A pursuit-evasion game control method and system based on inter-satellite attack of multiple spacecrafts

Abstract

The application discloses a kind of based on multi-spacecraft interplanetary attack pursuit and evasion game control method and system, establish the relative position dynamics model of pursuit spacecraft and escape spacecraft, and based on this calculation pursuit spacecraft and escape spacecraft local neighborhood error vector, introduce upper bound-Nash equilibrium thought, construct the virtual attack signal, construct the local neighborhood error feedback control model based on false data injection attack under the influence of false data injection attack, by minimizing the upper bound of objective function, the Nash equilibrium game strategy of spacecraft control system is obtained, the control method disclosed in the application can make spacecraft still can obtain the true value of disturbance and attack when being disturbed or attacked, solve the spacecraft pursuit and evasion game control problem when pursuit spacecraft and escape spacecraft information asymmetry when pursuit spacecraft is subjected to false data injection attack, can guarantee the safety of spacecraft and tracking purpose under complex interference.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of spacecraft control, and relates to a pursuit-evasion game control method and system based on interstellar attack of multiple spacecrafts. BACKGROUND

[0002] In the past decade, due to the rapid development of communication and computing technology, spacecraft cyber-physical systems (CPSs) have attracted extensive attention. CPSs integrate cyber space and physical world together by combining communication, computing and control technology. Given that CPSs are widely used in important fields including power grid, transportation network, unmanned aerial vehicles, etc., their security is crucial, and how to ensure the security of CPSs when they are attacked by external attacks has become a hot research topic for many scholars. The infrastructure in CPSs is widely distributed and connected through wireless communication networks. Due to the openness and broadcast nature of wireless media, wireless networks are vulnerable to jamming attacks. False data injection (FDI) attacks have become a major threat to remote estimation, information communication and control of CPSs, which can inject unknown data information into data packets, which will affect the normal operation of CPSs, cause significant performance degradation of the system, and even cause property or life loss.

[0003] For spacecraft pursuit-evasion game control, although the proposed method based on differential game theory has covered most of the scenarios of pursuit and evasion, it is assumed that neither of the two players is subject to any external disturbance or network attack, which is the basis for building and solving the game. However, in many practical application scenarios, network attacks and external disturbances are inevitable, and the participants who are disturbed or attacked cannot obtain the true value of the disturbance and attack, so they cannot use direct compensation to handle it, resulting in unknown items mixed in the information received by the participants, so the existing differential game method cannot be applied to the case where the participants are subject to network attacks or disturbances. SUMMARY

[0004] The purpose of the present application is to solve the problem of spacecraft pursuit-evasion game control when the spacecraft is subject to false data injection attacks and the information of the pursuit spacecraft and the escape spacecraft is asymmetric, and to solve the problem of affecting the safe operation and normal tracking of the spacecraft under complex disturbances, and to provide a pursuit-evasion game control method and system based on interstellar attack of multiple spacecrafts.

[0005] To achieve the above purpose, the following technical solutions are adopted:

[0006] A pursuit-evasion game control method based on interstellar attack of multiple spacecrafts, comprising the following steps:

[0007] S1: establishing a relative position dynamics model of the pursuit spacecraft and the escape spacecraft;

[0008] S2: based on the relative position dynamics model of the pursuit spacecraft and the escape spacecraft, local neighborhood error vectors of the pursuit spacecraft and the escape spacecraft are respectively established;

[0009] S3: an attack signal of false data injected by the escape spacecraft to the pursuit spacecraft is obtained, and based on the attack signal of false data and the local neighborhood error vector of the pursuit spacecraft obtained in S2, a local neighborhood error vector of the pursuit spacecraft after being attacked is calculated;

[0010] S4: based on the local neighborhood error vector of the pursuit spacecraft after being attacked, a control target function of the pursuit spacecraft is constructed, a control upper limit of the pursuit spacecraft target function is obtained based on the control target function of the pursuit spacecraft, a control target function of the escape spacecraft is established based on the local neighborhood error vector of the escape spacecraft obtained in S2, and a Nash game strategy of the escape spacecraft is obtained based on the control target function of the escape spacecraft.

[0011] Further improvement of the application lies in:

[0012] The step S1 comprises the following steps:

[0013] A group of N pursuit spacecrafts and an escape spacecraft are preset, and a discrete-time linear state space model is established for each spacecraft system:

[0014]

[0015] Wherein, represents the state of the i-th spacecraft system, including the relative distance in the x direction, the relative distance in the y direction, the relative distance in the z direction, the velocity in the x direction, the velocity in the y direction and the velocity in the z direction, represents a 6-dimensional Euclidean space; represents the control input of the i-th spacecraft, represents a 3-dimensional Euclidean space; When the spacecraft is the escape spacecraft, and represents the system matrix of the spacecraft orbital relative motion equation, and the specific expression is:

[0016]

[0017] Wherein, T is the sampling period;

[0018] The relative position of the pursuit spacecraft and the escape spacecraft is defined as:

[0019]

[0020] In the formula, represents pursuit; represents the state of the evader spacecraft system;

[0021] The definition vector is:

[0022]

[0023] Based on formula (3), the relative position dynamics model of the chasing spacecraft and the evading spacecraft is obtained:

[0024]

[0025] wherein,

[0026] The step S2 comprises the following steps:

[0027] The local neighborhood error vector of the chasing spacecraft is defined as the position difference of the chasing spacecraft i relative to its neighbors:

[0028]

[0029] wherein,

[0030] represents the state of the i-th chasing spacecraft system; represents the state of the j-th chasing spacecraft system; represents the state of the evading spacecraft system; represents the connectivity weight of the communication topology between the chasers; represents the information weight of the evading spacecraft obtained by the i-th chasing spacecraft; represents the relative position of the i-th chasing spacecraft and the evading spacecraft.

[0031] The step S2 further comprises the following steps:

[0032] The local neighborhood error of the evading spacecraft is defined as

[0033]

[0034] wherein,

[0035] The step S3 comprises the following steps:

[0036] The acquisition of the false data attack signal injected by the evading spacecraft to the chasing spacecraft comprises:

[0037] ​​​​​​​​The escape spacecraft transmits false data attack signals to the inter-satellite communication link of the pursuing spacecraft and the sensors detecting the escape spacecraft state information of each pursuer;

[0038] The escape spacecraft transmits false data attack signals to the inter-satellite communication link of the pursuing spacecraft and the sensors detecting the escape spacecraft state information of each pursuer; The false data attack signals injected by the escape spacecraft into the inter-satellite communication link of the first pursuing spacecraft are:

[0039]

[0040] The false data attack signals injected by the escape spacecraft into the sensors detecting the escape spacecraft state information of the first pursuing spacecraft are:

[0041]

[0042] In the formula, represents an uncertainty matrix, and the uncertainty matrix describes an error caused by the attack, and satisfies the condition:

[0043]

[0044] wherein, is a positive scalar;

[0045] The pursuing spacecraft , after being attacked, has a local neighborhood error vector as:

[0046]

[0047] In the formula, represents the false data attack signals suffered by the inter-satellite communication link of the first pursuing spacecraft transmitting information to the first pursuing spacecraft; represents the false data attack signals suffered by the sensors detecting the escape spacecraft state information of the pursuing spacecraft.

[0048] The step S4 comprises the following steps:

[0049] A control target function of the pursuing spacecraft is constructed:

[0050] The target function of the control system of the first pursuing spacecraft is:

[0051]

[0052] In the formula, represents an error neighborhood gain of the pursuing spacecraft i; represents a control variable gain of the pursuing spacecraft i; represents the control variable gain of the escaping spacecraft;

[0053] where the local neighborhood error feedback controller of the ith pursuer spacecraft is

[0054]

[0055] the local neighborhood error feedback controller of the jth pursuer spacecraft is

[0056]

[0057] the local neighborhood error feedback controller of the escaping spacecraft is

[0058]

[0059] wherein, are the control gains to be designed, are all positive definite symmetric matrices;

[0060] Based on the above-obtained local neighborhood error feedback controller, the target function is processed to obtain the upper limit of the target function as

[0061]

[0062] wherein,

[0063]

[0064]

[0065] Based on formula (12), the upper limit of the target function of the pursuer spacecraft is

[0066]

[0067] wherein, represents a 6x6 matrix, and all elements thereof are 1;

[0068] Based on formula (16), there is a set of strategy parameters and a set of positive definite matrices satisfying the Riccati-like backward recursive equation minimizing the upper limit of the target function

[0069]

[0070] wherein, and the local neighborhood error feedback gain needs to satisfy formula (18): ​​

[0071]

[0072] The step S4 further comprises the following steps:

[0073] The step of obtaining the Nash equilibrium strategy of the escape spacecraft based on the control objective function of the escape spacecraft comprises the following steps:

[0074] The step of establishing the control objective function of the escape spacecraft based on the local neighborhood error vector of the escape spacecraft,

[0075]

[0076] The local neighborhood error feedback controller of the jth pursuit spacecraft is designed as:

[0077]

[0078] The local neighborhood error feedback controller of the escape spacecraft is designed as:

[0079]

[0080] Wherein, are positive definite symmetric matrices;

[0081] The Nash equilibrium strategy of the escape spacecraft satisfies the condition that:

[0082]

[0083] Wherein,

[0084] The step of obtaining the control objective function of the escape spacecraft is:

[0085]

[0086] There are a set of strategy parameters and a set of positive definite matrices in formula (23) that satisfy the Riccati-type backward recursive equation to minimize the objective function

[0087]

[0088] Wherein, and The local neighborhood error feedback gain needs to satisfy formula (25):

[0089]

[0090] ​​A kind of pursuit and evasion game control system based on multi-spacecraft interplanetary attack, including dynamics model establishment module, local neighborhood error vector acquisition module, local neighborhood error vector acquisition module after being attacked and game strategy acquisition module;

[0091] Dynamics model establishment module is used to establish the relative position dynamics model of pursuit spacecraft and escape spacecraft;

[0092] Local neighborhood error vector acquisition module is used to establish the local neighborhood error vector of pursuit spacecraft and escape spacecraft based on the relative position dynamics model of pursuit spacecraft and escape spacecraft;

[0093] Local neighborhood error vector acquisition module after being attacked is used to obtain the false data attack signal injected by escape spacecraft to pursuit spacecraft, and the local neighborhood error vector of pursuit spacecraft after being attacked is calculated based on the false data attack signal and the local neighborhood error vector of pursuit spacecraft obtained in local neighborhood error vector acquisition module;

[0094] Game strategy acquisition module is used to construct the control target function of pursuit spacecraft based on the local neighborhood error vector of pursuit spacecraft after being attacked, obtain the control upper limit of pursuit spacecraft target function based on the control target function of pursuit spacecraft, establish the control target function of escape spacecraft based on the local neighborhood error vector of escape spacecraft obtained in local neighborhood error vector acquisition module, and obtain the Nash game strategy of escape spacecraft based on the control target function of escape spacecraft, which solves the spacecraft pursuit and evasion game control problem when pursuit spacecraft is attacked by false data injection and the information asymmetry between pursuit spacecraft and escape spacecraft, and ensures the safety of spacecraft and tracking purpose under complex interference.

[0095] A terminal device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, and the processor implements the steps of any one of the methods described herein when executing the computer program.

[0096] A computer-readable storage medium stores a computer program, and the computer program is executed by a processor to implement the steps of any one of the methods described herein.

[0097] Compared with the prior art, the present application has the following beneficial effects:

[0098] The application discloses a kind of based on multi-spacecraft interplanetary attack pursuit and evasion game control method, first establish the relative position dynamics model of pursuit spacecraft and escape spacecraft, and based on this calculation pursuit spacecraft and escape spacecraft local neighborhood error vector, introduce upper bound-Nash equilibrium thought, constructs the virtual attack signal, constructs the local neighborhood error feedback control model based on false data injection attack, under the influence of false data injection attack, by minimizing the upper bound of objective function, the Nash equilibrium game strategy of spacecraft control system is obtained, the control method disclosed in the application can make that spacecraft can obtain the real value of disturbance and attack when being disturbed or attacked, can adapt to spacecraft still can normally operate under network attack or interference, solve the spacecraft pursuit and evasion game control problem when pursuit spacecraft and escape spacecraft information asymmetry when pursuit spacecraft is subjected to false data injection attack, can guarantee the safety of spacecraft and tracking purpose under complex interference. BRIEF DESCRIPTION OF DRAWINGS

[0099] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed in the embodiments will be briefly introduced as follows, and it should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as a limitation on the scope, and for those skilled in the art, other related drawings can also be obtained without creative labor.

[0100] Figure 1 Flow chart of the control method disclosed in the present application;

[0101] Figure 2 Flow chart of the specific embodiment of the present application.

[0102] Figure 3 Simulation result graph using the method of the present application. DETAILED DESCRIPTION

[0103] In order to make the purpose, technical scheme and advantages of the embodiments of the present application more clear, the technical scheme in the embodiments of the present application will be described clearly and completely in combination with the drawings in the embodiments of the present application, and obviously, the described embodiments are part of the embodiments of the present application, not all the embodiments. The components of the embodiments of the present application described and shown in the drawings here can be arranged and designed in various different configurations.

[0104] Therefore, the detailed description of the embodiments of the present application provided in the drawings below is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor belong to the scope of protection of the present application.

[0105] It should be noted that similar reference numerals and letters refer to like items in the accompanying drawings, and once an item is defined in one drawing, it need not be further defined and explained in subsequent drawings.

[0106] In the description of the embodiments of the present application, it should be noted that if the terms "upper", "lower", "horizontal", "inner" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, or the orientation or positional relationship when the product of the application is used, only for the convenience of describing the application and simplifying the description, and it is not intended to indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the application. In addition, the terms "first", "second" and the like are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0107] In addition, if the term "horizontal" appears, it does not mean that the component must be absolutely horizontal, but can be slightly inclined. For example, "horizontal" only means that its direction is relatively more horizontal than "vertical", and does not mean that the structure must be completely horizontal, but can be slightly inclined.

[0108] In the description of the embodiments of the present application, it should also be noted that unless otherwise explicitly specified and limited, if the terms "arrangement", "installation", "connection", "connection" appear, they should be understood in a broad sense. For example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the communication between two elements inside. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0109] The present application will be described in further detail below with reference to the accompanying drawings:

[0110] Referring to Figures 1 to 2 The embodiments of the present application disclose a pursuit and evasion game control method based on inter-satellite attack of multiple spacecrafts, comprising the following steps:

[0111] Step 1: According to the two-body kinematics of the spacecraft, a discrete-time linear system model of the spacecraft and a relative position dynamics model of the pursuit spacecraft and the escape spacecraft are constructed;

[0112] Specifically, according to the flight state of the spacecraft, a discrete-time linear system model of the pursuit spacecraft inter-satellite communication link subjected to false data injection attack and the escape spacecraft is constructed respectively;

[0113] Consider a group of N pursuit spacecrafts and an escape spacecraft, and establish a discrete-time linear state space model for each spacecraft system:

[0114]

[0115] wherein, represents the i-th spacecraft system state, including x-direction relative distance, y-direction relative distance, z-direction relative distance, x-direction velocity, y-direction velocity and z-direction velocity, represents a 6-dimensional Euclidean space; represents the control input of the i-th spacecraft, represents a 3-dimensional Euclidean space; represents that the spacecraft is an escape spacecraft; and is the system matrix of the spacecraft relative motion equation, and the specific expression is:

[0116]

[0117] wherein,

[0118] The relative positions of the pursuit spacecraft and the escape spacecraft are defined as:

[0119]

[0120] In the formula, represents pursuit; represents the escape spacecraft system state;

[0121] The vector is defined as:

[0122]

[0123] Then, the relative position dynamics model can be obtained from (3) as:

[0124]

[0125] wherein, , ,

[0126] Step 2: According to the flight target of the spacecraft, local neighborhood error vectors are established for the pursuit spacecraft and the escape spacecraft respectively;

[0127] Before establishing the local neighborhood error vectors for the pursuit spacecraft and the escape spacecraft respectively, it further includes: defining a communication topology graph related to the pursuit spacecraft and the escape spacecraft;

[0128] Undirected graph represents the communication topology between the trackers, consisting of a pair , wherein is a set of tracker nodes, is a set of edges. We use numbers to represent​ or a pair of numbers to represent the link (edge) between chaser spacecraft i and chaser spacecraft j. The weighted adjacency matrix is defined as where is the connectivity weight of the undirected graph if is , otherwise is . The graph Laplacian matrix is defined as where is the in-degree matrix, as the weighted degree of chaser spacecraft i.

[0129] The directed graph represents the communication topology between chaser spacecraft and the evader spacecraft, consisting of a pair where represents a group of N chaser spacecraft and an evader spacecraft, and denotes a set of edges between the two parties. The graph only contains the communication between chaser spacecraft and the evader spacecraft, but not their internal communication. The edge denotes that chaser spacecraft i can obtain the information of the evader spacecraft, and gives its weight . The edge denotes that the evader spacecraft can obtain the information of chaser spacecraft i, and gives its weight .

[0130] The local neighborhood error vector is established for the chaser spacecraft:

[0131] The goal of the chaser spacecraft is to catch the evader spacecraft while maintaining their own team cohesion. Therefore, the relative distance between multiple spacecraft is defined as follows. The local neighborhood error vector is defined as the position difference of chaser spacecraft i relative to its neighbors:

[0132]

[0133] where, , , ;

[0134] denotes the system state of the i-th chaser spacecraft; denotes the system state of the j-th chaser spacecraft; denotes the system state of the evader spacecraft; denotes the connectivity weight of the communication topology between the chasers; denotes the weight of the information obtained by chaser spacecraft i from the evader spacecraft; represents the relative position of the ith pursuer spacecraft and the evader spacecraft.

[0135] The local neighborhood error vector for the evader is established as:

[0136] The goal of the evader is to choose a suitable strategy to maximize the distance from the pursuer spacecrafts. So we define the local neighborhood error of the evader as:

[0137]

[0138] where, The evader acquires the information weight of the ith pursuer spacecraft.

[0139] Step 3: To increase the escape probability of the evader, the evader designs false data attack signals to the inter-satellite communication link of the pursuer spacecraft and the sensor detecting the evader state information of each pursuer, and further obtains the local error neighborhood variable of the pursuer after being attacked;

[0140] Assuming that the evader knows the state information of all pursuer spacecrafts. The evader injects false data attack signals to the inter-satellite communication link of the pursuer spacecraft and the sensor detecting the evader state information of each pursuer in order to increase the probability of escape success.

[0141] The evader transmits information to the ith pursuer spacecraft. The false data attack signal injected by the evader to the inter-satellite communication link of the ith pursuer spacecraft is designed as follows:

[0142] The false data attack signal injected by the evader to the sensor detecting the evader state information of the ith pursuer spacecraft is designed as follows:

[0143]

[0144] where, the uncertainty matrix describes the error caused by the attack, satisfying the condition:

[0145]

[0146] where, is a positive scalar;

[0147] Therefore, for the pursuer spacecraft , after being attacked, its local neighborhood error becomes the following form:

[0148]

[0149] ​​

[0150] Indicates the first The pursuing spacecraft transmitted information to the first The inter-satellite communication link of the pursuing spacecraft was attacked by false data signals. This indicates a false data attack signal received by the sensors used by the pursuing spacecraft to detect the status of escapees.

[0151] 4: Process the constructed discrete-time linear system model of the pursuing spacecraft to obtain the upper bound of the pursuing spacecraft control system;

[0152] No. The objective function of the spacecraft control system in pursuit:

[0153]

[0154] In the formula, This represents the error neighborhood gain of the pursuing spacecraft i; The gain of the control variable representing the pursuit spacecraft i; This represents the gain of the control variables of the escaping spacecraft;

[0155] The design of the local neighborhood error feedback controller for the i-th pursuing spacecraft is as follows:

[0156]

[0157] The local neighborhood error feedback controller for the j-th pursuing spacecraft is designed as follows:

[0158]

[0159] in, All are control gains to be designed. They are all positive definite symmetric matrices.

[0160] No. The upper limit of the spacecraft tracking control system is as follows: Based on the local neighborhood error feedback controller, the objective function is processed to obtain the upper limit of the objective function; the upper limit of the obtained objective function is the upper limit of the spacecraft tracking control system.

[0161] Based on a local neighborhood error feedback controller, the objective function is processed to obtain its upper limit, specifically:

[0162]

[0163] in,

[0164] ;

[0165] ;

[0166] For equation (12), the upper bound of the objective function is:

[0167]

[0168] where, is a 6-by-6 matrix with all elements equal to 1;

[0169] Based on equation (16), there is a set of strategy parameters and a set of positive definite matrices The Riccati-like backward recursive equation satisfies the upper bound of the objective function minimization;

[0170]

[0171] where, and , the local neighborhood error feedback gain needs to satisfy equation (18):

[0172]

[0173] Construct the objective function of the escape spacecraft control system to obtain the Nash game strategy of the escape spacecraft:

[0174] The objective function of the escape spacecraft control system is:

[0175]

[0176] where, the local neighborhood error feedback controller of the jth pursuit spacecraft is designed as:

[0177]

[0178] The local neighborhood error feedback controller of the escape spacecraft is designed as equation:

[0179]

[0180] where, are all positive definite symmetric matrices;

[0181] The escape spacecraft Nash equilibrium satisfies the condition:

[0182]

[0183] where, ;

[0184] Based on the local neighborhood error feedback controller, the target function is processed to obtain the final form of the target function:

[0185]

[0186] There is a set of strategy parameters in formula (23) as shown in formula (24) And a set of positive definite matrices The Riccati-like backward recursive equation satisfies the target function Minimization:

[0187]

[0188] Wherein, And The local neighborhood error feedback gain Needs to satisfy formula (25):

[0189]

[0190] Referring to Figure 3 , Figure 3 The simulation result graph of the method of the application;

[0191] Figure 3 The simulation graph shown is a curve graph of the relative distance of a pursuit spacecraft and an escape spacecraft. The initial position of the pursuit spacecraft is represented in the reference satellite orbit coordinate system as The initial position of the escape spacecraft is represented in the reference satellite orbit coordinate system as The false data injection attack is persistent, and as can be seen from the simulation graph, the relative distance of each coordinate of the pursuit spacecraft and the escape spacecraft converges to 0 at the 1000th step length, indicating that the pursuit spacecraft successfully captures the escape spacecraft.

[0192] The application is based on the existing information game, which cannot solve the case that the participants are subjected to false data injection attacks or unknown interference. The application proposes an upper bound-Nash equilibrium idea, wherein the inter-satellite communication link of the pursuit spacecraft and the sensor for detecting the escape spacecraft state information of each pursuer are subjected to false data injection attacks. Based on the physical layer system performance, a local neighborhood error feedback control model based on false data injection attacks is constructed. Under the influence of the false data injection attack, by minimizing the upper bound of the target function, the Nash equilibrium game strategy of the spacecraft control system is obtained by using the complete square technique and the Riccati equation.

[0193] The embodiment of the application discloses a pursuit-escape game control system based on multi-spacecraft inter-satellite attack, comprising a dynamic model establishment module, a local neighborhood error vector acquisition module, an attacked local neighborhood error vector acquisition module and a game strategy acquisition module.

[0194] a dynamics model establishing module, configured to establish a relative position dynamics model of the pursuit spacecraft and the escape spacecraft;

[0195] a local neighborhood error vector obtaining module, configured to establish a local neighborhood error vector of the pursuit spacecraft and the escape spacecraft based on the relative position dynamics model of the pursuit spacecraft and the escape spacecraft;

[0196] a post-attack local neighborhood error vector obtaining module, configured to obtain a false data attack signal injected by the escape spacecraft to the pursuit spacecraft, and calculate a post-attack local neighborhood error vector of the pursuit spacecraft based on the false data attack signal and the local neighborhood error vector of the pursuit spacecraft obtained by the local neighborhood error vector obtaining module;

[0197] a game strategy obtaining module, configured to construct a control objective function of the pursuit spacecraft based on the post-attack local neighborhood error vector of the pursuit spacecraft, obtain an upper limit of the control objective function of the pursuit spacecraft based on the control objective function of the pursuit spacecraft, establish a control objective function of the escape spacecraft based on the local neighborhood error vector of the escape spacecraft obtained by the local neighborhood error vector obtaining module, and obtain a Nash game strategy of the escape spacecraft based on the control objective function of the escape spacecraft.

[0198] An embodiment of the present application provides a schematic diagram of a terminal device. The terminal device of the embodiment comprises a processor, a memory, and a computer program stored in the memory and capable of running on the processor. The processor implements the steps in each of the method embodiments when executing the computer program. Alternatively, the processor implements the functions of each module / unit in each of the apparatus embodiments when executing the computer program.

[0199] 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 application.

[0200] The terminal device can be a desktop computer, a notebook computer, a palm computer, a cloud server, and other computing devices. The terminal device can include, but is not limited to, a processor and a memory.

[0201] The processor can be a central processing unit (CPU), and can also be other general-purpose processors, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA) or other programmable logic device, discrete gate or transistor logic, discrete hardware components, etc.

[0202] The memory can be configured to store the computer programs and / or modules, and the processor can realize various functions of the terminal device by running or executing the computer programs and / or modules stored in the memory, and calling data stored in the memory.

[0203] The modules / units integrated in the terminal device, if realized in the form of software function units and sold or used as independent products, can be stored in a computer-readable storage medium. Based on such understanding, all or part of the processes in the above-mentioned embodiment methods can also be completed by a computer program instructing related hardware, and the computer program can be stored in a computer-readable storage medium. When the computer program is executed by a processor, the steps of the above-mentioned various method embodiments can be realized. The computer program includes computer program code, which can be in the form of source code, object code, executable file or some intermediate form. The computer-readable medium can include any entity or device capable of carrying the computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signal, telecommunication signal and software distribution medium, etc. It should be noted that the computer-readable medium can include or exclude contents according to the requirements of legislation and patent practice in different jurisdictions. For example, according to legislation and patent practice in some jurisdictions, the computer-readable medium does not include electrical carrier signals and telecommunication signals.

Claims

1. A pursuit-escape game control method based on multi-spacecraft inter-satellite attacks, characterized in that, Includes the following steps: S1: Establish a dynamic model of the relative positions of the pursuing spacecraft and the escaping spacecraft; S2: Based on the relative position dynamics model of the pursuing spacecraft and the escaping spacecraft, establish the local neighborhood error vectors of the pursuing spacecraft and the escaping spacecraft respectively; S3: Obtain the false data attack signal injected by the escape spacecraft into the pursuing spacecraft, and calculate the local neighborhood error vector of the pursuing spacecraft after being attacked based on the false data attack signal and the local neighborhood error vector of the pursuing spacecraft obtained in S2. S4: Based on the local neighborhood error vector of the pursuing spacecraft after being attacked, construct the control objective function of the pursuing spacecraft, obtain the upper limit of the control objective function of the pursuing spacecraft, establish the control objective function of the escaping spacecraft based on the local neighborhood error vector of the escaping spacecraft obtained in S2, and obtain the Nash game strategy of the escaping spacecraft based on the control objective function of the escaping spacecraft. Step S2 includes the following steps: The local error vector of the spacecraft will be pursued. Defined as the position difference between the pursuing spacecraft i and its neighbors: in, ; ; ; This indicates the state of the i-th pursuing spacecraft system; This indicates the status of the j-th pursuing spacecraft system; Indicates the status of the escaped spacecraft system; The connectivity weights represent the communication topology between trackers; This represents the information weights obtained by the pursuing spacecraft i from the escaped spacecraft; Indicates the relative positions of the i-th pursuing spacecraft and the escaping spacecraft; Step S2 further includes the following steps: The local neighborhood error of an escaped spacecraft is defined as... in, The escape spacecraft acquires the information weights of the pursuing spacecraft i; Step S3 includes the following steps: The acquisition of false data attack signals injected by the escaping spacecraft into the pursuing spacecraft includes: The escaped spacecraft transmits false data attack signals to the inter-satellite communication links of the pursuing spacecraft and to the sensors of each pursuer that detect the escaped spacecraft's status. The escape spacecraft toward the first The pursuing spacecraft transmitted information to the first The false data attack signal injected into the inter-satellite communication link of the pursuing spacecraft is: The escape spacecraft headed towards the first The false data attack signal injected into the sensors of the pursuing spacecraft to detect the escapee's status information is as follows: In the formula, Represents the uncertainty matrix, uncertainty matrix The error caused by the attack is described, and the following conditions are met: in, It is a positive scalar; Pursuit of spacecraft After being attacked, its local neighborhood error vector is: In the formula, Indicates the first The pursuing spacecraft transmitted information to the first The inter-satellite communication link of the pursuing spacecraft was attacked by false data signals. This indicates a false data attack signal received by the sensors used by the pursuing spacecraft to detect the status of escapees.

2. The pursuit-escape game control method based on multi-spacecraft inter-satellite attacks according to claim 1, characterized in that, Step S1 includes the following steps: Given a set of N pursuing spacecraft and one escape spacecraft, establish a discrete-time linear state-space model for each spacecraft system: in, This represents the state of the i-th spacecraft system, including relative distance in the x-direction, relative distance in the y-direction, relative distance in the z-direction, velocity in the x-direction, velocity in the y-direction, and velocity in the z-direction. Represents 6-dimensional Euclidean space; This represents the control input of the i-th spacecraft. Represents 3-dimensional Euclidean space; When this occurs, it indicates that the spacecraft is an escape spacecraft; and The system matrix representing the equations of relative motion of a spacecraft's orbit is specifically expressed as follows: in, T is the sampling period; The relative positions of the pursuing spacecraft and the escaping spacecraft are defined as follows: In the formula, Indicates pursuit; Indicates the status of the escaped spacecraft system; Define the vector as: Based on formula (3), the relative position dynamics model of the pursuing spacecraft and the escaping spacecraft is obtained: in, ; ; .

3. The pursuit-escape game control method based on multi-spacecraft inter-satellite attacks according to claim 1, characterized in that, Step S4 includes the following steps: Construct the control objective function for pursuing the spacecraft: No. The objective function of the control system for the pursuing spacecraft is: In the formula, This represents the error neighborhood gain of the pursuing spacecraft i; The gain of the control variable representing the pursuit spacecraft i; This represents the gain of the control variables of the escaping spacecraft. The local neighborhood error feedback controller for the i-th pursuing spacecraft is: The local neighborhood error feedback controller for the j-th pursuing spacecraft is: The local neighborhood error feedback controller for the escaped spacecraft is: in, All are control gains to be designed. They are all positive definite symmetric matrices; Based on the local neighborhood error feedback controller obtained above, the objective function is processed to obtain the upper limit of the objective function: in: ； ； Based on formula (12), the upper limit of the target function control for pursuing spacecraft is: in, This represents a 6x6 matrix with all elements equal to 1. Based on formula (16), there exists a set of strategy parameters as shown in formula (17). and a set of positive definite matrices The upper bound of the objective function is satisfied by the Ricardi-like backward recursive equation. Minimize: in, and Local neighborhood error feedback gain Formula (18) must be satisfied:

4. The pursuit-escape game control method based on multi-spacecraft inter-satellite attacks according to claim 3, characterized in that, Step S4 further includes the following steps: Obtaining the Nash game strategy for an escaping spacecraft based on its control objective function includes the following steps: The control objective function of the escape spacecraft is established based on the local neighborhood error vector of the escape spacecraft. The local neighborhood error feedback controller for the j-th pursuing spacecraft is designed as follows: The local neighborhood error feedback controller for the escape spacecraft is designed as follows: in, They are all positive definite symmetric matrices; The Nash game strategy of the escaped spacecraft satisfies the following condition: in, ; The control objective function for obtaining the escaped spacecraft is: Formula (23) contains a set of strategy parameters as shown in Formula (24). and a set of positive definite matrices Satisfying the Riccati-like backward recursive equation makes the objective function Minimize: in, and Local neighborhood error feedback gain Formula (25) must be satisfied:

5. A pursuit-escape game control system based on multi-spacecraft inter-satellite attacks to implement the method of claim 1, characterized in that, It includes a dynamics model establishment module, a local neighborhood error vector acquisition module, a local neighborhood error vector acquisition module after being attacked module, and a game strategy acquisition module; The dynamics model building module is used to build the relative position dynamics model of the pursuing spacecraft and the escaping spacecraft; The local neighborhood error vector acquisition module is used to establish the local neighborhood error vectors of the pursuing spacecraft and the escaping spacecraft based on the relative position dynamics model of the pursuing spacecraft and the escaping spacecraft, respectively. The local neighborhood error vector acquisition module after being attacked is used to acquire the false data attack signal injected by the escaping spacecraft into the pursuing spacecraft. Based on the false data attack signal and the local neighborhood error vector of the pursuing spacecraft acquired in the local neighborhood error vector acquisition module, the local neighborhood error vector of the pursuing spacecraft after being attacked is calculated. The game strategy acquisition module is used to construct the control objective function of the pursuing spacecraft based on the local neighborhood error vector of the pursuing spacecraft after being attacked. It then obtains the upper limit of the pursuing spacecraft's objective function control. Based on the local neighborhood error vector of the escaping spacecraft obtained in the local neighborhood error vector acquisition module, it establishes the control objective function of the escaping spacecraft. Finally, it obtains the Nash game strategy of the escaping spacecraft based on the control objective function. This solves the spacecraft pursuit-escape game control problem when the pursuing spacecraft is attacked by false data injection and there is information asymmetry between the pursuing and escaping spacecraft. It can ensure the safety of the spacecraft and the tracking objective under complex interference.

6. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1-4.

7. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-4.

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