Method for planning communication link of star-burst cooperative operation

Abstract

The application relates to a star missile communication link planning method for missile group cooperative combat, and comprises the following steps: S100, determining a dynamic model of the distance between a missile and a target and an external control function of the dynamic model; S200, constructing a directed time-varying topology graph; S300, judging star missile cooperation feasibility according to the dynamic model, the external control function and the directed time-varying topology graph; and S400, determining an energy loss function which is positively related to the change rate of the external control function, and optimizing the star missile communication link by minimizing the energy loss function. The application converts the missile group cooperative combat communication link into a directed time-varying topology graph, and proposes an energy loss function, so that the communication topology planning problem is converted into an energy loss function minimization solving problem, the star missile cooperative combat communication problem is ingeniously converted into a mathematical optimization problem of the directed time-varying topology graph model, the problem is simplified, and the missile group cooperative combat capability is greatly improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of satellite application technology, and particularly relates to a star-missile communication link planning method for missile group cooperative combat. BACKGROUND

[0002] Compared with single means attack and defense missiles, missile group cooperative combat has higher striking efficiency, and has stronger striking ability to enemy high-value targets such as aircraft carrier battle groups and destroyer formation. The missile group can achieve omnidirectional saturated attack on the target by planning the attack angle and attack route, and finally reaching at the same time or reaching at different attack positions at the same time, thereby improving the penetration probability of the missile and the striking ability to the target.

[0003] With the rapid development of space technology, satellite resources are becoming more and more abundant, and space-based equipment will be applied in modern integrated cross-domain cooperative combat and play an important role. Using space-based equipment to improve the ability of missile group cooperative combat is a further innovation and improvement of missile group cooperative combat. On the one hand, the satellite system can realize high-precision monitoring and sensing in all dimensions of a large range of battlefield by dynamically adjusting the constellation connection relationship. On the other hand, the missile group system effectively reduces the communication and information processing links between the missile groups by using the advantages of space-based information support, thereby improving the security and reliability of information transmission, and enhancing the flexibility and anti-destroying ability of the missile group in the battlefield.

[0004] Modern war is mainly based on precision strike, and star-missile link planning will become a key factor affecting the effectiveness of star-missile cooperative combat.

[0005] In modern warfare, fast-paced, long-range strike has become the main mode of operation on the battlefield. Many countries are developing missile cooperative data link technology, so that the penetration missiles can cooperate through the inter-missile data link to improve the penetration probability and strike effect of the missile. The research on the satellite-missile communication link between weapon systems and command and control platforms has been a research hotspot in the industry and academia for a long time. The article published in 2001, "Foreign Missile Satellite Data Link Transmission System Tracking Research", discusses the development status and application of foreign satellite-missile link systems, focuses on analyzing the key technologies in the satellite-missile link, and puts forward some countermeasures and suggestions; the article published in 2007, "Channel Modeling and Simulation of Satellite-Missile Link in Missile Flight Control Data Link", based on the characteristics of the satellite relay missile flight control data link satellite-missile link, establishes the statistical and simulation model of the channel, and based on the model, the Monte Carlo simulation is carried out in three communication environments of sea surface, plain and mountain area; the article published in 2014, "Missile-Satellite Communication Link Simulation Based on Trajectory Data", proposes a satellite-missile communication link simulation scheme of single satellite-single missile, through adding specific trajectory data files and calculation modules, the satellite-missile communication link is simulated more accurately, a complete satellite-missile communication link model is built, and the communication link situation, communication channel characteristics and other data in the whole flight process of the missile are obtained through simulation.

[0006] The above researches are all aimed at traditional communication satellites. Traditional satellite communication adopts high-orbit relay satellites, and due to the restriction of satellite orbit, development cost and other factors, the number of communication satellites used for missile communication is small, and the current research work is limited to the application scenario of single satellite-single missile. In recent years, low-orbit communication is becoming a hot application in the military field. Compared with high-orbit communication, the communication delay is reduced from hundreds of milliseconds to tens of milliseconds, which is more effective for super-high-speed missile control, and the communication transmission loss is reduced by dozens of dB, which is the basis for the identification of communication terminal miniaturization and high-speed data transmission. Especially with the breakthrough of innovative technologies such as SpaceX, low-orbit satellite systems are being deployed on a large scale, and the system capacity, cost, reliability, development and deployment period have significant advantages.

[0007] However, the low-orbit communication satellite has a low orbit height and a small coverage area on the ground, and multiple satellites must be networked to achieve global coverage, and the multi-satellite-multi-missile communication planning problem is still blank. SUMMARY

[0008] Therefore, the present application aims to provide a satellite-missile communication link planning method for missile group cooperative combat, so as to solve the technical vacancy in the multi-satellite-multi-missile communication planning.

[0009] The satellite-missile communication link planning method for missile group cooperative combat provided by the embodiment of the present application comprises:

[0010] S100, determining a dynamic model of a distance between a missile and a target and an external control function of the dynamic model;

[0011] S200, constructing a directed time-varying topology graph;

[0012] S300, determining a star-missile cooperation feasibility according to the dynamic model, the external control function and the directed time-varying topology graph;

[0013] S400, determining an energy loss function positively related to a variation rate of the external control function, and optimizing the star-missile communication link by minimizing the energy loss function.

[0014] Further, the step S100 comprises:

[0015] a distance ρ i between a missile i and a target

[0016]

[0017] wherein u i is a control input of the missile i with respect to the distance ρ i , and t is a time;

[0018] The external control function is represented as a control protocol of the satellite i:

[0019]

[0020]

[0021] wherein k i is a control gain, is a distance of the satellite observed missile j1,...,j r to the target, is a time of the satellite observed and calculated missile j1,...,j r to reach the target, and j≠1,j∈{j1,...,j r}.

[0022] Further, the step S200 comprises:

[0023] The directed time-varying topology graph is constructed as:

[0024] G(t)=(V,E(t),A(t))

[0025] wherein a vertex set V is a missile system {1,...,n}, E(t) is an edge set, A(t)=[a ij (t)] n×n ∈R n×n is a corresponding adjacency matrix.

[0026] Furthermore, step S200 also includes:

[0027] For any time t, satellite i obtains information about missiles j1,...,j based on its own observations and inter-satellite link communication. r Information, if j,l∈{j1,...,j r If l≠1, then (j,l)∈E, and a lj =1; if j,l∈{j1,...,j r If l = 1, then And a lj =0;

[0028] The switching time of G(t) is represented as t k For k = 1, 2, ..., the duration for which G(t) maintains the same communication status after the k-th handover is denoted as T. k k = 1, 2..., the initial time is represented as t0 = 0, and in the corresponding time interval [t k-1 ,t k The communication topology of the missile system is represented as follows:

[0029] Communication topology The union is represented as in, Let be a continuous, non-empty, uniformly bounded time interval, and

[0030] Further, step S300 includes:

[0031] The directed time-varying topology is determined based on the dynamic model and the external control function. Does it contain a spanning tree with the leader as the root node?

[0032] If so, then coordinated attacks between spacecraft and missiles can be achieved;

[0033] If not, then a combined space-missile strike cannot be achieved.

[0034] Furthermore, the directed time-varying topology graph is determined. Does it contain a spanning tree rooted at the leader node?

[0035] when And communication topology The corresponding weighted Laplace matrix is ​​matrix sum matrix At that time, communication topology satisfies that it contains a spanning tree with node 1 as the root, the corresponding weighted Laplacian matrix has and only has one zero eigenvalue, and all other eigenvalues are in the third and fourth quadrants of the complex plane, and In the case where node 1 has no predecessor, the topology The first row of the corresponding weighted Laplacian matrix is all zero, and the vector (1, 0,..., 0) T is a matrix and corresponds to a zero eigenvalue; then the communication topology The corresponding Laplacian matrix is represented as When and , the matrix and satisfy that there is and only is one zero eigenvalue, and the eigenvector corresponding to the zero eigenvalue is (1, 0,..., 0) T , and other eigenvalues all have positive real parts.

[0036] Further, the energy loss function is represented as:

[0037]

[0038] where u = [u1,..., u n ] T , ρ = [ρ1,..., ρ n ] T , η i > 0 and γ i > 0 are weights of energy consumption loss of the missile i when adjusting the state based on the leader missile, a i (t) = 1 if and only if there is j ≠ i, (j, i) ∈ E, otherwise, a i (t) = 0.

[0039] Further, optimizing the satellite missile communication link by minimizing the energy loss function comprises:

[0040] The constellation system selects, according to the external control function, a missile in the missile group that minimizes the energy loss function after establishing a communication link to establish a communication link.

[0041] According to an aspect of the present application, the present application maps the communication process of the missile group on a directed time-varying topology graph, each missile is mapped as a vertex of the graph, and the communication between the missiles through the satellite system is mapped as an edge of the graph. The dynamic establishment of the communication link between the satellite system and the missile group is mapped as the time-varying characteristic of the directed graph. The communication planning problem of the cooperative attack process of the missile group is converted into an optimization problem of the directed time-varying topology graph, which realizes the automation of the communication planning process of the missile group and greatly improves the working efficiency of the missile group.

[0042] According to an aspect of the present application, the present application proposes a speed function which is positively related to the distance between the missile and the target, can gradually coordinate the arrival time of the missile through step-by-step implementation of the speed control, and finally can realize the consistent arrival time, as the external control function required by the dynamic model. The function is matched with the operation characteristic that the satellite system and the missile group need to go through multiple time windows to realize the cooperative operation of the whole missile system, and ensures the communication feasibility of the cooperative operation of the satellite system and the missile group.

[0043] According to an aspect of the present application, the present application completes the feasibility determination of the missile group cooperation based on the characteristic parameters of the directed time-varying topology graph, and converts the gradual realization of the simultaneous attack on the target by the missile group cooperation into the problem of determining whether the directed time-varying topology graph contains a spanning tree with the leading missile as the root node. If the spanning tree exists, the missile group cooperation can realize the simultaneous attack; if the spanning tree does not exist, the missile group cooperation cannot realize the simultaneous attack.

[0044] According to an aspect of the present application, the present application proposes an energy loss function which is positively related to the difference between the estimated arrival time and the change rate of the estimated arrival time control, and realizes the optimization of the communication link of the missile group by minimizing the energy loss function. BRIEF DESCRIPTION OF DRAWINGS

[0045] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description only constitute some embodiments of the present application, and other drawings can also be obtained by those skilled in the art without any creative effort on the basis of these drawings.

[0046] Figure 1 The flowchart of the missile group cooperative operation satellite-missile communication link planning method of the embodiment of the present application;

[0047] Figure 2 The principle diagram of the missile group cooperative operation satellite-missile communication link planning method of the embodiment of the present application. DETAILED DESCRIPTION

[0048] The description of the embodiments in this specification should be taken in conjunction with the accompanying drawings, which should form part of the complete specification. In the drawings, the shape or thickness of the embodiments may be exaggerated and may be indicated in a simplified or convenient manner. Furthermore, parts of the various structures in the drawings will be described separately; it is worth noting that elements not shown in the figures or not described in words are in a form known to those skilled in the art.

[0049] The descriptions of the embodiments herein, including any references to directions and orientations, are for ease of description only and should not be construed as limiting the scope of the invention. The following description of preferred embodiments involves combinations of features, which may exist independently or in combination; the invention is not particularly limited to the preferred embodiments. The scope of the invention is defined by the claims.

[0050] In the constellation system, any satellite i, orbiting the Earth, will activate its power and begin continuous observation of the missile swarm when it approaches. Indicates the k-th power-on time of satellite i, and simultaneously lets This represents the duration of satellite i's k-th activation. The initial time is denoted as t0. At this time, if satellite j exists and satellite i and satellite j can establish an inter-satellite link, they can exchange their respective observation information on the missile group. Assume that satellite i is... At any given moment, based on its own observations and inter-planetary link communication, it obtains information about missiles j1,...,j. r Location and speed information.

[0051] The main function of this invention embodiment is to, based on the information obtained from satellite i, target missiles j1,...,j r Based on relevant information, design and calculate missile j1,...,j r exist Control input u during the satellite power-on time after the specified time j ,j=j1,...,j r And continuously transmit updated control inputs to missiles j1,...,j r Simultaneously, based on the designed control inputs, the startup time of the constellation system is planned, and sufficient conditions for the missile swarm to achieve simultaneous attack under star-missile coordination are given.

[0052] like Figure 1 and Figure 2 As shown, this embodiment of the invention provides a method for planning a space-missile communication link in missile swarm cooperative operations. The planning method includes:

[0053] S100, a dynamic model for determining the distance between the missile and the target, and an external control function for the dynamic model.

[0054] That is, a velocity function that is positively correlated with the distance between the missile and the target, can be gradually coordinated by implementing velocity control in stages, and can eventually achieve consistent arrival times, is determined as the external control function required by the dynamic model.

[0055] Consider a mission to strike a target using a swarm system of n missiles and a constellation system of m satellites. The mission objective is to achieve simultaneous and precise strikes on the target by all missiles in a predetermined formation through satellite-to-satellite and satellite-to-missile communication. In the swarm system, it is assumed that the target is fixed and its location information is known to all missiles.

[0056] Initially, all missiles flew towards the target along predetermined trajectories. i Let ρ be the distance between missile i and the target. i The dynamic model is as follows:

[0057]

[0058] Among them, u i For missile i about ρ i The control input. Without loss of generality, assume that missile 1 in the missile system is the lead missile, and u1(t) = 0 always holds true. During the target engagement, all missiles communicate only with the satellite. At any time t, when satellite i establishes communication with missile j, satellite i will design the control input u1(t) of missile j based on its acquisition information of the missile group. j and will update u j It is continuously transmitted to the missile.

[0059] The external control function is represented as the control protocol for satellite i. Specifically, it is assumed that satellite i operates during the power-on period. Inside, missiles j1,...,j were continuously observed. r Position and velocity information. (Let) This represents the missiles j1,...,j observed by the satellite. r The distance from the target, let This represents the missile j1,...,j values ​​obtained through satellite observation and calculation. r The time to reach the target is given by any j ≠ 1, j ∈ {j1, ..., j}. r Satellite i continuously calculates the following protocol:

[0060]

[0061]

[0062] Where, k i To control the gain, missiles j1,...,j r observed by satellite i, missiles j1,...,j r observed by satellite i and calculated by satellite i, r} and send to missiles j1,...,j r until satellite i is shut down.

[0063] S200, constructing a directed time-varying topology graph.

[0064] The directed time-varying topology graph is:

[0065] G(t) = (V, E(t), A(t))

[0066] wherein, vertex set V is missile system {1,...,n}, E(t) is edge set, A(t) = [a ij (t)] n×n ∈R n×n is an adjacency matrix corresponding to V and E(t). At any time t, assuming satellite i obtains missiles j1,...,j r information according to its own observation and inter-satellite link communication, if j, l ∈ {j1,...,j r}, l≠1, then (j, l) ∈ E, and the corresponding a lj =1. Otherwise, the corresponding a lj =0. The communication change of G(t) is determined by the communication link establishment between satellite and missile group. At any time, when satellite i obtains missiles j1,...,j r information directly or through inter-satellite link and establishes communication link with them, it is equivalent to establishing communication link between missiles j1,...,j r in G(t). G(t) is switched with time.

[0067] Let t k ,k = 1, 2,... represent the switching time of G(t), i.e., the switching time of communication link establishment between satellite group system and missile system. Let T k ,k = 1, 2,... represent the duration of keeping the communication unchanged after the kth switching of G(t), i.e., the time of keeping the communication link establishment between satellite group system and missile system after the kth switching. t0=0 represents the initial time.

[0068] Let represent the communication topology of the missile system in the corresponding time interval [t k-1 ,t k ). All communication topologies satisfy that the first node has no predecessor node. Let denotes a series of continuous, non-empty, uniformly bounded time intervals, and Let denotes the communication topology of the union.

[0069] S300, determining star-missile coordination feasibility according to the dynamic model, the external control function and the directed time-varying topology graph.

[0070] That is, based on the characteristic parameters of the directed time-varying topology graph, the feasibility of star-missile coordination is determined.

[0071] Considering that the star-missile coordination can achieve simultaneous attack on the target, the dynamic model of the missile system is (1), and the star group system designs the control input of the corresponding missile in the missile system through protocols (2) and (3), then the star-missile coordination can achieve asymptotic simultaneous attack on the target can be converted into whether the directed time-varying topology graph contains a spanning tree with the leader missile as the root node. If yes, the star-missile coordination can achieve simultaneous attack; if no, the star-missile coordination cannot achieve simultaneous attack.

[0072] First, introduce Lemma 1 and Lemma 2.

[0073] Lemma 1: Introduce the average system theory, and analyze the effectiveness of the star-missile coordination attack in achieving simultaneous attack on the target by the missile group using control protocols (2) and (3) by means of the average system theory.

[0074] Consider the following linear time-invariant system:

[0075]

[0076] where A(·): R→R n×n , it is assumed that there exists a strictly increasing time sequence t k , k = 0, 1, …, and satisfies t k+1 -t k ≤ T, where T > 0, for any t k , it is assumed that there is a time-invariant system as follows:

[0077]

[0078] Asymptotically stable, then:

[0079] ① There exists α * > 0, which satisfies the following time-varying system:

[0080]

[0081] which satisfies for all α > α *, the system (4) is asymptotically stable.

[0082] ② The above α * can be uniquely determined by T>0, and there is the following implicit function relationship between them:

[0083]

[0084] where, K v > 0, K>0, v>0 are the corresponding parameters.

[0085] ③ The α * satisfies

[0086] Lemma 2: The determination method of whether the directed time-varying topological graph contains a spanning tree with the leader as the root node.

[0087] Let the matrix respectively represent the graph corresponding Laplacian matrix. Let and Then the matrix and satisfy, there exists and only exists one eigenvalue of 0, and the corresponding eigenvalue of (1,0,...,0) T , the rest of the eigenvalues all have positive real parts.

[0088] Proof of Lemma 2: Since , the matrix and the matrix can be regarded as the weighted Laplacian matrix corresponding to the communication topology . Since the communication topology satisfies that it contains a spanning tree with node 1 as the vertex, the corresponding weighted Laplacian matrix has and only has one eigenvalue of 0, and all other eigenvalues are in the third and fourth quadrants of the complex plane. Since , node 1 has no predecessor node, then the topology corresponds to all weighted Laplacian matrices whose first row is all 0, and the vector (1,0,...,0) T is the eigenvalue of the matrix and corresponding to the eigenvalue of 0.

[0089] Further, based on Lemma 1 and Lemma 2, the following is proved:

[0090] First, combined with the time-varying topology , (2) is rewritten as the following form:

[0091]

[0092] Furthermore, (5) can be written in the following matrix form:

[0093]

[0094] Where τ=[τ1,...,τ n ] T L(t)=[l ij (t)] n×n ∈R n×n , l ij (t) satisfies that when i≠j, l ij (t)=-k i a ij (t), when i = j

[0095] In fact, for protocols (5) and (3), if there exists a time t at which all missiles arrive at the target at the same time as the lead missile, and after time t, the estimated arrival time of all missiles at the target continues to be consistent with the lead missile, then this strike on the target can achieve the desired mission, that is, all missiles can arrive at the target simultaneously.

[0096] Next, let ξ i =τ i -τ1, i=2,...,n, then ξ i The system model can be written as:

[0097]

[0098] Consider L(t), a 1j = 0 always holds true, L(t) can be written as Where β(t) is an n-1 dimensional vector, and H(t)∈R (n-1)×(n-1) Furthermore, let ξ = [ξ2, ..., ξ] n ] T (7) can be written in the following matrix form:

[0099]

[0100] For time interval Consider a series of subsystems:

[0101]

[0102] Its corresponding average system is:

[0103]

[0104] Among them, the system matrix Satisfy any t k =ls ...,l s+1 -1, and

[0105] Since for each time interval a general continuous-time linear system of the form (9) can be summarized. So one of the sufficient conditions for the stability of system (7) is that for any s = 0, 1,..., system (9) is stable.

[0106] Definition It can be written as the following block matrix If the assumption 2 is true, i.e. The corresponding communication topology contains a spanning tree with node 1 as the root node, and node 1 has no predecessor node. Then according to Lemma 2, There exists and only exists one eigenvalue of 0, and the rest of the eigenvalues have positive real parts, so The eigenvalues of have positive real parts, and system (9) is asymptotically stable. Correspondingly, system (7) is asymptotically stable. At this time, all missiles eventually estimate the arrival time consistent with the leading missile. Therefore, the star-missile cooperation can asymptotically achieve simultaneous attack on the target. The above theorem is proved.

[0107] S400, determining an energy loss function positively related to the rate of change of the external control function, and optimizing the star-missile communication link by minimizing the energy loss function.

[0108] For convenience of description, a typical quadratic function is used, which contains two parts of variables of the difference of the estimated arrival time and the rate of change of the estimated arrival time control. The energy loss function is:

[0109]

[0110] Where, u = [u1,...,u n ] T , ρ = [ρ1,...,ρ n ] T , η i > 0 and γ i > 0 are the weights of the energy loss of missile i when adjusting the state based on the leading missile, a i (t) = 1 if and only if there is j ≠ i, (j, i) ∈ E, otherwise, a i (t) = 0. a i (t) satisfies any time t ≥ 0, if the constellation system monitors missile i and other missiles at the same time, a i (t) = 1. Otherwise, a i(t) = 0. Considering that all missiles in the swarm discussed in this method are homogeneous, without loss of generality, it is assumed that for any i≠j, η i = η j , γ i = γ j .

[0111] In star-missile coordination, only the constellation system within the on-time, i.e., selecting different missiles to establish communication links, affects the simultaneous strike effectiveness of the missile swarm. The optimization problem of the star-missile communication link is converted into the constellation system applying protocols (2) and (3), through selecting appropriate missiles and establishing communication links with them, so that the energy loss function, i.e., J(u, p), is minimized.

[0112] Considering that the dynamic model of the missile system is (1), the constellation system designs the control input of the corresponding missile in the missile system through protocols (2) and (3). Assuming that the initial conditions of the missile swarm system are fixed, the on-time and time interval of the constellation system are certain, then the method of optimizing formula (10) by the star-missile communication link planning is that within any on-time of the constellation, the communication link established by the missile swarm through the constellation system is a directed star topology centered on the leader missile, and the weight is

[0113] First, Lemma 3 is introduced. The LQR problem is introduced, and the optimal method of star-missile link planning in star-missile coordination is analyzed by means of the optimal control in the LQR problem.

[0114] Consider the following system:

[0115]

[0116] And define the loss function as:

[0117]

[0118] Where R is a positive definite matrix, Q is a semi-positive definite matrix and satisfies Q = H T H. If (A, B) is controllable and (A, H) is observable, then the optimal control that minimizes the energy loss function (10) is:

[0119] u(t) = -R -1 B T Px(t) (13)

[0120] Where P is a symmetric positive definite matrix and satisfies the following Riccati equation;

[0121] A T P+PA+Q-PBR -1 B T P = 0 (14)

[0122] Based on Lemma 3, the following is proved:

[0123] Since L i represents the missile j i observed by the constellation system, combining equation (3), J(u, p) can be transformed as:

[0124]

[0125] where η > 0, γ > 0. Since and L(t) can be written as the following block matrix form:

[0126]

[0127] Let ξ i = τ i - τ1, ξ = [ξ2,..., ξ n ] T , consider always holds, and there is written in the matrix form as follows:

[0128]

[0129] So equation (15) can be converted to:

[0130]

[0131] The optimization problem of the star missile communication link planning is converted to design reasonable a(t) and H(t) to make equation (17) optimal, while

[0132] On the other hand, according to Lemma 3, consider the following system:

[0133]

[0134] and define the loss function as:

[0135]

[0136] where Q = ηI n-1 , R = γI n-1 . In system (18), A = 0 (n-1)×(n-1) , B = I n-1 , Obviously, (A, B) is controllable and (A, H) is observable. According to Lemma 3, there exists a symmetric positive definite matrix P that satisfies:

[0137] Q - PR -1 P = 0 (20)

[0138] and the optimal control input of formula (19) is:

[0139] u(t) = -R -1 Px(t).

[0140] Let R -1 act on both sides of formula (20) and have The optimal control input is Substitute u * (t) into formula (19) and have

[0141] Referring to system (18), consider system (16), if the communication link established by the missile group through the constellation system is a directed star topology centered on the leading missile in each time interval , and the weight is , formula (17) can be expressed as:

[0142]

[0143] Since the constellation system does not detect the missile system when δ(t) = 0, all missiles continue to fly towards the target at the speed at the last shutdown time of the constellation system, and at this time, any missile i, before receiving the control input designed by the constellation system, its ξ i remains unchanged. Therefore, there is ξ i (t k +T k ) = ξ i (t k+1 ), where k = 1, 2,... Therefore, there is At this time, the star missile link planning method is optimal control. The theorem 2 is proved.

[0144] In summary:

[0145] The present application maps the star missile communication process on a directed time-varying topology graph, each missile is mapped as a vertex of the graph, and the communication between the missiles through the satellite system is mapped as the edge of the graph. The dynamic establishment of the communication link between the satellite system and the missile group is mapped as the time-varying characteristics of the directed graph. The communication planning problem of the missile group cooperative attack process is converted into an optimization problem of the directed time-varying topology graph, which not only realizes the automation of the star missile communication planning process, but also greatly improves the working efficiency of the star missile system cooperation.

[0146] The application proposes a speed function positively related to the distance between the missile and the target, which can gradually coordinate the arrival time of the missile through step-by-step implementation of speed control, and finally realize the consistency of the arrival time, as an external control function required by the dynamic model. The function matches the operation characteristics of the satellite system and the missile group, which need to go through multiple time windows to realize the coordinated operation of the whole missile system, and ensures the communication feasibility of the coordinated operation of the satellite system and the missile group.

[0147] The application determines the feasibility of satellite-missile coordination based on the characteristic parameters of the directed time-varying topology graph, and converts the gradual realization of the satellite-missile coordination to the simultaneous attack on the target into the problem of whether the directed time-varying topology graph contains a spanning tree with the leading missile as the root node. If the spanning tree exists, the satellite-missile coordination simultaneous attack can be realized; if the spanning tree does not exist, the satellite-missile coordination simultaneous attack cannot be realized.

[0148] The application proposes an energy loss function positively related to the difference between the estimated arrival time and the control rate of the estimated arrival time, and realizes the optimization of the satellite-missile communication link by minimizing the energy loss function.

[0149] The application first adopts the satellite-missile communication link planning method based on the directed time-varying topology graph model of the missile group coordinated operation, proposes to convert the communication link model of the missile group coordinated operation into a directed time-varying topology graph, and converts the feasibility problem of the communication link support of the missile group coordinated operation into the spanning tree determination problem with the leading missile as the root node; further proposes an energy loss function, and converts the communication topology planning problem into the minimum solving problem of the energy loss function. The application first converts the complex satellite-missile coordinated operation communication support problem into a mathematical optimization problem of the directed time-varying topology graph model, which will greatly improve the support capability of the space-based equipment for the missile group coordinated operation.

[0150] The application can be applied to the cooperative communication problems of the heterogeneous communication satellite constellation system composed of high, medium and low orbit satellites and the missile group.

[0151] The above only describes the preferred embodiments of the application and is not used to limit the application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the application shall be included in the protection scope of the application.

Claims

1. A method for planning a communication link of a star projectile for a swarm cooperative engagement, characterized in that, The planning method comprises: S100, determining a dynamic model of a distance between a missile and a target and an external control function of the dynamic model; S200, constructing a directed time-varying topology graph; S300, judging satellite-missile cooperative feasibility according to the dynamic model, the external control function and the directed time-varying topology graph; S400, determining an energy loss function positively related to a change rate of the external control function, and optimizing the satellite-missile communication link by minimizing the energy loss function; Step S100 comprises: The distance p between the missile i and the target i The dynamics model is: where u i is the control input of the missile i with respect to the distance p i t is the time. The external control function is expressed as a control protocol of a satellite i: where k i is a control gain, is the distance of the missile j1,...,j r from the target, is the time of arrival of the missile j1,...,j r at the target, and j≠1,j∈{j1,...,j r}. Step S200 comprises: The directed time-varying topology graph is constructed as: G(t) = (V, E(t), A(t)) Wherein, the vertex set V is a missile system {1,...,n}, E(t) is an edge set, A(t)=[a ij (t)] n×n ∈R n×n is a corresponding adjacency matrix.

2. The method of claim 1, wherein: Step S200 further comprises: For any time t, satellite i gets the information of missiles j1,...,j r according to its own observation and inter-satellite link communication, if j,l∈{j1,...,j r},l≠1, then (j,l)∈E, and a lj =1; if j,l∈{j1,...,j r},l=1, then and a lj =0; The switching time of G(t) is denoted as t k The duration of G(t) keeping the same communication situation after the kth switching is denoted as T k The initial time is denoted as t0=0, and the communication topology of the missile system in the corresponding time interval [t k-1 ,t k ) is denoted as Communication topology and denoted by wherein, is a continuous non-empty and uniformly bounded time interval, and 3. The method according to claim 1 or 2, wherein, Step S300 comprises: determining the directed time varying topology graph from the dynamics model and the external control function whether a spanning tree rooted at the leader missile is included If yes, satellite-missile cooperative attack can be realized; If no, satellite-missile cooperative attack cannot be realized.

4. The method of claim 3, wherein, determining the directed time-varying topology graph whether a spanning tree rooted at the leader node is included When and the communication topology is a matrix and a matrix , the communication topology satisfies that it contains a spanning tree with node 1 as the root, the corresponding weighted Laplacian matrix has only one zero eigenvalue, and all other eigenvalues are in the third and fourth quadrants of the complex plane, and In the case where node 1 has no predecessor, the topology corresponds to a weighted Laplacian matrix whose first row is all zeros, and the vector (1, 0,..., 0) T is a matrix and corresponds to an eigenvector of the zero eigenvalue; then the communication topology corresponds to a Laplacian matrix represented as When and , the matrices and both satisfy that there is only one eigenvalue of zero, and the eigenvector corresponding to the eigenvalue of zero is (1, 0,..., 0) T , and other eigenvalues all have positive real parts.

5. The method of claim 4, wherein, The energy loss function is expressed as: where u = [u1,..., uN]T, v = [v1,..., vN]T, and n ] T , p = [p1,..., pN]T, and n ] T , ηi > 0 and γi > 0 are the weights of energy consumption loss of missile i when adjusting the state based on the leader missile, and i a i (t) = 1 if and only if there exists j ≠ i, (j, i) ∈ E, otherwise, i a i (t) = 0.

6. The method of claim 5, wherein: Optimizing the satellite-missile communication link by minimizing the energy loss function comprises: The satellite constellation selects, according to the external control function, a missile in the missile group that minimizes the energy loss function after establishing a communication link, and establishes a communication link.

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