making integrated control method and system based on distributed optimization. Background Art

[0002] With the development of modern defense technology, multi-constrained guidance missions require not only spatial and temporal constraints but also the coordinated efforts of multiple aircraft. Therefore, traditional proportional guidance laws are unable to meet these complex guidance requirements. Collaborative guidance technology, a combination of complex network systems and aircraft guidance and control, can aggregate the limited capabilities of individual missiles, giving swarms more powerful and complex guidance capabilities. Collaborative guidance not only overcomes the limitations of individual missiles in terms of damage and detection, but also increases the group's hit probability, enhances saturation attack effectiveness, and expands the kill range. This technology holds significant academic research significance and engineering application value.

[0003] Spatiotemporal constraint collaborative guidance not only considers the spatiotemporal constraints of individual missiles but also the collaborative tasks of missile groups. Chen designed a multi-stage distributed guidance law and used the integral sliding mode technology to design a distributed guidance law, so that simultaneous impact can be achieved under the condition of topology switching, and angle constraints can be achieved by using fixed-time sliding mode control and augmented proportional guidance law. Dong proposed an angle guidance law in vector form and proved that the trajectory generated by the basic guidance law does not change with speed. Then, the distributed time constraint guidance law is obtained according to the remaining flight time, and finally the result is applied to the spatiotemporal constraint guidance task under aerodynamic drag constraints. Zhang designed an actual control law based on the integral sliding mode based on the distributed time error, and used the preset time technology to design the line of sight normal guidance law to achieve spatiotemporal constraints. Tao analyzed the trajectory length based on the angle guidance law under the relative motion model, predicted the remaining flight time, and designed a collaborative time guidance law according to a specific optimal problem.

[0004] While these studies consider collaborative missions and spatiotemporal constraints, the desired angle is often given in advance. Considering the terminal line-of-sight angle decision is crucial in the collaborative guidance process. If the expected impact angle of a multi-missile system is unreasonable, it can lead to large initial timing errors, potentially causing the failure of the time-sensitive collaborative mission. Furthermore, while some desired angles meet the required impact angle spacing for a multi-missile system, these angles may result in extended flight times. This increased flight time increases energy consumption and reduces the efficiency of quick-acting missions. The desired angle decision problem in a multi-missile system can be formulated as a multivariable optimization problem. Distributed optimization methods can effectively determine the desired terminal line-of-sight angle that minimizes flight time, subject to the constraints of the required terminal angle spacing. In summary, the problem of integrated spatiotemporal guidance and decision-making design based on distributed optimization remains an open question. Summary of the Invention

[0005] The purpose of this application is to provide a space-time guidance-decision-making integrated control method and system based on distributed optimization, which improves the attack effectiveness of the missile group by controlling the normal acceleration and expected terminal line of sight angle of multiple missiles.

[0006] To achieve the above objectives, this application provides the following solutions:

[0007] In a first aspect, the present application provides a spatiotemporal guidance-decision-making integrated control method based on distributed optimization, comprising:

[0008] Build a dynamic model for each missile in the swarm striking a stationary target and determine the remaining flight time of each missile;

[0009] Determining a space-time-constrained distributed guidance law for each missile based on a dynamic model of each missile in the swarm striking a stationary target, the remaining flight time of each missile, and a preset convergence time for swarm time coordination; the space-time-constrained distributed guidance law is a normal acceleration;

[0010] Determining a distributed optimization problem for the desired terminal sight angle based on the remaining flight time of each missile and the desired terminal sight angle of each missile; the desired terminal sight angle being the sight angle at the end of guidance;

[0011] Determining an angle decision protocol for each missile based on a distributed optimization problem of a preset convergence time for the angle decision and the desired terminal sight angle;

[0012] Based on the angle decision protocol of each missile and the space-time constrained distributed guidance law of each missile, the space-time guidance decision integrated control protocol of each missile is determined, and the normal acceleration and expected terminal line of sight angle of each missile are controlled based on the space-time guidance decision integrated control protocol of each missile.

[0013] In a second aspect, the present application provides a spatiotemporal guidance-decision-making integrated control system based on distributed optimization, comprising:

[0014] The dynamic model establishment and remaining flight time determination module is used to establish the dynamic model of each missile in the missile group striking a stationary target and determine the remaining flight time of each missile;

[0015] a space-time constraint distributed guidance law determination module, connected to the dynamics model establishment and remaining flight time determination module, for determining the space-time constraint distributed guidance law for each missile in the swarm based on the dynamics model of each missile striking a stationary target, the remaining flight time of each missile, and a preset convergence time coordinated with the swarm time; the space-time constraint distributed guidance law is a normal acceleration;

[0016] a distributed optimization problem determination module, connected to the dynamic model establishment and remaining flight time determination and time-space constraint distributed guidance law determination modules, for determining a distributed optimization problem of an expected terminal sight angle based on the remaining flight time of each missile and the expected terminal sight angle of each missile; the expected terminal sight angle is the sight angle at the end of guidance;

[0017] An angle decision protocol determination module is connected to the distributed optimization problem determination module and the dynamic model establishment and remaining flight time determination module, and is used to determine the angle decision protocol of each missile based on the distributed optimization problem of the preset convergence time of the angle decision and the desired terminal line of sight angle;

[0018] The space-time guidance decision integrated control module is connected to the angle decision protocol determination module and the space-time constraint distributed guidance law determination module. It is used to determine the space-time guidance decision integrated control protocol of each missile based on the angle decision protocol of each missile and the space-time constraint distributed guidance law of each missile, and control the normal acceleration and expected terminal line of sight angle of each missile based on the space-time guidance decision integrated control protocol of each missile.

[0019] According to the specific embodiments provided in this application, this application has the following technical effects:

[0020] The present application provides a space-time guidance-decision-making integrated control method and system based on distributed optimization. First, by adjusting the parameters in the dynamic model, the requirements of mission changes can be quickly adapted to improve the flexibility of the guidance-decision-making integrated control method; second, through the space-time constraint distributed guidance law of each missile, the normal acceleration is adjusted so that the missiles in a multi-missile group can achieve space-time coordinated strikes on stationary targets; third, through the distributed optimization problem of the expected terminal sight angle, the time for all missiles to arrive at the target together is consistent and helps to shorten the arrival time of the missile group; then, through the angle decision protocol of each missile, the expected terminal sight angle is adjusted to improve the strike effect; finally, through the space-time guidance decision integrated control protocol of each missile, the normal acceleration and expected terminal sight angle of each missile are controlled, thereby improving the attack effectiveness of multiple missiles from multiple aspects. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0022] Figure 1 This is an application environment diagram of a spatiotemporal guidance-decision-making integrated control method based on distributed optimization in one embodiment of the present application;

[0023] Figure 2 A schematic flow chart of a spatiotemporal guidance-decision-making integrated control method based on distributed optimization provided in one embodiment of the present application;

[0024] Figure 3 A guidance geometry diagram of the i-th missile and a stationary target in a spatiotemporal guidance-decision-making integrated control method based on distributed optimization provided in one embodiment of the present application;

[0025] Figure 4 This is a diagram showing the missile trajectory simulation results using the spatiotemporal guidance-decision-making integrated control method provided in one embodiment of the present application;

[0026] Figure 5 This is a diagram showing the simulation results of missile sight angle decision and tracking curve using the spatiotemporal guidance-decision-making integrated control method provided in one embodiment of the present application;

[0027] Figure 6 This is a diagram showing the simulation results of a missile sight rate curve using a spatiotemporal guidance-decision-making integrated control method provided in one embodiment of the present application;

[0028] Figure 7 This is a simulation result diagram of a missile lead angle curve using a spatiotemporal guidance-decision-making integrated control method provided in one embodiment of the present application;

[0029] Figure 8 This is a simulation result diagram of the remaining flight time curve of a missile using the time-space guidance-decision-making integrated control method provided in one embodiment of the present application.

[0030] Figure 9 This is a simulation result diagram of the normal acceleration curve of a missile using the spatiotemporal guidance-decision-making integrated control method provided in one embodiment of the present application;

[0031] Figure 10 This is a simulation result diagram of the adaptive gain curves of multiple missiles using the spatiotemporal guidance-decision-making integrated control method provided in one embodiment of the present application;

[0032] Figure 11 This is a diagram showing trajectory simulation results for a comparison group without the spatiotemporal guidance-decision-making integrated control method provided in an embodiment of the present application;

[0033] Figure 12 A diagram showing the remaining flight time simulation results for a comparison group without the spatiotemporal guidance-decision-making integrated control method provided in one embodiment of the present application;

[0034] Figure 13 A schematic diagram of the functional modules of a spatiotemporal guidance-decision-making integrated control system based on distributed optimization provided in one embodiment of the present application. DETAILED DESCRIPTION

[0035] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0036] In order to make the purpose, features and advantages of this application more obvious and easy to understand, this application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0037] The time-space guidance-decision-making integrated control method based on distributed optimization provided in the embodiment of the present application can be applied to Figure 1 In the application environment shown, the terminal 102 communicates with the server 104 via a network. The data storage system can store data that the server 104 needs to process. The data storage system can be set up separately, integrated on the server 104, or placed on the cloud or other servers. Terminal 102 can send dynamic model parameters to server 104. After receiving the dynamic model parameters, server 104 establishes a dynamic model for each missile in the swarm striking a stationary target and determines the remaining flight time of each missile. Based on the dynamic model for each missile in the swarm striking a stationary target, the remaining flight time of each missile, and a preset convergence time for the swarm time coordination, server 104 determines a time-space-constrained distributed guidance law for each missile. Based on the remaining flight time of each missile and the desired terminal line-of-sight angle of each missile, server 104 determines a distributed optimization problem for the desired terminal line-of-sight angle. Based on the preset convergence time for the angle decision and the distributed optimization problem for the desired terminal line-of-sight angle, server 104 determines an angle decision protocol for each missile. Based on the angle decision protocol for each missile and the time-space-constrained distributed guidance law for each missile, server 104 determines an integrated time-space guidance decision control protocol for each missile, and controls the normal acceleration and desired terminal line-of-sight angle of each missile based on the control protocol. Server 104 can provide feedback to terminal 102 on the obtained normal acceleration and desired terminal line-of-sight angle of each missile. In addition, in some embodiments, the spatiotemporal guidance-decision-making integrated control method based on distributed optimization can also be implemented by the server 104 or the terminal 102 alone.

[0038] Terminal 102 may include, but is not limited to, various desktop computers, laptops, smartphones, tablet computers, IoT devices, and portable wearable devices. IoT devices may include smart speakers, smart TVs, smart air conditioners, and smart car devices. Portable wearable devices may include smart watches, smart bracelets, and head-mounted devices. Server 104 may be implemented as a standalone server or a server cluster consisting of multiple servers, or may be a cloud server.

[0039] In an exemplary embodiment, Figure 2 As shown, a time-space guidance-decision-making integrated control method based on distributed optimization is provided. The method is executed by a computer device, specifically a computer device such as a terminal or a server, or a terminal and a server. In the embodiment of the present application, the method is applied to Figure 1 The server 104 in the example is used as an example to illustrate the process, including the following steps 201 to 205.

[0040] Step 201: Establish a dynamic model for each missile in the swarm to strike a stationary target, and determine the remaining flight time of each missile.

[0041] The process of establishing the dynamic model of the i-th missile attacking a stationary target is as follows: the guidance geometry diagram of the i-th missile and the stationary target is as follows: Figure 3 As shown. Among them, (X, Y) represents the inertial coordinate system, M i is the i-th missile in the group, M1 is the first missile in the group, v1 is the speed of the first missile, is the Nth in the group f missiles, For Nth f The speed of a missile.

[0042] Based on the guidance geometry of the i-th missile and the stationary target, the dynamic model of the i-th missile hitting the stationary target is obtained as follows:

[0043]

[0044] Among them, λ i is the sight angle of the i-th missile, R i is the distance between the i-th missile and the target, γ i is the yaw angle of the i-th missile, σ i is the lead angle of the i-th missile, v i is the speed of the i-th missile, a i is the normal acceleration of the i-th missile, is the first-order derivative of the yaw angle of the i-th missile, is the first-order derivative of the missile-target distance of the i-th missile, The first derivative of the sight angle of the i-th missile, is the first-order derivative of the lead angle of the i-th missile, i=1,2,...,N f ,σ i =γ i -λ i .

[0045] Step 202 determines a distributed guidance law with space-time constraints for each missile in the swarm based on the dynamic model of each missile striking a stationary target, the remaining flight time of each missile, and the preset convergence time for swarm time coordination. The distributed guidance law with space-time constraints is the normal acceleration. The preset convergence time for swarm time coordination is the time point at which all missiles in the swarm are expected to arrive at the target simultaneously.

[0046] In an exemplary embodiment of the present application, step 202 is replaced by the following steps 301 to 303:

[0047] Step 301: Based on the dynamic model of each missile in the missile group attacking a stationary target, determine the optimal guidance law for each missile's expected terminal sight angle constraint.

[0048] Specifically, the specific process of determining the optimal guidance law for the i-th missile's desired terminal sight angle constraint is as follows.

[0049] Based on the proportional guidance law, we can get Where N is the proportional coefficient. From formula (1) we can get Integrating both sides of this equation, we can get (N-1)(λ i (t f )-λ i (t0))=σ i (t f )-σ i (t0), where t0 and t f are the guidance start time and guidance end time respectively, λ i (t f ) is the sight angle at the end of the i-th missile guidance, λ i (t0) is the sight angle at the beginning of the i-th missile guidance, σ i (t f ) is the lead angle at the beginning of the i-th missile guidance, σ i (t0) is the lead angle at the end of the i-th missile guidance. Considering the current time t as the initial time, the proportional guidance law can make the terminal lead angle 0, that is, σ i (t f ), and then the expected end sight angle can be defined as:

[0050]

[0051] Let a i =a png,i +a l,i , where a png,i represents the proportional guidance law, a l,i is an additional item to be designed to handle the end angle constraint. Based on formula (1) and formula (2), we can get:

[0052]

[0053] Let the virtual control quantity u i =a l,i / (v i 2 cosσ i ), the lead angle σ of the i-th missile i Considered as a small angle. According to the small angle assumption, sinσ can be set i =σ i and cosσ i =1, the optimal angle guidance problem can be described as:

[0054]

[0055] Among them, R 0,i =R i (t0) is the missile-target distance at the start of the i-th missile guidance, J is the index function, λ d,i is the expected terminal sight angle of the i-th missile, λ f0,i is the initial sight angle of the i-th missile, σ 0,i is the initial lead angle of the i-th missile, m is the power of the missile-target matrix in the index function, satisfying m>0, λ f,i (t0) is the expected terminal sight angle at the start of the i-th missile guidance, λ f,i (t f ) is the expected terminal sight angle at the end of the i-th missile guidance.

[0056] The Hamiltonian function of the optimal angle guidance problem formula (4) can be written as:

[0057]

[0058] Where H is the Hamiltonian function of the optimal angle guidance problem, and C σ,i is the corresponding Lagrange multiplier. According to the minimum principle, the following formula (6) holds:

[0059]

[0060] Then we can get:

[0061]

[0062] Where C1 and C2 are constants. Substitute the result of formula (7) into formula (4) and calculate the missile-target distance R of the i-th missile. i Points earned:

[0063]

[0064] in:

[0065]

[0066] and R 0,i =R i (t0). Let N = m = 2, u i ,σ i and λ f,i It can be expressed as:

[0067]

[0068] Considering the current moment as the initial moment, use R i ,σ i ,λ f,i Replace R respectively 0,i ,σ 0,i ,λ f0,i , then the optimal guidance law of the i-th missile with the expected terminal sight angle constraint is:

[0069]

[0070] Among them, λ f,i =2λ i -γ i .

[0071] Step 302 : determining a collision time control feedback item for each missile based on the remaining flight time of each missile, the preset convergence time of the missile group time coordination, and the dynamic model.

[0072] Specifically, the specific process of controlling the feedback term based on determining the collision time of the i-th missile is as follows.

[0073] Based on the dynamic model of the i-th missile in formula (1), determine the remaining flight time t of the i-th missile go,i for:

[0074]

[0075] Based on small angles and Taylor's theorem, we can approximate From formula (10), the approximate analytical expression of the remaining flight time of the i-th missile can be obtained as:

[0076]

[0077] Similarly, using R i ,λ f,i ,σ i Replace R respectively 0,i ,λ f0,i ,σ 0,i , we can get:

[0078]

[0079] Among them, e λf,i =λ d,i -λ f,i is the difference between the expected terminal sight angle and the initial sight angle of the i-th missile. For the i-th missile, its normal acceleration a i Can be designed as:

[0080]

[0081] Among them, a t,i is the collision time control feedback item to be designed. From formula (1) and formula (2), we can know that:

[0082]

[0083] in, is the first derivative of the difference between the expected terminal sight angle and the initial sight angle of the i-th missile. Taking the derivative of formula (14) and considering the lead angle σ as a small angle, we have cosσ=1-σ 2 / 2 and sinσ=σ, while ignoring the higher-order terms of σ. From formula (14) and formula (16), we can get:

[0084]

[0085] in, is the first-order derivative of the remaining flight time of the i-th missile, η i is the intermediate variable that appears in the derivative of the remaining flight time. For the i-th missile, design its normal acceleration a i for:

[0086]

[0087] Among them, a i is the normal acceleration of the i-th missile, v i is the speed of the i-th missile, The first derivative of the sight angle of the i-th missile, σ i is the lead angle of the i-th missile, λ i is the sight angle of the i-th missile, Ri is the distance between the i-th missile and the target, N f is the number of missiles in the swarm, t go,i is the remaining flight time of the i-th missile, t go,j is the remaining flight time of the j-th missile, ∈1 is a small value greater than zero, is the difference between the expected terminal sight angle and the initial sight angle of the i-th missile, η i is the intermediate variable that appears in the derivative of the remaining flight time, Q(η i ) To prevent η i The singular neutralization term, k1 is the basic feedback coefficient, k 2,i is the preset time feedback coefficient, and β(t) is the time function that ensures the preset time convergence. For the i-th missile, the collision time control feedback term is:

[0088]

[0089] Among them, Q(η i ) is expressed as:

[0090]

[0091] β(t) is expressed as:

[0092]

[0093] k 2,i The differential expression of is:

[0094]

[0095] In addition, t0+T d >0 is the preset convergence time of time coordination, α2,l,k 2,i (t0), k1>0, α1>3 are all constants, t0 is the guidance start time, t is the current time, T d is the preset convergence time of the collision time error, and both ∈1 and ∈2 are small values ​​greater than 0.

[0096] Step 303 determines a distributed guidance law with space-time constraints for each missile based on the optimal guidance law constrained by the desired terminal line-of-sight angle and the collision time control feedback term for each missile. By analyzing the remaining flight time and proposing the collision time control feedback term, a complete distributed guidance law with space-time constraints is obtained. By adjusting the normal acceleration of the missiles, multiple missiles can achieve a coordinated space-time strike on a stationary target.

[0097] Step 203: Determine a distributed optimization problem of the expected terminal sight angle based on the remaining flight time of each missile and the expected terminal sight angle of each missile; the expected terminal sight angle is the sight angle at the end of guidance.

[0098] In an exemplary embodiment of the present application, step 203 is replaced by the following steps 401 to 403:

[0099] Step 401, when the relationship between the initial sight angle of each missile, the initial lead angle of each missile and the expected terminal sight angle of each missile is satisfied, the predicted minimum collision time of each missile group is determined based on the remaining flight time of each missile and the expected terminal sight angle of each missile.

[0100] In an exemplary embodiment of the present application, step 401 specifically includes steps 501 and 502:

[0101] Step 501, when the relationship between the initial sight angle of each missile, the initial lead angle of each missile and the expected terminal sight angle of each missile is satisfied, the minimum arrival time of each missile is determined based on the remaining flight time of each missile and the expected terminal sight angle of each missile.

[0102] The specific process of determining the minimum value of the arrival time of the i-th missile is as follows.

[0103] Let f i (λ d,i )=t go,i (t=t0), then the following equation holds:

[0104]

[0105] It can be obtained that for λ d,i , f i (λ d,i ) is a strongly convex function. When λ d,i =λ f0,i +13σ 0,i / 12 o'clock, there Among them, f i,min (λ d,i ) is the minimum remaining flight time of the i-th missile, t go,i,min (t0) is the minimum arrival time of the i-th missile. For the collision time t of the multi-missile system f Can satisfy t f ≥t go,i,min (t0), i=1,2,...,N f Based on the above analysis, the minimum collision time of the bullet group can be expressed as Among them, t go,1,min (t0) is the minimum arrival time of the first missile, t go,2,min (t0) is the minimum value of the second missile arrival time, For N fThe minimum arrival time of the missiles.

[0106] Step 502: Determine the predicted minimum collision time of each missile group based on the minimum arrival time of each missile.

[0107] in, t fm,i is the minimum collision time of the missile group predicted by the i-th missile, a ij =1 means there is communication between the i-th missile and the j-th missile, otherwise, a ij =0 means that there is no communication between the i-th missile and the j-th missile.

[0108] Step 402: Determine the optimization function of the missile group based on the predicted minimum collision time of each missile and the expected terminal sight angle of each missile. The specific process of determining the optimization function of the missile group is as follows.

[0109] First, based on the predicted minimum collision time of the missile group and the expected terminal sight angle of the missile, the optimization function of the missile is determined. The expression of the optimization function of the missile is: Among them, t go,i (t0,λ d,i ) is the remaining flight time of the i-th missile corresponding to the expected terminal sight angle at the initial guidance time, c>0 is the penalty term in the optimization function, and t0 is the initial guidance time.

[0110] Secondly, the optimization function of the missile group is determined based on the optimization function of the i-th missile. The expression of the optimization function of the missile group is:

[0111] Step 403: Based on the expected terminal sight angle of each missile and the optimization function of the missile group, a distributed optimization problem for the expected terminal sight angle is determined. The distributed optimization problem for the expected terminal sight angle is to set the expected terminal sight angle of each missile, minimize the optimization function of the missile group under the constraint of the expected terminal sight angle interval between missiles, and obtain the optimal expected terminal sight angle of each missile. The expression of the distributed optimization problem for the expected terminal sight angle is:

[0112]

[0113] in, is a vector composed of the desired end sight angle as the optimization variable, is the optimal expected end sight angle vector of the P1 problem, is the expected terminal sight angle interval within the projectile group, H ij is the expected terminal sight angle interval between the i-th missile and the j-th missile, λ d is the desired end sight angle, t fmis the minimum collision time of the projectile group.

[0114] Step 204: Determine an angle decision protocol for each missile based on a predetermined convergence time for angle decision and the distributed optimization problem of the desired terminal sight angle. The predetermined convergence time for angle decision is such that all missiles reach the target synchronously at the same time according to the predetermined angle.

[0115] In an exemplary embodiment of the present application, step 204 specifically includes steps 601 and 602.

[0116] Step 601, solve the distributed optimization problem of the expected terminal sight angle to obtain the optimal expected terminal sight angle of each missile, the predicted minimum collision time of the final missile group of each missile, and the time to determine the optimal solution.

[0117] The predicted final minimum collision time of each missile and the time to determine the optimal solution are obtained in the process of unifying the minimum collision time of each missile. The specific process of unifying the minimum collision time of the i-th missile is:

[0118] For the first iteration, q = 1, binding t fm,i =t go,i,min (t0) and N fmax , where t fm,i is the minimum collision time of the missile group predicted by the i-th missile, q is the number of iterations, N fmax is the total number of communications, the total number of communications satisfies N fmax >N f .

[0119] make Among them, t fm,i is the minimum collision time of the missile group predicted by the i-th missile, a ij Indicates whether there is communication between the i-th missile and the j-th missile. When a ij =1 means that there is communication between the i-th missile and the j-th missile, otherwise, a ij =0 means that there is no communication between the i-th missile and the j-th missile; in each iteration, the i-th missile will update the minimum collision time of the missile group predicted by the i-th missile based on the lower limit of the flight time of the communicable missiles in the missile group and its own flight time.

[0120] Let q=q+1, if q<N fmax , then continue the above process, if q≥N fmax , then record the current time t1 and in, is the predicted minimum collision time of the final missile group of the i-th missile, t1 is the number of communications between the i-th missile and other missiles, and N fmaxThe time after the first communication is also the time to determine the optimal solution. At each iteration, the minimum arrival time of each missile will change. The reason for the change in the minimum arrival time of each missile is that the expected terminal sight angle at each moment will change. Therefore, when solving the distributed optimization problem of the expected terminal sight angle, the missile arrives at N fmax The time after the first communication is the time to obtain the final missile group minimum collision time predicted by the missile and the time to find the optimal expected terminal line of sight angle, that is, the time of the optimal solution.

[0121] Step 602 , based on the preset convergence time of the angle decision and the optimal expected terminal sight angle of each missile, the predicted final minimum collision time of each missile group and the time to determine the optimal solution, determine the angle decision protocol for each missile.

[0122] Among them, the angle decision protocol of the i-th missile is:

[0123]

[0124] Among them, t1+T g is the preset convergence time for angle decision, t is the current time, t0 is the initial time of guidance, and t1 is the time to determine the optimal solution. is the first-order derivative of the expected terminal sight angle of the i-th missile, λ d,i is the expected terminal sight angle of the i-th missile, λ f,i is the initial sight angle of the i-th missile, a ij Indicates whether there is communication between the i-th missile and the j-th missile, H ij is the distance between the expected terminal sight angle of the i-th missile and the expected terminal sight angle of the j-th missile, λ d,j is the expected terminal sight angle of the j-th missile, T g is the preset convergence time of the desired angle, h1 is the feedback coefficient, ρ and is the exponential gain of the error, is the final minimum collision time of the missile group predicted by the i-th missile, is the optimal expected terminal sight angle of the j-th missile, is the optimal expected terminal sight angle of the i-th missile. h1>0,T g >0 are all constants, c is a constant greater than 0. λ d,i (t0) = λ f0,i +13σ i / 12,

[0125] Step 205, based on the angle decision protocol of each missile and the space-time constraint distributed guidance law of each missile, determine the space-time guidance decision integrated control protocol of each missile, and control the normal acceleration and expected terminal line of sight angle of each missile based on the space-time guidance decision integrated control protocol of each missile.

[0126] For the i-th missile, the process of spatiotemporal guidance-decision-making integrated control based on distributed optimization can be further described as steps 701 to 704:

[0127] Step 701, bind a series of parameter values, parameter range: ∈1, ∈2, k1, α2, l, k 2,i (t0), h1, c>0, α1>3, 0<ρ<1, The expected formation vector H within the binding multi-missile system.

[0128] Step 702, λ d,i (t0) = λ f0,i +13σ 0,i / 12, execute the above-mentioned minimum collision time uniformization process for each missile.

[0129] Step 703: Obtain the predicted minimum collision time of each missile group and the optimal solution time from the minimum collision time unification process of each missile. Define the preset convergence time t1+T for angle decision g The preset convergence time t0+T coordinated with time d .

[0130] Step 704, obtain the cost function g i (λ d,i ,t fm,i ), and then the guidance decision integrated control protocol can be expressed as formula (18)-formula (25).

[0131] This application applies an integrated guidance-decision-making control method to a multi-missile system, enabling autonomous desired angle decisions and simultaneous multi-directional strike guidance for multiple missiles against stationary targets. This solves the problem of space-time-constrained guidance and real-time angle decision-making for missiles targeting stationary targets, improving the effectiveness of multiple missiles against stationary targets.

[0132] In an exemplary embodiment of the present application, specific guidance and decision-making tasks are implemented through a guidance and decision-making integrated control protocol.

[0133] Missile simulation conditions: The initial positions of the four missiles are (-50m, -55m), (50m, -50m), (50m, 50m), and (-50m, 50m). The initial position of the target is (4000m, 4000m). The speeds of the four missiles are 120m / s, 130m / s, 110m / s, and 125m / s, respectively. The yaw angles of the four missiles are 60°, 50°, 45°, and 40°, respectively.

[0134] Decision guidance parameter setting: In the guidance decision integrated control protocol, ε1=1,ε2=0.5°,k1=1,t0=0s,t1=0.5s,T d =15s, T g =6.5s, N fmax =5, α1=3.5, α2=0.01, l=15 3.5 , c=10, h1=7.5, ρ=0.95, k 2,i (t0) = 4, where i = 1, 2, ..., N f Expected formation H = [30°, 10°, -10°, -30°] T .

[0135] Result analysis: The simulation result diagram of the spatiotemporal guidance-decision-making integrated control method is as follows: Figures 4-10 The simulation results of the collaborative guidance trajectory and the remaining flight time without the use of the space-time guidance-decision integration control method are shown in the figure. Figure 11-12 As shown. Among them, the expected end sight angle directly takes the value of the expected angle formation, that is, λ d,i =H(i),i=1,2,...,N f , H(i) is the expected terminal sight angle of the i-th missile, and the other conditions remain unchanged. Figure 4 It can be seen that the four missiles can achieve the attack on the target under the implementation of the decision-guidance integrated control protocol formula (18) to formula (25). Figure 5 It can be seen that the decision link can achieve the desired terminal sight angle decision within the preset time, and the guidance link can achieve the tracking of the desired terminal sight angle at the end of the attack. Figure 6 It can be seen that at the end of the attack, the sight rate can be 0. Figure 7 It can be seen that during the missile movement, the lead angle is within the limit of plus or minus 90 degrees, and the lead angle at the end of the strike is 0, which is conducive to the requirement of precise strike. Figure 8 It can be seen that the remaining flight time of the four missiles can converge after the preset time, thus achieving the time coordination task. Figure 9 It can be seen that the overload of the four missiles can converge to 0 at the end. Figure 10It can be seen that the minimum collision time can be consistent after 5 communications. Figure 4 and Figure 11 as well as Figure 8 and Figure 12 As can be seen, the flight time of the control group was nearly 10 seconds longer than that of the group with the decision-making process. This indicates that if the desired terminal sight angle is not set properly and the guidance process lacks a decision-making link, the total flight time can be easily extended when implementing a space-time coordinated guidance mission, which is not conducive to penetration requirements.

[0136] Based on the same inventive concept, the embodiment of the present application also provides a method for realizing the above-mentioned time-space guidance-decision-making integrated control system based on distributed optimization, such as Figure 13 As shown, including:

[0137] The dynamic model establishment and remaining flight time determination module 801 is used to establish a dynamic model of each missile in the missile group striking a stationary target and determine the remaining flight time of each missile.

[0138] The space-time constraint distributed guidance law determination module 802 is connected to the dynamic model establishment and remaining flight time determination module 801, and is used to determine the space-time constraint distributed guidance law of each missile based on the dynamic model of each missile in the swarm striking a stationary target, the remaining flight time of each missile, and the preset convergence time coordinated with the swarm time; the space-time constraint distributed guidance law is the normal acceleration.

[0139] The distributed optimization problem determination module 803 is connected to the dynamic model establishment and remaining flight time determination module 801 and the time-space constraint distributed guidance law determination module 802, and is used to determine the distributed optimization problem of the expected terminal line of sight angle based on the remaining flight time of each missile and the expected terminal line of sight angle of each missile; the expected terminal line of sight angle is the line of sight angle at the end of guidance.

[0140] The angle decision protocol determination module 804 is connected to the distributed optimization problem determination module 803 and the dynamic model establishment and remaining flight time determination module 801, and is used to determine the angle decision protocol of each missile based on the preset convergence time of the angle decision and the distributed optimization problem of the desired terminal line of sight angle.

[0141] The space-time guidance decision integrated control module 805 is connected to the angle decision protocol determination module 804 and the space-time constraint distributed guidance law determination module 802, and is used to determine the space-time guidance decision integrated control protocol of each missile based on the angle decision protocol of each missile and the space-time constraint distributed guidance law of each missile, and control the normal acceleration and expected terminal line of sight angle of each missile based on the space-time guidance decision integrated control protocol of each missile.

[0142] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0143] Those skilled in the art will appreciate that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0144] The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0145] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0146] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A space-time guidance-decision-making integrated control method based on distributed optimization, characterized in that: The time-space guidance-decision-making integrated control method based on distributed optimization includes: Build a dynamic model for each missile in the swarm striking a stationary target and determine the remaining flight time of each missile; Determining a space-time-constrained distributed guidance law for each missile based on a dynamic model of each missile in the swarm striking a stationary target, the remaining flight time of each missile, and a preset convergence time for swarm time coordination; the space-time-constrained distributed guidance law is a normal acceleration; Determining a distributed optimization problem for the desired terminal sight angle based on the remaining flight time of each missile and the desired terminal sight angle of each missile; the desired terminal sight angle being the sight angle at the end of guidance; Determining an angle decision protocol for each missile based on a distributed optimization problem of a preset convergence time for the angle decision and the desired terminal sight angle; Based on the angle decision protocol of each missile and the space-time constraint distributed guidance law of each missile, a space-time guidance decision integrated control protocol for each missile is determined, and the normal acceleration and the desired terminal line of sight angle of each missile are controlled based on the space-time guidance decision integrated control protocol for each missile; Among them, based on the dynamic model of each missile in the swarm striking a stationary target, the remaining flight time of each missile and the preset convergence time of the swarm time coordination, the time-space constraint distributed guidance law of each missile is determined, specifically including: Based on the dynamic model of each missile in the swarm striking a stationary target, the optimal guidance law is determined for each missile under the desired terminal sight angle constraint. Determining a collision time control feedback term for each missile based on the remaining flight time of each missile, a preset convergence time of the missile group time coordination, and the dynamic model; Determine the space-time constrained distributed guidance law for each missile based on the optimal guidance law constrained by the desired terminal sight angle of each missile and the collision time control feedback term of each missile; Based on the remaining flight time of each missile and the expected terminal sight angle of each missile, a distributed optimization problem is solved to determine the expected terminal sight angle, specifically including: Determining a predicted minimum collision time of each missile group based on the remaining flight time of each missile and the expected terminal sight angle of each missile while satisfying a relationship between the initial sight angle of each missile, the initial lead angle of each missile, and the expected terminal sight angle of each missile; Determine the optimization function of the missile group based on the predicted minimum collision time of each missile and the expected terminal sight angle of each missile; Based on the expected terminal sight angle of each missile and the optimization function of the missile group, the distributed optimization problem of the expected terminal sight angle is determined.

2. The time-space guidance-decision-making integrated control method based on distributed optimization according to claim 1 is characterized in that: The dynamic model of the i-th missile attacking a stationary target is: Among them, λ i is the sight angle of the i-th missile, R i is the distance between the i-th missile and the target, γ i is the yaw angle of the i-th missile, σ i is the lead angle of the i-th missile, v i is the speed of the i-th missile, a i is the normal acceleration of the i-th missile, is the first-order derivative of the yaw angle of the i-th missile, is the first-order derivative of the missile-target distance of the i-th missile, The first derivative of the sight angle of the i-th missile, is the first-order derivative of the lead angle of the i-th missile.

3. The time-space guidance-decision-making integrated control method based on distributed optimization according to claim 1 is characterized in that: The space-time constrained distributed guidance law of the i-th missile is: Among them, a i is the normal acceleration of the i-th missile, v i is the speed of the i-th missile, The first derivative of the sight angle of the i-th missile, σ i is the lead angle of the i-th missile, λ i is the sight angle of the i-th missile, R i is the distance between the i-th missile and the target, N f is the number of missiles in the swarm, t go,i is the remaining flight time of the i-th missile, t go,j is the remaining flight time of the j-th missile, ∈1 is a small value greater than zero, is the difference between the expected terminal sight angle and the initial sight angle of the i-th missile, η i is the intermediate variable that appears in the derivative of the remaining flight time, Q(η i ) is to prevent η i The singular neutralization term, k1 is the basic feedback coefficient, k 2,i is the preset time feedback coefficient, and β(t) is the time function that ensures the preset time convergence.

4. The time-space guidance-decision-making integrated control method based on distributed optimization according to claim 1 is characterized in that: The optimization function of the bullet group is: Among them, t go,i is the remaining flight time of the i-th missile, g i (λ d,i ,t fm,i ) is the optimization function of the i-th missile, λ d,i is the expected terminal sight angle of the i-th missile, t fm,i is the minimum collision time of the missile group predicted by the i-th missile, λ d is the desired end sight angle, t fm is the minimum collision time of the projectile group, G(λ d ,t fm ) is the optimization function of the bullet group.

5. The time-space guidance-decision-making integrated control method based on distributed optimization according to claim 1 is characterized in that: The distributed optimization problem of the expected terminal sight angle is: Among them, λ D is a vector composed of the desired terminal sight angle of each missile as the optimization variable, is the optimal expected end sight angle vector of the P1 problem, H ij is the distance between the expected terminal sight angle of the i-th missile and the expected terminal sight angle of the j-th missile, λ d is the desired end sight angle, t fm is the minimum collision time of the projectile group, G(λ d ,t fm ) is the optimization function of the bullet group, N f is the number of missiles, st is the constraint condition, λ d,i is the expected terminal sight angle of the i-th missile, λ d,j is the expected terminal sight angle of the j-th missile.

6. The time-space guidance-decision-making integrated control method based on distributed optimization according to claim 1 is characterized in that: Based on the preset convergence time of the angle decision and the distributed optimization problem of the desired terminal sight angle, the angle decision protocol of each missile is determined, specifically including: Solving the distributed optimization problem of the expected terminal sight angle to obtain the optimal expected terminal sight angle for each missile, the predicted minimum collision time of the final missile group for each missile, and the time to determine the optimal solution; The angle decision protocol for each missile is determined based on the preset convergence time of the angle decision, the optimal expected terminal line of sight angle of each missile, the predicted minimum collision time of the final missile group for each missile, and the time to determine the optimal solution.

7. The time-space guidance-decision-making integrated control method based on distributed optimization according to claim 1 is characterized in that: The angle decision protocol for the i-th missile is: Among them, t1+T g is the preset convergence time for angle decision, t is the current time, t0 is the initial time of guidance, and t1 is the time to determine the optimal solution. is the first-order derivative of the expected terminal sight angle of the i-th missile, λ d,i is the expected terminal sight angle of the i-th missile, λ f,i is the initial sight angle of the i-th missile, a ij Indicates whether there is communication between the i-th missile and the j-th missile, H ij is the distance between the expected terminal sight angle of the i-th missile and the expected terminal sight angle of the j-th missile, λ d,j is the expected terminal sight angle of the j-th missile, T g is the preset convergence time of the desired angle, h1 is the feedback coefficient, ρ and is the exponential gain of the error, is the final minimum collision time of the missile group predicted by the i-th missile, is the optimal expected terminal sight angle of the j-th missile, is the optimal expected terminal sight angle of the i-th missile.

8. A space-time guidance-decision-making integrated control system based on distributed optimization, applying the space-time guidance-decision-making integrated control method based on distributed optimization according to any one of claims 1 to 7, characterized in that: The space-time guidance-decision-making integrated control system based on distributed optimization includes: The dynamic model establishment and remaining flight time determination module is used to establish the dynamic model of each missile in the missile group striking a stationary target and determine the remaining flight time of each missile; a space-time constraint distributed guidance law determination module, connected to the dynamics model establishment and remaining flight time determination module, for determining the space-time constraint distributed guidance law for each missile in the swarm based on the dynamics model of each missile striking a stationary target, the remaining flight time of each missile, and a preset convergence time coordinated with the swarm time; the space-time constraint distributed guidance law is a normal acceleration; a distributed optimization problem determination module, connected to the dynamic model establishment and remaining flight time determination module and the time-space constraint distributed guidance law determination module, for determining a distributed optimization problem of an expected terminal sight angle based on the remaining flight time of each missile and the expected terminal sight angle of each missile; the expected terminal sight angle is the sight angle at the end of guidance; An angle decision protocol determination module is connected to the distributed optimization problem determination module and the dynamic model establishment and remaining flight time determination module, and is used to determine the angle decision protocol of each missile based on the distributed optimization problem of the preset convergence time of the angle decision and the desired terminal line of sight angle; The space-time guidance decision integrated control module is connected to the angle decision protocol determination module and the space-time constraint distributed guidance law determination module. It is used to determine the space-time guidance decision integrated control protocol of each missile based on the angle decision protocol of each missile and the space-time constraint distributed guidance law of each missile, and control the normal acceleration and expected terminal line of sight angle of each missile based on the space-time guidance decision integrated control protocol of each missile.

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