Multi-target collaborative interception distribution and guidance method

Abstract

The invention relates to a multi-target collaborative interception distribution and guidance method, and belongs to the technical field of collaborative optimization methods. In order to solve the defect that the MARL distribution method in the prior art cannot completely ensure the feasibility of the distribution result, the invention provides a multi-target collaborative interception distribution and guidance method, the thought of MARL and a consistent auction strategy are introduced in the method, and the feasibility of the distribution result is ensured by utilizing bidding and negotiation in a bullet group aiming at some specific conditions. The method comprises the following steps: determining a communication network in a missile group and an intercepted kinematics model; establishing a multi-target dynamic allocation optimization model; solving the multi-target dynamic allocation optimization model by adopting a distributed dynamic allocation method based on a neural network; a multi-interception-projectile cooperative guidance law is designed and realized, and after respective interception targets are determined, the interception projectiles need to fly to the targets under the guidance of the multi-interception-projectile cooperative guidance law before next distribution or before interception is finished.

Description

Technical Field

[0001] The invention relates to a multi-target collaborative interception allocation and guidance method, belonging to the technical field of collaborative optimization methods. Background Art

[0002] With the improvement of target mobility and the advancement of anti-interception methods, the traditional combat style of a single interceptor missile independently intercepting has become difficult to adapt to the complex and changeable modern battlefield environment. The coordinated combat of multiple interceptors can not only improve the success rate of intercepting targets, but also make up for the gap between the performance of interceptors and targets, and achieve the combat purpose of exchanging multiple low-cost interceptors for high-value targets. Therefore, the coordinated combat of multiple interceptors and the scientific issues involved in the combat process have received more extensive research and attention.

[0003] At present, the research on multi-interceptor coordinated operations can be roughly classified into the following two directions: one is to focus on the control problem in the process of multi-interceptor and single-target engagement (MSE), aiming to propose a control algorithm to achieve simultaneous interception of targets by a group of missiles. The other is to focus on the target allocation problem in the process of multi-interceptor and multi-target engagement (MME), aiming to design an evaluation model and allocation algorithm to ensure the accuracy and efficiency of allocation decisions.

[0004] For the multi-target dynamic allocation problem, there are two main research trends: one is to use centralized modeling and solving to uniformly allocate missile groups in time and space. This type of centralized method has good global characteristics, but because it needs to repeatedly solve the global optimization problem in each allocation, it is slightly insufficient in solution efficiency; this type of method requires a control center to complete the above calculations and send the allocation results to the missile group, which imposes a considerable burden on the communication in the MME process; the other main trend is to rely on information exchange between nodes for allocation, also known as distributed allocation. Representatives of this type of allocation method include consensus based auction algorithm (CBAA) and consensus based bundle algorithm (CBBA). These two algorithms simulate auction behavior in market activities, and the intelligent agent (i.e., interceptor missile) determines the ownership of the target through bidding and negotiation. Although CBAA and CBBA can still achieve convergence of allocation results without a control center, it may take several rounds of negotiation before all intelligent agents reach a consensus, resulting in a large amount of communication costs.

[0005] In recent research results, researchers have attempted to use multi-agent reinforcement learning (MARL) to solve the goal allocation problem.

[0006] This type of method requires multiple offline trainings to enhance the generalization ability of the neural network model, so that each agent can learn the next action from the policy network based on independent observations in the new task environment. Compared with centralized methods and auction-based distributed allocation methods, MARL-based allocation methods do not rely on the control center and do not require multiple negotiations to reach a consensus, so they have higher research value. However, for multi-constrained target allocation problems, MARL-based allocation methods cannot fully guarantee the feasibility of the allocation results, so further research and discussion is needed. Summary of the invention

[0007] The purpose of the present invention is to solve the problem that the allocation method of MARL in the prior art cannot fully guarantee the feasibility of the allocation result, and to provide a multi-target collaborative interception allocation and guidance method. The method introduces the idea of ​​MARL and the consistency auction strategy, and for certain specific situations, utilizes the bidding and negotiation within the missile group to ensure the feasibility of the allocation result.

[0008] In order to solve the above problems, the present application is implemented through the following technical solutions: A multi-target coordinated interception allocation and guidance method, which is special in that it includes the following steps: S1. Determine the communication network within the missile group and the kinematic model of interception; S2, establishing a multi-objective dynamic allocation optimization model according to step S1; S3, using a distributed dynamic allocation method based on a neural network to solve the multi-objective dynamic allocation optimization model of step S2; S4. Design and implement a coordinated guidance law for multiple interceptor missiles. After determining their respective interception targets in step S3, each interceptor missile must fly to the target under the guidance of the coordinated guidance law for multiple interceptor missiles before the next allocation occurs or the interception ends.

[0009] Furthermore, the communication network within the group is determined in step S1 as follows: Interceptor missiles ( ) targets were intercepted, among which, ( ) indicates the Interceptor missiles, ( ) indicates the Each interceptor missile transmits information through the communication network. The communication network consists of a connection diagram between interceptor missiles Describe, among which, To intercept missiles, is the edge set; When there is an edge , At that time, The interceptor missile can The interceptor missile transmits the information. If the edge , then The interceptor missile could not reach the The interceptor missile transmits the information. ; The connection diagram is undirected and connected, and its Laplacian matrix It has the following properties: 1) There is only one zero eigenvalue, and the rest of the eigenvalues ​​are positive real numbers; 2) Let The minimum and maximum positive eigenvalues ​​are and , then .

[0010] Furthermore, the kinematic model of the interception in step S1 refers to the interception missile With the goal Motion model: Setting the inertial coordinate system and the line of sight coordinate system , In the inertial coordinate system Next, interceptor missile The equation of motion is: , In the formula, for The position in the inertial coordinate system, for speed, for The pitch angle, for The yaw path angle; Target The equation of motion for is: , In the formula, for The position in the inertial coordinate system, for speed, for The pitch angle, for The yaw path angle; Relative to The sight coordinate system is obtained by rotating the inertial coordinate system. In the sight coordinate system, express and The relative distance and Respectively Relative to The sight inclination and sight deflection angles; When the interceptor The target of the assignment is When , , If the missile is intercepted later The allocation target of no longer changes, then: .

[0011] Furthermore, the step S2 specifically includes the following steps: S21. Confirm Moment The interceptor missile The comprehensive guidance advantage of each target; S22, determine the The overall threat level of the target; S23. Determine the expected interception effectiveness of the missile group against the target group; S24. Determine the optimal allocation matrix and constraints.

[0012] Furthermore, the comprehensive guidance advantage in step S21 includes The interceptor missile The guidance advantage of the target line of sight angular velocity, The interceptor missile The remaining flight time of the target and the guidance advantage of the The interceptor missile The guidance advantage of the target field of view constraint; Among them, the The interceptor missile The guidance advantage of the target line of sight angular velocity is: , In the formula, represents the weight coefficient, express Relative to The line of sight inclination rate, express Relative to The line of sight deflection rate; The said The interceptor missile The guidance advantage of the remaining flight time of a target is: , In the formula, represents the weight coefficient, Indicates The interceptor missile The remaining flight time of a target is defined as: , Indicates The estimated remaining flight time of the interceptor missile, i.e. The remaining flight time of an interceptor missile against the currently assigned target; Since at the initial moment of guidance , the targets of the interceptor missiles have not yet been determined, for: , Where: Indicates The interceptor missile The remaining flight time for each target, represents the optimal allocation matrix Line Elements of a column; The The interceptor missile The guidance advantage of a target with respect to the field of view constraint is defined as: , where: represents the weight coefficient, is time t Relative to The sight angle, is time t The pitch angle, is time t Relative to The sight angle, is time t The yaw path angle; Said Moment The interceptor missile The comprehensive guidance advantage of a target is expressed as: .

[0013] Furthermore, in step S22, The overall threat level of a target includes speed threat level, maximum normal / lateral acceleration threat level and type threat level, where the speed threat level is: , Where: Maximum speed , the maximum normal / lateral acceleration threat degree is: , maximum normal / lateral acceleration satisfy: , The threat level of the type is: , Where: Indicates Quantized value of target type, Indicates Quantized value of target type, The overall threat level is .

[0014] Furthermore, the expected interception efficiency of the missile group against the target group in step S23 is specifically as follows: the comprehensive guidance advantage of a single interceptor missile is regarded as its expected interception success rate for the target, and the missile group is defined as The expected interception effectiveness of a target is: , Considering the overall threat level of the target in step S22, the expected interception effectiveness of the missile group against the target group is: .

[0015] Further, the details of step S24 are as follows: Based on the expected interception effect obtained in step S23, the optimal allocation matrix is ​​obtained as follows: , is the allocation matrix, where , ; The constraints of the optimal allocation matrix are: , , , represents the allocation matrix Any element of The value is either 0 or 1. At that time, The interceptor missile will be assigned to A goal, when At that time, The interceptor missile is not assigned to goals; , This means that one interceptor missile can only be assigned to one target, and each target must be assigned at least one interceptor missile.

[0016] Furthermore, the distributed dynamic allocation method based on neural network in step S3 specifically includes the following steps: S31, offline training: the offline training includes building a neural network and network training, The construction of the neural network is specifically as follows: the swarm completes multiple rounds of training with the participation of the central node, and one training round is usually composed of several allocation decisions. In each decision, the central node uses a particle swarm optimization algorithm to solve the optimal allocation problem; After completing all training rounds, the guidance advantage of each interceptor in each allocation decision is calculated. , target threat , and the distribution results Save it, , The expanded vector As network input, assign the result As the network output, for each interceptor Build a neural network; The neural network adopts a feedforward network structure with multiple hidden layers. The mapping relationship between the input and output of each layer of the network is expressed as: , In the formula, Indicates Layer, The output of a neuron, , represents the weight vector of the neuron, is the threshold of the neuron, For the The column vector composed of the output of each neuron in the layer; The activation functions of the hidden layer and the output layer are respectively selected as S-shaped growth curve functions With the linear transfer function ,for , both satisfy: , ,Will The output vector generated after inputting the network is recorded as , then the network output error of a single sample is expressed as: ; The network training is performed by optimizing the weights of each neuron. With threshold , so that the network output of all samples has mean square error Minimum, ; The network is trained using the adaptive moment estimation algorithm, and the trained network is expressed as follows: ; S32, online decision-making: the online decision-making includes autonomous allocation and consistency auction strategies; The online decision is as follows: The guidance advantage and target threat (vector) in the online decision stage are respectively denoted as , , Each interceptor missile will The guidance advantage and target threat are input into the trained neural network to generate an uncorrected allocation plan: , right After correction, the autonomous allocation results of each interceptor missile are obtained: , , , Each interceptor will share the results with neighboring nodes, so every node in the communication network will know the distribution of each target. , ; The consistency auction strategy is as follows: is undirected and connected, there exists a path from Departure and finally return Path; The nodes on the path are Make a quotation according to , update the current highest price and send the price together with the list of bidders Send to the next bidder; When a bidder When the current highest price is received again, if: , then the bidder's bid is successful, let: , , In the absence of a central node, internal communication within the swarm is used to successfully avoid missing allocation results.

[0017] Furthermore, in the step S31, the central node adopts the particle swarm optimization algorithm to solve the optimal allocation problem. For the situation that the multi-objective dynamic allocation optimization model is not satisfied during the particle update process, the following correction is made: the position of a particle after a certain update is recorded as ; Step 1: Order , , , Step 2: If the first round of revisions There is a column in , so that , then in all the Randomly select a column from the columns of : If the column is taken as Column, then in all Randomly select a row from the rows ,make , .

[0018] Furthermore, in step S4, based on the fact that all interceptor missiles successfully intercept their respective targets at the same time, the remaining flight time tends to be consistent, and the line of sight angular rate converges to 0, a multi-interceptor missile cooperative guidance law is designed, including a cooperative guidance law in the line of sight direction and a cooperative guidance law in the line of sight normal direction, as follows: In the line of sight, according to , get: , set up , let the virtual control input be: According to the above formula, ; Order: Replace with its observed value , and according to the above two formulas, we get The guidance instructions in the line of sight direction are: ; In the line of sight normal direction, set , , and the virtual control input is: , , according to: , ,get , ; make: , ,Will , Replace with observed values , ,get The guidance instructions in the normal direction of the line of sight are: ,as well as .

[0019] Furthermore, the implementation of the multi-interceptor coordinated guidance law in step S4 is as follows: After the guidance instructions in the sight direction and sight normal direction, the control input of the interceptor missile in the sight system is obtained as follows: , , after rotation transformation, we get Acceleration command in inertial system , , In the formula, , , In order to observe all targets synchronously, the following transformation is used to obtain the guidance instructions under the line of sight system: , , , and update the observer; The observer is: , , Among them, the measurable state , They are , as well as ; for The observed value of , Disturbance , as well as Observed value of , , The above observer can observe all targets synchronously and continuously update as the interception mission proceeds to ensure that the disturbance observation information of the target is obtained immediately when the interception target changes.

[0020] This application proposes a distributed dynamic allocation method based on neural networks: the idea of ​​MARL is introduced, multiple neural networks are used to "learn" the centralized allocation results offline, and the trained neural networks are deployed on interceptor missiles, so that each interceptor missile can make decisions quickly based on the mission environment. On this basis, a consistency auction strategy is introduced. For certain specific situations, bidding and negotiation within the missile group are used to ensure the feasibility of the allocation results; a fixed-time convergent collaborative guidance law is designed: when the target allocation results change frequently, a fixed-time observer and a distributed collaborative guidance law are used to enable the multi-interceptor missile system to achieve stability in each decision cycle, and an interception effectiveness evaluation model based on guidance advantage is proposed, which takes into account the impact of the offset of control quantities such as line of sight angular velocity and remaining flight time on the allocation decision, so that the evaluation model can simultaneously reflect the target value and the difficulty of interception; the MME problem is explored in three-dimensional space, and the coordination of the missile group in time and space is taken into consideration at the same time.

[0021] Simulation results show that the interceptor missile using the method of the present application can achieve the global optimal collaborative interception effect through autonomous decision-making, control and internal communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is a flow chart of the present invention; Figure 2 This is a diagram of the implementation process of multi-target coordinated interception; Figure 3 This is a diagram of a multi-interceptor missile-multi-target engagement scenario; Figure 4 It is a schematic diagram of the three-dimensional motion of the interceptor missile and the target; Figure 5 This is a diagram of the implementation process of a single decision in the offline training phase; Figure 6 for Figure 5 Flowchart of particle swarm algorithm; Figure 7 It is a neural network structure diagram; Figure 8 This is the expected change in interception effectiveness in Example 1; Fig. 9 Allocate decision time for each case 1; Fig.10 This is the expected change in interception effectiveness in Example 2; Fig.11 Allocate decision time for each instance of Example 2. DETAILED DESCRIPTION

[0023] The following is a specific implementation of the present invention with reference to the accompanying drawings to further illustrate the composition of the present invention.

[0024] Explanation of symbols: and denote the set of real numbers and the set of positive integers respectively, Represents a real variable About time No. Derivatives, and Has the same meaning as symbol function. satisfy: hour, ; hour, ; hour, . and Square The minimum and maximum eigenvalues ​​of . or middle, or It is only used as a superscript or subscript and has no other meaning. In addition, this paper uses the symbol and denote the continuous-time system and the discrete allocation decision moment, respectively.

[0025] Example 1. A multi-target cooperative interception allocation and guidance method, the specific process is as follows Figure 1 The complete implementation process of this method is shown in Figure 2As shown, the following steps are included: S1. Determine the communication network within the missile group and the kinematic model of interception; S2, establishing a multi-objective dynamic allocation optimization model according to step S1; S3, using a distributed dynamic allocation method based on a neural network to solve the multi-objective dynamic allocation optimization model of step S2: S4. Design and implement a coordinated guidance law for multiple interceptor missiles. After determining their respective interception targets in step S3, each interceptor missile must fly to the target under the guidance of the coordinated guidance law for multiple interceptor missiles before the next allocation occurs or the interception ends.

[0026] Furthermore, the communication network within the group is determined in step S1 as follows: Interceptor missiles ( ) target interception engagement scenario such as Figure 3 As shown, ( ) indicates the Interceptor missiles, ( ) indicates the Each interceptor missile transmits information through the communication network. The communication network consists of a connection diagram between interceptor missiles Describe, among which, To intercept missiles, is the edge set; When there is an edge , At that time, The interceptor missile can The interceptor missile transmits the information. If the edge , then The interceptor missile could not reach the The interceptor missile transmits the information. ; Definition Graph The adjacency matrix of , and the Laplacian matrix is: , Where: ,when hour, ; If for any edge in the graph , both have , then it is called a graph is an undirected graph; the adjacency matrix and Laplacian matrix of an undirected graph are both symmetric matrices; For undirected graphs , definition: If the graph If there is a path connecting any two nodes, and the path consists of alternating nodes and edges, then it is called an undirected graph. For connected.

[0027] The connection diagram is undirected and connected, and its Laplacian matrix It has the following properties: 1) There is only one zero eigenvalue, and the rest of the eigenvalues ​​are positive real numbers; 2) Let The minimum and maximum positive eigenvalues ​​are and , then .

[0028] Furthermore, the kinematic model of the interception in step S1 is as follows: Figure 4 The interceptor missile With the goal Motion model: Setting the inertial coordinate system and the line of sight coordinate system , In the inertial coordinate system Next, interceptor missile The equation of motion is: , In the formula, for The position in the inertial coordinate system, for speed, for The pitch angle, for The yaw path angle; Target The equation of motion for is: , In the formula, for The position in the inertial coordinate system, for speed, for The pitch angle, for The yaw path angle; for and , assuming that all interceptors and targets are powered by engine thrust, and both can be regarded as point masses in three-dimensional space, then and The acceleration can be decomposed into three mutually orthogonal components in the inertial coordinate system, which are expressed as as well as ; Relative to The sight coordinate system is obtained by rotating the inertial coordinate system. In the sight coordinate system, express and The relative distance and Respectively Relative to The sight inclination and sight deflection angles; exist right In the process of interception, there are usually , and stipulates right The interception end time satisfy , if there is , is a small positive number, then Successful interception .

[0029] Due to any interception missile Only one target can be intercepted at a time, so the interceptor missile should be reasonably determined based on the status information of the interceptor missile and the target. With the goal The corresponding relationship between the interceptor missile and the target is determined, that is, the interceptor missile-target allocation is performed; during the interception process, the interceptor missile-target allocation should be dynamically changed as the status of both parties changes, which is called multi-target dynamic allocation, to ensure the optimal coordinated interception effect; when the interceptor missile The target of the assignment is When , , If the missile is intercepted later The allocation target of no longer changes, then: .

[0030] When the following conditions are met, the missile group is said to have completed the coordinated interception of the target group: a) For all intercepting missiles ( ), , , Established; b) For any target , there is at least one interceptor missile , satisfy ; Indicates that all interceptor missiles successfully intercepted their respective targets; , It means that all interceptor missiles complete the interception of the target at the same time, that is, the missile group reaches a consensus on the interception time; condition b) means that the missile group successfully intercepts all targets.

[0031] Furthermore, the multi-target dynamic allocation refers to dynamically determining the correspondence between each interceptor missile and the target to ensure that the missile group intercepts all targets in order to obtain the best coordinated interception effect. The step S2 specifically includes the following steps: S21. Confirm Moment The interceptor missile The comprehensive guidance advantage of each target; S22, determine the The overall threat level of the target; S23. Determine the expected interception effectiveness of the missile group against the target group; S24. Determine the optimal allocation matrix and constraints.

[0032] Furthermore, the comprehensive guidance advantage in step S21 includes The interceptor missile The guidance advantage of the target line of sight angular velocity, The interceptor missile The remaining flight time of the target and the guidance advantage of the The interceptor missile The guidance advantage of the target field of view constraint; Among them, the The interceptor missile According to the quasi-parallel approach principle, when the interceptor missile's line of sight angular velocity to the target is stable near the origin, the interceptor missile can hit the target with a sufficiently small miss distance. Therefore, by controlling the line of sight angular velocity to converge to 0, all interceptor missiles can successfully intercept their respective targets. When the interceptor missile's line of sight angular velocity to a target is larger, more energy is consumed to control its line of sight angular velocity to converge to 0, and the interceptor missile's guidance advantage to this target is smaller.

[0033] Therefore, the The interceptor missile The guidance advantage of the target line of sight angular velocity is: , In the formula, represents the weight coefficient, express Relative to The line of sight inclination rate, express Relative to The line of sight deflection rate.

[0034] If the missile group wants to intercept the target group at the same time, the first way is to coordinate the remaining flight time of each interceptor missile to make it consistent. The smaller the difference between the remaining flight time of the interceptor missile and its adjacent nodes, the easier it is to achieve the above goal, and the greater the guidance advantage of the interceptor missile.

[0035] The said The interceptor missile The guidance advantage of the remaining flight time of a target is: , In the formula, represents the weight coefficient, Indicates The interceptor missile The remaining flight time of a target is defined as: , Indicates The estimated remaining flight time of the interceptor missile, i.e. The remaining flight time of an interceptor missile against the currently assigned target; Since at the initial moment of guidance , the targets of the interceptor missiles have not yet been determined, for: , Where: Indicates The interceptor missile The remaining flight time for each target, represents the optimal allocation matrix Line Elements of a column; The radar seeker of the interceptor missile has a certain detection field of view. The interceptor missile should try its best to ensure that the target is within the field of view during flight, that is, the interceptor missile's field of view angle of the target always meets the field of view constraint. It is usually stipulated that the interceptor missile's field of view angle does not exceed , then the field of view constraint can be expressed as: , , when the interceptor missile's field of view of a target exceeds the field of view constraint, its guidance advantage over the target will be smaller, so the first The interceptor missile The guidance advantage of a target with respect to the field of view constraint is defined as: , where: represents the weight coefficient, is time t Relative to The sight angle, is time t The pitch angle, is time t Relative to The sight angle, is time t The yaw path angle; Said Moment The interceptor missile The comprehensive guidance advantage of a target is expressed as: .

[0036] Furthermore, in step S22, The overall threat level of a target includes speed threat level, maximum normal / lateral acceleration threat level and type threat level; The target speed has a great influence on its threat level. When the target is a missile or other aircraft carrying a warhead, the greater its penetration speed, the more difficult it is to intercept, and the greater the damage effect on the target by its own momentum. Therefore, the speed threat level is: , Among them, the maximum speed , the target’s maximum acceleration measures its ability to escape capture and interception; The greater the maximum normal / lateral acceleration of the target, the greater the possibility that the target will take more drastic maneuvers to escape interception. Therefore, the maximum normal / lateral acceleration threat level is: , Maximum normal / lateral acceleration satisfy: Targets can be classified and quantified according to their size, function (reconnaissance / strike), strike capability (number of ammunition carried or type of warhead), etc.

[0037] Small cruise missiles / reconnaissance aircraft, medium tactical missiles / fighter jets / medium bombers, and large strategic ballistic missiles / heavy bombers are quantified as 1, 2, and 3 respectively, and then normalized. The threat level of a target with respect to its type is expressed as , Indicates Quantized value of target type, Indicates The quantitative value of the target type, the overall threat level is .

[0038] Furthermore, the expected interception efficiency of the missile group against the target group in step S23 is specifically as follows: the comprehensive guidance advantage of a single interceptor missile is regarded as its expected interception success rate for the target, and the missile group is defined as The expected interception effectiveness of a target is: , Considering the overall threat level of the target in step S22, the expected interception effectiveness of the missile group against the target group is: .

[0039] Further, the details of step S24 are as follows: Based on the expected interception effect obtained in step S23, the current decision time is set to , given the state information of each interceptor missile and target at this moment, the optimal allocation matrix is: , Decision Moment , , is the time interval between two allocation decisions, i.e., the allocation decision interval. is the allocation matrix, where , ; The constraints of the optimal allocation matrix are: , , , represents the allocation matrix Any element of The value is either 0 or 1. At that time, The interceptor missile will be assigned to A goal, when At that time, The interceptor missile is not assigned to goals; , This means that one interceptor missile can only be assigned to one target, and each target must be assigned at least one interceptor missile.

[0040] Before designing the cooperative guidance law, it is necessary to determine the existing knowledge used by the cooperative guidance law: Lemma 1 From The system consists of a first-order intelligent agent, and the communication network between the agents is shown in Figure Describe: The dynamic equations for each agent are: , ,in is the system status, is the control input; If the figure is undirected and connected, and , so many intelligent systems can be reached a consensus within , Established; Control gain , positive odd number , , satisfy: ; Convergence time satisfy: .

[0041] Lemma 2 Consider the following first-order system: ,in, is the system status, is the control input; if , then the first-order system has a fixed time The interior converges to the origin; Control gain , positive odd number , , satisfy: ; Convergence time satisfy: .

[0042] Lemma 3 Consider the following first-order perturbed system: ,in, is the measurable system state, is the control input, is a continuous and smooth unknown disturbance that satisfies: , ; Construct the following observer: , In the formula, , They are and The observed value is recorded as the observation error , ; If the parameter , , , , Respectively meet: a) , ,in is a sufficiently small positive number; b) , and the polynomial and All of them are Hurwitz's; The observation error , At a fixed time The inner convergence is 0, and for any given positive definite matrix , , convergence time satisfy: , The positive symmetric matrix , They satisfy the algebraic Lyapunov equation respectively: , , , .

[0043] The design condition of the cooperative guidance law in step S3 is: if the current moment is ,and is the most recent allocation time, and there is ,Regulation , , , as well as , , ; According to the remaining flight time calculation formula, the remaining flight time can be obtained , abbreviated as , , , , , as well as .

[0044] Estimated remaining flight time Actually equivalent to , and satisfies: when hour, On the contrary, when hour, ; If all interceptors are to successfully intercept their respective targets, it is necessary to design , so that the following conditions hold: for a given as well as , the remaining flight time tends to be consistent: , ; The line of sight angular rate converges to 0: and , .

[0045] Before proceeding to step S3, the following concepts are given: Training round: The whole process of a coordinated interception from beginning to end is called a training round. A training round usually consists of several allocation decisions. The allocation results of each round are recorded as , , , indicating the Round, The optimal allocation matrix of the sub-allocation is recorded separately. , , .

[0046] Central node: In each training round, the central node is responsible for making decisions at each decision moment. Solve to obtain the optimal allocation matrix , and the distribution result Inform every interceptor The interceptor missile uses the collaborative guidance law to obtain guidance instructions, update its own status in real time, and The guidance advantage of each target Feedback to the central node.

[0047] In the offline training phase, the swarm needs to complete multiple rounds of training with the participation of the central node. A training round usually consists of several allocation decisions. In each decision, the central node uses the particle swarm optimization algorithm to solve the optimal allocation problem. The PSO algorithm process is similar to the implementation process of a single decision. Figure 5 shown.

[0048] Furthermore, the distributed dynamic allocation method based on neural network in step S3 specifically includes the following steps: S31, offline training: the offline training includes building a neural network and network training, The construction of the neural network is specifically as follows: the swarm completes multiple rounds of training with the participation of the central node, and one training round is usually composed of several allocation decisions. In each decision, the central node uses a particle swarm optimization algorithm to solve the optimal allocation problem; After completing all training rounds, the guidance advantage of each interceptor in each allocation decision is calculated. , target threat , and the distribution results Save it, , The expanded vector As network input, assign the result As the network output, for each interceptor Construct a neural network; the neural network adopts a multi-hidden layer feedforward network structure, and the mapping relationship between the input and output of each layer of the network is expressed as: , In the formula, Indicates Layer, The output of a neuron, , represents the weight vector of the neuron, is the threshold of the neuron, For the The column vector composed of the output of each neuron in the layer; The activation functions of the hidden layer and the output layer are respectively selected as S-shaped growth curve functions With linear transfer function ,for , both satisfy: , ,Will The output vector generated after inputting the network is recorded as , then the network output error of a single sample is expressed as: ; The network training is performed by optimizing the weights of each neuron. With threshold , so that the network output of all samples has mean square error Minimum, ; The network is trained using the adaptive moment estimation algorithm, and the trained network is expressed as follows: , Each neural network is essentially a mapping of guidance advantage and target threat to the optimal allocation result. Therefore, after completing the training of all neural networks and deploying them on interceptors in sequence, distributed dynamic allocation decisions can be performed without a central node. S32, online decision-making: the online decision-making includes autonomous allocation and consistency auction strategies; The online decision is as follows: The guidance advantage and target threat (vector) in the online decision stage are respectively denoted as , , Each interceptor missile will The guidance advantage and target threat are input into the trained neural network to generate an uncorrected allocation plan: , right After correction, the autonomous allocation results of each interceptor missile are obtained: , , , Each interceptor will share the results with neighboring nodes, so every node in the communication network will know the distribution of each target. , ; In order to avoid a target not being assigned, the consistency auction strategy is as follows: is undirected and connected, there exists a path from Departure and finally return Path; The nodes on the path are Make a quotation according to , update the current highest price and send the price together with the list of bidders Send to the next bidder; When a bidder When the current highest price is received again, if: , then the bidder's bid is successful, let: , , In the absence of a central node, internal communication within the swarm is used to successfully avoid missing allocation results.

[0049] Furthermore, in the step S31, the central node adopts the particle swarm optimization algorithm to solve the optimal allocation problem. For the situation that the multi-objective dynamic allocation optimization model is not satisfied during the particle update process, the following correction is made: the position of a particle after a certain update is recorded as ; Step 1: Order , , , Step 2: If the first round of revisions There is a column in , so that , then in all the Randomly select a column from the columns of : If the column is taken as Column, then in all Randomly select a row from the rows ,make , .

[0050] Furthermore, the cooperative guidance law in step S4 is a multi-interceptor cooperative guidance law with fixed time convergence. According to the fact that all interceptors successfully intercept their respective targets at the same time, the remaining flight time tends to be consistent, and the line of sight angular rate converges to 0, the multi-interceptor cooperative guidance law is designed, including the cooperative guidance law in the line of sight direction and the cooperative guidance law in the line of sight normal direction, which is specifically as follows: In the line of sight, according to , get: , set up , let the virtual control input be: According to the above formula, ; Order: Replace with its observed value , and according to the above two formulas, we get The guidance instructions in the line of sight direction are: ; In the line of sight normal direction, set , , and the virtual control input is: ,

[0051] according to: , ,get , ; make: , ,Will , Replace with observed values , ,get The guidance instructions in the normal direction of the line of sight are: ,as well as .

[0052] Furthermore, the implementation of the multi-interceptor coordinated guidance law in step S4 is as follows: After the guidance instructions in the sight direction and sight normal direction, the control input of the interceptor missile in the sight system is obtained as follows: , , after rotation transformation, we get Acceleration command in inertial system , , In the formula, , , In order to observe all targets synchronously, the following transformation is used to obtain the guidance instructions under the line of sight system: , , , and update the observer; By adopting the coordinated guidance law of multiple interceptor missiles, the remaining flight time of the missile group can reach a consensus within a fixed time, and the line-of-sight angular velocity of all interceptor missiles with respect to the current target will converge to 0 within a fixed time.

[0053] Furthermore, the design of the observer is as follows: With the goal For relative motion in the line of sight coordinate system, the equation of motion is: , , , In the formula, and Respectively by and After rotation transformation, we can obtain: The acceleration vector Equivalent to design Control input in line of sight coordinate system , and for the target The movement acceleration Unknown disturbances formed in the line-of-sight coordinate system , an estimate is required; Assumption: For any interceptor missile With the goal , disturbance satisfy: , , , , , , according to Lemma 3 and the assumption, construct the following observer , , Among them, the measurable state , They are , as well as ; for Observed value of , Disturbance , as well as Observed value of , , , The above-mentioned observer can observe all targets synchronously and continuously update as the interception mission proceeds to ensure that the disturbance observation information of the target is obtained immediately when the interception target changes.

[0054] This application explores the problem of target allocation and coordinated interception in the process of multiple interceptor missiles engaging multiple targets, proposes a distributed dynamic allocation method based on neural networks and a coordinated interception guidance law with fixed-time convergence, and gives a complete implementation of the engagement of multiple interceptor missiles with multiple targets. Compared with similar achievements, this application expands the engagement situation to three-dimensional space, and simultaneously considers the coordination of missile groups in time and space. In addition, this application combines the two core issues of target allocation and guidance control by introducing a guidance advantage model; by designing a coordinated guidance law with fixed-time convergence, it ensures that the missile group completes the interception of the target at the same time. Finally, the MARL idea is adopted, and neural networks are used to realize the distributed decision-making of multiple interceptor missiles, which greatly improves the overall decision-making efficiency of the missile group.

[0055] Example 2: This example conducts a digital simulation experiment to verify the effectiveness of the multi-target cooperative interception allocation and guidance method proposed in this application.

[0056] Interception scene setting The interception scenario is set as 7 interceptors intercepting 3 air targets. The communication network between the interceptors is described by the following adjacency matrix: The initial states of the interceptor missile and the target are given in Table 1 and Table 2 respectively. The algorithm parameters in the offline training and online decision-making process are set as follows: , cooperative guidance law parameters: , , ,Particle swarm algorithm parameters: population size is 200, maximum number of iterations is 100, neural network parameters: the number of hidden layer network layers is 3, and the number of neurons in each layer is 10, 15, and 15 respectively; After calculation, it can be obtained that the upper bound of the convergence time of the cooperative guidance law is is about 0.8912 s, It is about 0.55 s, so the allocation decision interval is selected .

[0057] In addition, in order to make the interception process more in line with the actual situation, we limited the control input of the interceptor missile in the line of sight coordinate system. The preset threshold values ​​are 200 m / s 2 , -200m / s 2 .

[0058] Table 1 Interceptor missile initial state , Table 2 Target initial state , Allocate decision interval , guidance advantage weight coefficient: , , , observer parameters: , , , , , , In the above scenario, the missile group will complete a total of 500 rounds of offline training, and the target type, speed, and maneuvering acceleration in each round will be randomly generated within a specific range. After obtaining a total of more than 70,000 sets of samples, the neural network will be trained in turn and deployed on the interceptor missile.

[0059] The missile group that has completed the neural network deployment can perform online interception tasks against targets of specific types and speeds. The following two examples are provided.

[0060] Example 1: In Example 1, the type (quantitative value), maximum speed, maximum normal / lateral acceleration and acceleration command of each target are given in Table 3 (the target acceleration command cannot be obtained in advance), and the simulation intercepts an enemy formation consisting of 2 reconnaissance aircraft and 1 heavy bomber. The simulation results will be Figure 8-Figure 9 Given.

[0061] Table 3 Target information of Example 1 , Example 2: In Example 2, the type (quantitative value), maximum velocity, maximum normal / lateral acceleration, and acceleration command of each target are given in Table 4 (the target acceleration command cannot be obtained in advance), and the simulation intercepts three enemy medium-sized tactical missiles with different performance. The simulation results will be presented in Figure 10-11 Given.

[0062] Table 4 Target information of Example 2 ,

[0063] Simulation results analysis: Figure 8 It can be seen that after three dynamic allocation decisions, the overall expected interception efficiency of the missile group gradually stabilized, and the allocation results of each interceptor missile did not change thereafter. Under the action of the cooperative guidance law, each interceptor missile flew to its respective target with a smooth trajectory and achieved synchronous interception using internal communication.

[0064] Fig. 9 , Fig.11 The changes of the remaining flight time of each interceptor missile in the above two examples are shown respectively. It can be seen that when the allocation result changes, the remaining flight time of each interceptor missile will also change greatly, but thanks to the design of the cooperative guidance law, the remaining flight time of each interceptor missile will reach a consensus again before the next allocation occurs. According to the changes of the relative distance between the missile and the target in the two examples. It can be seen that in addition to the drastic changes with the allocation result, the relative distance between each interceptor missile and its target can be reduced smoothly. According to the changes of the acceleration of each interceptor missile. It can be seen that in the initial stage of the interception, due to the deviation between the line of sight angular rate and the remaining flight time and their predetermined values, and affected by the changes in the allocation results, the acceleration of each interceptor missile changes greatly and continues to be "saturated"; while in the middle and final stages of the interception, the acceleration changes of each interceptor missile gradually tend to be gentle.

[0065] Tables 5 and 6 give the cooperative interception results of Example 1 and Example 2, respectively. It can be seen that in the above two examples, all interceptors intercept the target with a sufficiently small miss distance and reach a consensus on the interception time.

[0066] In addition, in order to compare the performance difference between the centralized-PSO algorithm used in the offline training stage and the distributed-neural network algorithm used in the online decision stage, we conducted comparative experiments under the above two examples. After a few allocation decisions, both algorithms can stabilize the overall expected interception effectiveness of the swarm. This shows that the neural network has well learned the allocation decision behavior of the swarm in the offline training stage, and has produced the global optimal allocation result through distributed decision-making without a central node. Affected by the size of the swarm and the calculation method (repeated iterative solution), the single decision time of the centralized-PSO algorithm is mostly more than 0.04 s; while the single decision time of the distributed-neural network algorithm is mostly less than 0.01 s. Therefore, compared with the centralized-PSO algorithm, the distributed-neural network algorithm has stronger timeliness.

[0067] The above simulation results show that the multi-target collaborative interception allocation and guidance method designed in this application can not only meet the needs of multi-target collaborative interception tasks, but also achieve the global optimal collaborative interception effect through the autonomous decision-making, control and internal communication of each interceptor missile.

Claims

1. A multi-target coordinated interception allocation and guidance method, characterized in that: The following steps are involved: S1. Determine the communication network within the missile group and the kinematic model of interception; S2, establishing a multi-objective dynamic allocation optimization model according to step S1; S3, using a distributed dynamic allocation method based on a neural network to solve the multi-objective dynamic allocation optimization model of step S2; S4. Design and implement a coordinated guidance law for multiple interceptor missiles. After determining their respective interception targets in step S3, each interceptor missile must fly to the target under the guidance of the coordinated guidance law for multiple interceptor missiles before the next allocation occurs or the interception ends.

2. A multi-target coordinated interception allocation and guidance method according to claim 1, characterized in that: The communication network within the group is determined in step S1 as follows: Interceptor missiles ( ) targets to be intercepted, and information is transmitted between the interceptor missiles through the communication network; The communication network consists of a connection diagram between interceptor missiles Describe, among which, To intercept missiles, is the edge set; When there is an edge , At that time, The interceptor missile can The interceptor missile transmits the information. If the edge , then The interceptor missile could not reach the The interceptor missile transmits the information. ; The kinematic model of interception refers to the interceptor missile With the goal Motion model: Setting the inertial coordinate system and the line of sight coordinate system , In the inertial coordinate system Next, interceptor missile The equation of motion is: , In the formula, for The position in the inertial coordinate system, for speed, for The pitch angle, for The yaw path angle; Target The equation of motion for is: , In the formula, for The position in the inertial coordinate system, for speed, for The pitch angle, for The yaw path angle; Relative to The sight coordinate system is obtained by rotating the inertial coordinate system. In the sight coordinate system, express and The relative distance and Respectively Relative to The sight inclination and sight deflection angles; When the interceptor The target of the assignment is When , , If the missile is intercepted later The allocation target of no longer changes, then: .

3. A multi-target coordinated interception allocation and guidance method according to claim 1 or 2, characterized in that: The step S2 specifically includes the following steps: S21. Confirm Moment The interceptor missile The comprehensive guidance advantage of each target; S22, determine the The overall threat level of the target; S23. Determine the expected interception effectiveness of the missile group against the target group; S24. Determine the optimal allocation matrix and constraints.

4. A multi-target coordinated interception allocation and guidance method according to claim 3, characterized in that: The comprehensive guidance advantage in step S21 includes the The interceptor missile The guidance advantage of the target line of sight angular velocity, The interceptor missile The remaining flight time of the target and the guidance advantage of the The interceptor missile The guidance advantage of the target field of view constraint; Among them, the The interceptor missile The guidance advantage of the target line of sight angular velocity is: , In the formula, represents the weight coefficient, express Relative to The line of sight inclination rate, express Relative to The line of sight deflection rate; The said The interceptor missile The guidance advantage of the remaining flight time of a target is: , In the formula, represents the weight coefficient, Indicates The interceptor missile The remaining flight time of a target is defined as: , Indicates The estimated remaining flight time of the interceptor missile, i.e. The remaining flight time of an interceptor missile against the currently assigned target; Since at the initial moment of guidance , the targets of the interceptor missiles have not yet been determined, for: , Where: Indicates The interceptor missile The remaining flight time for each target, represents the optimal allocation matrix Line Elements of a column; The The interceptor missile The guidance advantage of a target with respect to the field of view constraint is defined as: , where: represents the weight coefficient, is time t Relative to The sight angle, is time t The pitch angle, is time t Relative to The sight angle, is time t The yaw path angle; Said Moment The interceptor missile The comprehensive guidance advantage of a target is expressed as: .

5. A multi-target coordinated interception allocation and guidance method according to claim 3, characterized in that: In step S22, The overall threat level of a target includes speed threat level, maximum normal / lateral acceleration threat level and type threat level, where the speed threat level is: , Where: Maximum speed , The maximum normal / lateral acceleration threat level is: , Maximum normal / lateral acceleration satisfy: , The threat level of the type is: , Where: Indicates Quantized value of target type, Indicates Quantized value of target type, The overall threat level is .

6. A multi-target coordinated interception allocation and guidance method according to claim 3, characterized in that: The expected interception efficiency of the missile group against the target group in step S23 is as follows: The comprehensive guidance advantage of a single interceptor missile is regarded as its expected interception success rate of the target, and the missile group is defined as The expected interception effectiveness of a target is: , Considering the overall threat level of the target in step S22, the expected interception effectiveness of the missile group against the target group is: .

7. A multi-target coordinated interception allocation and guidance method according to claim 3, characterized in that: The details of step S24 are as follows: Based on the expected interception effect obtained in step S23, the optimal allocation matrix is ​​obtained as follows: , is the allocation matrix, where , ; The constraints of the optimal allocation matrix are: , , , represents the allocation matrix Any element of The value is either 0 or 1. At that time, The interceptor missile will be assigned to A goal, when At that time, The interceptor missile is not assigned to goals; , This means that one interceptor missile can only be assigned to one target, and each target must be assigned at least one interceptor missile.

8. A multi-target coordinated interception allocation and guidance method according to claim 3, characterized in that: The distributed dynamic allocation method based on neural network in step S3 specifically includes the following steps: S31, offline training: the offline training includes building a neural network and network training, The construction of the neural network is specifically as follows: the swarm completes multiple rounds of training with the participation of the central node, and one training round is usually composed of several allocation decisions. In each decision, the central node uses a particle swarm optimization algorithm to solve the optimal allocation problem; After completing all training rounds, the guidance advantage of each interceptor in each allocation decision is calculated. , target threat , and the distribution results Save it, , The expanded vector As network input, assign the result As the network output, for each interceptor Build a neural network; The neural network adopts a feedforward network structure with multiple hidden layers. The mapping relationship between the input and output of each layer of the network is expressed as: , In the formula, Indicates Layer, The output of a neuron, , represents the weight vector of the neuron, is the threshold of the neuron, For the The column vector composed of the output of each neuron in the layer; The activation functions of the hidden layer and the output layer are respectively selected as S-shaped growth curve functions With linear transfer function ,for , both satisfy: , , Will The output vector generated after inputting the network is recorded as , then the network output error of a single sample is expressed as: ; The network training is performed by optimizing the weights of each neuron. With threshold , so that the network output of all samples has mean square error Minimum, ; The network is trained using the adaptive moment estimation algorithm, and the trained network is expressed as follows: ; S42, online decision-making: the online decision-making includes autonomous allocation and consistency auction strategies; The online decision-making is as follows: the guidance advantage and target threat in the online decision-making stage are respectively denoted as , , Each interceptor missile will The guidance advantage and target threat are input into the trained neural network to generate an uncorrected allocation plan: , right After correction, the autonomous allocation results of each interceptor missile are obtained: , , , Each interceptor will share the results with neighboring nodes, so every node in the communication network will know the distribution of each target. , ; The consistency auction strategy is as follows: Due to the connection diagram between the interceptor missiles is undirected and connected, there exists a path from Departure and finally return Path; The nodes on the path are Make a quotation according to , update the current highest price and send the price together with the list of bidders Send to the next bidder; When a bidder When the current highest price is received again, if: , then the bidder's bid is successful, let: , , In the absence of a central node, internal communication within the swarm is used to successfully avoid missing allocation results.

9. A multi-target coordinated interception allocation and guidance method according to claim 8, characterized in that: In the step S31, the central node adopts the particle swarm optimization algorithm to solve the optimal allocation problem. For the situation that the multi-objective dynamic allocation optimization model is not satisfied during the particle update process, the following correction is made: the position of a particle after a certain update is recorded as ; Step 1: Order , , , Step 2: If the first round of revisions There is a column in , so that , then in all the Randomly select a column from the columns of : If the column is taken as Column, then in all Randomly select a row from the rows ,make , .

10. A multi-target coordinated interception allocation and guidance method according to claim 3, characterized in that: In step S4, based on the fact that all interceptor missiles successfully intercept their respective targets at the same time, the remaining flight time tends to be consistent, and the line of sight angular rate converges to 0, the coordinated guidance rate of multiple interceptor missiles is designed, including the coordinated guidance rate in the line of sight direction and the coordinated guidance rate in the line of sight normal direction, as follows: In the line of sight, according to , get: , set up , let the virtual control input be: According to the above formula, ; Order: Replace with its observed value , and according to the above two formulas, we get The guidance instructions in the line of sight direction are: ; In the line of sight normal direction, set , , and the virtual control input is: , , according to: , ,get , ; make: , ,Will , Replace with observed values , ,get The guidance instructions in the normal direction of the line of sight are: ,as well as ; The implementation of the coordinated guidance law of multiple interceptor missiles in step S4 is specifically as follows: When comprehensive After the guidance instructions in the sight direction and sight normal direction, the control input of the interceptor missile in the sight system is obtained as follows: , , after rotation transformation, we get Acceleration command in inertial system , ， In the formula, , , In order to observe all targets synchronously, the following transformation is used to obtain the guidance instructions under the line of sight system: , , , and update the observer; The observer is: , , Among them, the measurable state , They are , as well as ; for The observed value of , Disturbance , as well as Observed value of The observer observes all targets synchronously and is continuously updated as the interception mission progresses to ensure that the disturbance observation information of the target is obtained immediately when the interception target changes.

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