Multi-spacecraft pursuit game method and system based on incomplete information

Abstract

The invention discloses a multi-spacecraft pursuit game method and system based on incomplete information, and the method comprises the steps: building a differential game model under the background of incomplete information through combining a motion model of a satellite, employing a local belief updating method and a global belief updating method, solving the built differential game model, introducing a belief factor by a pursuit party, and achieving the pursuit game of multiple spacecrafts through the local belief updating method and the global belief updating method. In the belief updating process, the potential real evasion strategy of the opposite side is inferred and learned in real time, the optimal hunting strategy is gradually achieved, information of the two sides is completely known and different in existing research, and by means of the method, for some non-cooperative target satellites high in concealment and maneuverability, a tracer can acquire the optimal hunting strategy when the escape strategy of the escaper is unknown. And self-adaptive control under uncertainty is realized, so that the purpose of efficient hunting is achieved.

Description

Technical Field

[0001] This invention belongs to the field of satellite communication and satellite control technology, and relates to a multi-spacecraft pursuit and escape game method and system based on incomplete information. Background Technology

[0002] With the continuous development of satellite communication technology and the increasingly fierce international space competition, on-orbit resources are becoming increasingly scarce, and the risks of collisions and malicious approaches faced by on-orbit satellites are rising dramatically. To gain dominance and information control in space, the spacecraft orbital pursuit and escape game problem has become a research hotspot in the international aerospace field. The mainstream solution method for the spacecraft pursuit and escape problem is differential game theory, which studies how two parties simultaneously act on a system represented by the same differential equation, striving to achieve their respective optimal goals. The Hamilton-Jacobi-Bellman equation is used to transform it into a two-point boundary value problem, suitable for handling continuous-time dynamic game problems.

[0003] However, when facing highly concealed and maneuverable non-cooperative target satellites, our side struggles to track and identify their true intentions, and cannot accurately obtain or predict the enemy's cost function in advance. This presents a challenge in designing efficient pursuit strategies, and traditional numerical solutions for differential games are insufficient. Therefore, in complex adversarial environments with incomplete information, to ensure the effective completion of the encirclement mission, our multiple satellites need to possess online learning and strategy adaptation capabilities. Research on how to learn the unknown cost function of non-cooperative targets is therefore essential. Summary of the Invention

[0004] The purpose of this invention is to solve the problem in the prior art that when facing some highly concealed and maneuverable non-cooperative target satellites, it is difficult for us to track and identify their true intentions, and in the complex adversarial environment of incomplete information, it is impossible to design an efficient pursuit strategy. The invention provides a multi-spacecraft pursuit and escape game method and system based on incomplete information.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] A multi-spacecraft pursuit-escape game method based on incomplete information includes the following steps:

[0007] Construct satellite dynamics models and encirclement formation models;

[0008] A differential game model is established based on satellite dynamics model and encirclement formation model;

[0009] Based on the differential game model and combined with the objectives of each satellite, performance indicators for both sides of the game are established.

[0010] Solve for the performance indicators of both sides in the game to obtain their control strategies;

[0011] The optimal strategies for both sides of the game are obtained by iteratively updating the local and global beliefs of their control strategies.

[0012] A further improvement of the present invention is that:

[0013] The differential game model is expressed by the following equation:

[0014]

[0015] Where, x cE x represents the difference between the state variables of the two pursuit satellites. ic u represents the difference between the current state variable of the tracking satellite and the ideal formation position. c ,u Pi ,u E Let A represent the thrust acceleration of the virtual center of the tracking team, the i-th tracking satellite, and the escape satellite, respectively; let B represent the state matrix and B represent the control matrix.

[0016] The relative error of the tracker is established based on the differential game model:

[0017] δ P =x ic +x cE

[0018] The relative error of the escapee is established based on the differential game model:

[0019]

[0020] Among them, g iE Indicates the communication weight; when the escapee can detect the state information of the i-th tracker, g iE =1, otherwise g iE =0.

[0021] The established performance metrics for both sides of the game include:

[0022] The goal of building a tracker:

[0023]

[0024] Among them, Q P ,R P ,R E Both are weight matrices. and This represents the various escape strategies of escaping satellites; δ P Indicates the relative error of the tracker; u Pi Represents the i-th tracking satellite; u E This represents the thrust acceleration of the escaping satellite;

[0025] Introducing the belief parameter p(θ|θ) i The optimal control problem of the tracker is described as follows:

[0026]

[0027] Where p(θ|θ) i ) indicates that for each possible The probability, p(θ|θ) i )∈[0,1],E(J Pi ) represents the performance index function.

[0028] The established performance metrics for both sides of the game include:

[0029] The goal of building the escapee:

[0030]

[0031] Among them, Q E This is the weight matrix. δ E The relative error of the escapee; g iE Indicates communication weight;

[0032] The optimal control problem for escapees is described as follows:

[0033] E:maxJ E

[0034] Among them, J E This represents a performance metric function.

[0035] The process of solving for the performance indicators of both sides of the game to obtain their control strategies includes:

[0036] Constructing a solution to the Bayes-Hamilton-Jacobi equation:

[0037]

[0038] By introducing the minimax principle, we obtain the expected Hamiltonian function corresponding to the tracker:

[0039]

[0040] Assume λ = P i θ δ P ,get:

[0041]

[0042] The stalker's control strategy:

[0043]

[0044] Among them, Q P ,R P ,R E Both are weight matrices; δ P Indicates the relative error of the tracker; u Pi Represents the i-th tracking satellite; u E This represents the thrust acceleration of the escaping satellite.

[0045] By introducing the minima principle, we obtain the expected Hamiltonian function corresponding to the escapee:

[0046]

[0047] Assume λ = P e δ E ,get:

[0048]

[0049] Strategies for gaining control over the escapees:

[0050]

[0051] Where, δ E Q represents the relative error of the escapee; E This is the weight matrix.

[0052] The game involves iterative updates of local and global beliefs regarding the control strategies of both sides, including:

[0053] The Bayesian belief update method is used for local belief iterative update:

[0054]

[0055] Where, x k ,x k+1 These represent the state value at time k and the state value at time k+1, respectively. This indicates that at time k, the i-th pursuing satellite believes... The belief value of the true strategy. This indicates that at time k+1, the i-th pursuing satellite believes... The belief value of the true strategy. This represents the likelihood between the observed value and the predicted value under each possible strategy;

[0056] The global belief iterative update includes:

[0057]

[0058] Where W represents the set of neighbors and w represents the number of neighbors.

[0059] A multi-spacecraft pursuit and escape game system based on incomplete information includes:

[0060] Each satellite model building module is used to build satellite dynamics models and encirclement formation models;

[0061] The differential game model building module is used to build differential game models based on satellite dynamics models and encirclement formation models.

[0062] The performance index construction module is used to establish the performance indexes of both sides in the game based on the differential game model and the objectives of each satellite.

[0063] The control strategy acquisition module is used to solve the performance indicators of the two players and obtain their control strategies.

[0064] The iterative update module is used to perform local and global belief iterative updates on the control strategies of both sides of the game to obtain the optimal strategy for both sides.

[0065] A terminal device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of any of the methods described in this invention.

[0066] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of any of the methods described in this invention.

[0067] Compared with the prior art, the present invention has the following beneficial effects:

[0068] This invention discloses a multi-spacecraft pursuit-escape game method based on incomplete information. Combining the satellite's motion model and utilizing local and global belief update methods, a differential game model is established under incomplete information conditions. The pursuer introduces a belief factor and infers and learns the opponent's potential real evasion strategies in real time during the belief update process, gradually achieving the optimal capture strategy. In existing studies, the information of both parties is completely different. Through this invention, when facing some highly concealed and maneuverable non-cooperative target satellites, the pursuer can achieve adaptive control under uncertainty when the escape strategy of the escapee is unknown, thereby achieving the goal of efficient capture.

[0069] Furthermore, in the context of incomplete information, the pursuer introduces a belief factor, transforming the differential game problem into solving the partial differential Bayes-Hamilton-Jacobi equation. By solving the expected Hamiltonian function through the minimax strategy, the theoretically optimal analytical solution for both sides is obtained. With the help of local and global belief update methods, the pursuer infers and learns the opponent's potential real avoidance strategies in real time during the belief update process, gradually realizing the optimal capture strategy. The pursuer can achieve adaptive control under uncertainty when the escape strategy of the escapee is unknown, thereby achieving the goal of efficient capture. Attached Figure Description

[0070] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0071] Figure 1 This is a flowchart of the method of the present invention;

[0072] Figure 2 This is a schematic diagram of satellite communication and desired formation according to an embodiment of the present invention;

[0073] Figure 3 The simulation diagram for the escape strategy θ1 of the present invention (where a is the trajectory diagram of the tracking satellite and the escape satellite, and b is the belief change of the tracking satellite 1-5). Figure 1 c is the tracking satellite 1-5 belief change Figure 1 ;d is the change in belief of tracking satellites 1-5 Figure 1 ). Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0075] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0076] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0077] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0078] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0079] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0080] The present invention will now be described in further detail with reference to the accompanying drawings:

[0081] See Figure 1 This invention discloses a multi-spacecraft pursuit and escape game method based on incomplete information scenarios, addressing the problem of unknown escape strategies. The method specifically includes the following steps:

[0082] Step 1, Construct satellite dynamics model and tracking encirclement formation model:

[0083] Specifically, constructing a satellite dynamics model includes:

[0084] Establish an LVLH reference coordinate system, and describe the motion of each satellite using the CW equations within this system:

[0085]

[0086] in, μ is the gravitational constant, and a0 is the reference orbital radius.

[0087] The above equations can be expressed as state equations, defined as follows: u i =

[0088] [u x u y u z ] T Let i = P, E, where P represents the tracking satellite (multiple tracking satellites exist in this system) and E represents the escaping satellite (one escaping satellite exists in the system). Then:

[0089]

[0090] in,

[0091]

[0092] Specifically, the encirclement formation model includes:

[0093] Multiple tracking satellites are connected via a communication topology. Those within the system cannot obtain global information, but only neighboring information. The virtual center, based on the average state of its neighbors, is given by the following formula:

[0094]

[0095] Where W represents the neighbor set, and the weight matrix A = [a ij When satellites can communicate with each other, a ij =1; otherwise a ij =0.

[0096] The desired target is a circular, evenly distributed formation of satellites for encirclement and capture. The ideal formation position of each satellite based on the virtual center is given by the following formula:

[0097]

[0098] Where N represents the number of pursuing satellites, and r represents the radius of the desired encirclement formation.

[0099] Step 2, establish the differential game model:

[0100]

[0101] Where, x cE x represents the difference between the state variables of the two pursuit satellites. ic u represents the difference between the current state variable of the tracking satellite and the ideal formation position. c ,u Pi ,u Edenoted as the thrust accelerations of the virtual center of the tracking team, the i-th tracking satellite, and the escape satellite, respectively.

[0102] For the tracker, maintaining formation control while pursuing non-cooperative targets is crucial, so the relative error is established as follows:

[0103] δ P =x ic +x cE (8)

[0104]

[0105] For the fleeing party, it needs to get away from the pursuing party as quickly as possible, so the relative error is established as follows:

[0106]

[0107] Where g is when the escapee can detect information about the i-th pursuer. iE =1, otherwise g iE =0.

[0108] Step 3: Based on the differential game model and the objectives of each satellite, establish performance indicators for both sides of the game, specifically including:

[0109] For the tracker, the goal is to minimize the distance between itself and the escapee, as well as the ideal formation position, while minimizing fuel consumption. Therefore, the objective of designing the tracker is:

[0110]

[0111] Among them, Q P ,R P ,R E This is the weight matrix. and There are multiple escape strategies for escape satellites. Tracking satellites cannot accurately acquire or predict the specific escape strategy of escaping satellites in advance, but R can be determined by expert knowledge. E A finite number of sets.

[0112] Therefore, the belief parameter p(θ|θ) is introduced. i ) represents each possible The probability, p(θ|θ) i The optimal control problem for a tracker can be described as follows: (0, 1)

[0113]

[0114] For the escapee, the goal is to increase the relative distance between themselves and the pursuer while minimizing fuel consumption. Therefore, the objective of the escapee is designed as follows:

[0115]

[0116] Among them, Q E This is the weight matrix.

[0117] Therefore, the optimal control problem for the escapee can be described as:

[0118] E:maxJ E (15)

[0119] The proof of the existence of Nash equilibrium is as follows:

[0120] Proof: According to the above definition, {u Pi} and {u E All of these are compact metric spaces. The performance index function E(J) Pi ) and J E It is continuous and bounded. We can obtain:

[0121]

[0122] From (16)-(17), we can see that E(J) Pi For u Pi It is concave, and has a minimum value; J E For u E It is convex and has a maximum value. Therefore, for the above differential game, the Nash equilibrium strategy always exists.

[0123] Step 4: Solve for the performance indicators of both sides in the game to obtain their control strategies. Specifically, construct the corresponding Bayes-Hamilton-Jacobi equations to obtain the expected Hamiltonian function, and use the minimum principle to solve for the control strategies of both sides, including:

[0124] For the tracker, the Bayes-Hamilton-Jacobi equation is as follows:

[0125]

[0126] in,

[0127] The problem is solved using the minimax principle, and the expected Hamiltonian function is defined as follows:

[0128]

[0129] Assume λ = Pi θ δ P

[0130]

[0131] We can obtain:

[0132]

[0133] Among them, P i θ Satisfies the following Riccati equation:

[0134]

[0135] For the escapee, the Hamilton function is defined as:

[0136]

[0137] Assume λ = P e δ E

[0138]

[0139] We can obtain:

[0140]

[0141] Among them, P e Satisfies the Riccati equation:

[0142] Step 5: Perform local and global belief iteration updates on the control strategies of both players to obtain the optimal strategies for both sides.

[0143] Specifically, the Bayesian belief update process is as follows:

[0144] The escapee has a finite set of possible evasion strategies, each with a different control cost matrix. The escaping satellite secretly selects a certain strategy as its true escape strategy. The pursuing satellite cannot obtain or predict the opponent's precise maneuvering information in advance. Therefore, it updates its beliefs for all possible types within the strategy set. The Bayesian belief update method used is as follows:

[0145]

[0146] Where, x k ,x k+1 These represent the state value at time k and the state value at time k+1, respectively. This indicates that at time k, the i-th pursuing satellite believes... The belief value of the true strategy. This indicates that at time k+1, the i-th pursuing satellite believes... The belief value of the true strategy. This represents the likelihood between the observed value and the predicted value under each possible strategy.

[0147] First, set an initial uniform belief, predict the escapee's maneuver state under all possible strategies at the next moment, compare it with the observation value to obtain the likelihood of this possible strategy, and then combine it with the prior belief to calculate the local posterior belief using formula (27).

[0148] After obtaining local posterior beliefs, the pursuer shares its current belief value with its communicable neighbors, averaging its local belief value with the information obtained from its neighbors to complete a global belief update. The specific update method is as follows:

[0149]

[0150] Where W represents the set of neighbors and w represents the number of neighbors.

[0151] By combining local and global belief updates, the belief of each pursuing satellite is continuously updated and the pursuit strategy is changed in real time until the belief approaches 0 or 1. The true escape strategy is successfully identified, and the pursuit strategy gradually approaches the optimal solution through continuous learning, ultimately achieving the capture.

[0152] This invention utilizes game theory, combined with satellite motion models and Bayesian belief update techniques. Under conditions of incomplete information, the pursuer introduces a belief factor, transforming the differential game problem into solving partial differential Bayes-Hamilton-Jacobi equations. By solving the expected Hamiltonian function through a minimax strategy, the theoretically optimal analytical solution for both sides is obtained. Using both local and global belief update methods, the potential real evasion strategies of the target are inferred and learned in real time during the belief update process, gradually achieving the optimal capture strategy. Unlike existing studies where both sides have complete knowledge, this invention allows the tracker to achieve adaptive control under uncertainty when facing highly concealed and maneuverable non-cooperative target satellites, even without knowing the escape strategy of the fleeing target, thus achieving efficient capture.

[0153] The present invention also discloses a specific experimental example. In order to verify the correctness and effectiveness of the theory, the present invention considers an actual attack and defense game that occurs in a satellite system.

[0154] See satellite communications and expected formation for the pursuing side. Figure 2 .

[0155] The reference satellite's orbital angular velocity n0 = 7.2722 × 10⁻⁶ -5 rad / s, take N=5, Ω={θ1, θ2, θ3}, g iE =[11 1 1 1]、R P =0.5×Ι3、 Q P =Q E =Ι6, r = 0.3km. The initial positions and velocities of each satellite are shown in Table 1, and the initial beliefs are shown in Table 2.

[0156] Table 1 Initial positions and velocities of each satellite

[0157]

[0158] Table 2 Initial Beliefs for Each Satellite

[0159]

[0160] When the escapee adopts escape strategies θ1 and θ2 respectively Figure 3 a) The motion trajectories of all satellites are shown. The encirclement is completed at 11.4s. It can be seen that the tracking satellites 1-5 continuously and dynamically adjust their beliefs about the escape type of the escapee. They not only move closer to the escapee E, but also adjust their own positions according to the relative error state with their neighbors. Finally, they form an encirclement formation and form a cooperative pursuit strategy under incomplete information. This verifies the effectiveness of the control strategy based on Bayesian belief update in driving the multi-satellite cooperative approach to the target. Figure 3 bd illustrates the belief changes of all tracking satellites. It can be seen that their belief in the true escape type of escaper E gradually increases over time and converges to 1, while the belief in other types rapidly decays and converges to 0. The convergence rate varies due to differences in communication between the satellites.

[0161] This embodiment also discloses a multi-spacecraft pursuit and escape game system based on incomplete information, including:

[0162] Each satellite model building module is used to build satellite dynamics models and encirclement formation models;

[0163] The differential game model building module is used to build differential game models based on satellite dynamics models and encirclement formation models.

[0164] The performance index construction module is used to establish the performance indexes of both sides in the game based on the differential game model and the objectives of each satellite.

[0165] The control strategy acquisition module is used to solve the performance indicators of the two players and obtain their control strategies.

[0166] The iterative update module is used to perform local and global belief iterative updates on the control strategies of both sides of the game to obtain the optimal strategy for both sides.

[0167] A schematic diagram of a terminal device according to an embodiment of the present invention. The terminal device of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps in the various method embodiments described above. Alternatively, when the processor executes the computer program, it implements the functions of each module / unit in the various device embodiments described above.

[0168] The computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention.

[0169] The terminal device can be a desktop computer, laptop computer, cloud server, or other device with strong computing power. The terminal device may include, but is not limited to, a processor and memory.

[0170] The optimal choice for the processor is a multi-core high-speed central processing unit (CPU).

[0171] The memory can be used to store the computer program and / or module. The processor implements various functions of the terminal device by running or executing the computer program and / or module stored in the memory and calling the data stored in the memory.

[0172] If the modules / units integrated into the terminal device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0173] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for a non-complete information based multi-spacecraft pursuit-evasion game, characterized in that, The method comprises the following steps: constructing a satellite dynamics model and a hunting formation model; establishing a differential game model based on the satellite dynamics model and the hunting formation model; based on the differential game model, combining the targets of each satellite, establishing performance indexes of both sides of the game; solving the performance indexes of both sides of the game to obtain control strategies of both sides of the game; performing local belief iterative updating and global belief iterative updating on the control strategies of both sides of the game to obtain optimal strategies of both sides of the game.

2. The non-complete information based multi-spacecraft pursuit-evasion game method according to claim 1, wherein, The differential game model is expressed by the following formula: where x cE represents the difference between the state variables of the two chaser satellites, x ic represents the difference between the current state variable of the chaser satellite and the ideal formation position, u c , u Pi , u E represent the thrust acceleration of the virtual center of the chasing team, the i-th chaser satellite and the escape satellite respectively, A represents the state matrix, and B represents the control matrix; Based on the differential game model, the relative error of the pursuer is established: delta P = x ic + x cE Based on the differential game model, the relative error of the evader is established: where g iE represents the communication weight; g iE = 1 when the evader can detect the i-th pursuer state information, otherwise g iE = 0.

3. The non-complete information based multi-spacecraft pursuit-evasion game method according to claim 1, wherein, The performance indexes of both sides of the game are established, including: constructing a target of the pursuer: where Q P , R P , R E are weight matrices, and denotes the multiple escape strategies of the escaping satellite; δ P denotes the relative error of the pursuer; u Pi denotes the ithpursuing satellite; u E denotes the thrust acceleration of the escaping satellite; The belief parameter p(θ | θ i The optimal control problem for the pursuer is described as Where p(θ|θ) i ) indicates that for each possible The probability, p(θ|θ) i )∈[0,1],E(J Pi ) represents the performance index function.

4. The non-complete information based multi-spacecraft pursuit-evasion game method according to claim 3, characterized in that, The performance indexes of both sides of the game are established, including: constructing a target of the evader: where Q E is a weight matrix, δ E denotes the relative error of the escapee; g iE denotes the communication weight; The optimal control problem of the evader is described by the following formula: E: max J E where J E represents a performance index function.

5. The non-complete information based multi-spacecraft pursuit-evasion game method according to claim 1, wherein, Solving the performance indexes of both sides of the game to obtain the control strategies of both sides of the game comprises: constructing a solving equation Bayes-Hamilton-Jacobi: The maximum-minimum principle is introduced to solve the expected Hamilton function corresponding to the pursuer: Assume λ = P i θ δ P , we get: The control strategy of the pursuer is obtained: where Q P , R P , and R E are weight matrices; δ P represents the relative error of the tracker; u Pi represents the ith tracking satellite; and u E represents the thrust acceleration of the escape satellite.

6. The non-complete information based multi-spacecraft pursuit-evasion game method according to claim 5, wherein, The maximum-minimum principle is introduced to solve the expected Hamilton function corresponding to the evader: Assume λ = P e δ E , we get: The control strategy of the evader is obtained: where δ E represents the relative error of the escapee; Q E is the weight matrix.

7. The non-complete information based multi-spacecraft pursuit-evasion game method according to claim 1, wherein, The local belief iterative updating and the global belief iterative updating on the control strategies of both sides of the game comprise: The local belief iterative updating is performed by using a Bayesian belief updating method: Where, x k ,x k+1 These represent the state value at time k and the state value at time k+1, respectively. This indicates that at time k, the i-th pursuing satellite believes... The belief value of the true strategy. This indicates that at time k+1, the i-th pursuing satellite believes... The belief value of the true strategy. This represents the likelihood between the observed value and the predicted value under each possible strategy; The global belief iterative updating comprises: wherein, W represents a neighbor set, and w represents a neighbor number.

8. A non-complete information based multi-spacecraft pursuit-evasion game system, characterized in that, The method comprises the following steps: a satellite model construction module, configured to construct a satellite dynamics model and a hunting formation model; a differential game model construction module, configured to establish a differential game model based on the satellite dynamics model and the hunting formation model; a performance index construction module, configured to, based on the differential game model, combine targets of each satellite, and establish performance indexes of both sides of the game; a control strategy acquisition module, configured to solve the performance indexes of both sides of the game to obtain control strategies of both sides of the game; an iterative updating module, configured to perform local belief iterative updating and global belief iterative updating on the control strategies of both sides of the game to obtain optimal strategies of both sides of the game.

9. A terminal device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1-7.

10. A computer-readable storage medium storing a computer program, the computer program comprising instructions that, when executed by a computer, cause the computer to perform the method of any one of claims 1 to 9. The computer program is executed by the processor to implement the steps of the method according to any one of claims 1-7.

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