A control method and system for anti-spoofing attack satellite formation

Abstract

The application discloses a control method and system for an anti-spoofing attack satellite formation, and in the case that a satellite formation system is subjected to a spoofing attack link destruction, a controller design method capable of guaranteeing the system to realize consistent formation is designed, the realization of the method is distributed, and through real-time interaction of link information, the satellite formation system is autonomously caused to tend to a predetermined formation configuration, the distributed realization method improves the reliability of the system to a certain extent, and the failure of a single satellite node does not affect the task execution of the overall system, meanwhile, by designing controller parameters for each satellite node, the system can have a certain attack resistance when subjected to a network spoofing attack, the accuracy of satellite sensor measurement is guaranteed, the control strategy is difficult to achieve the expected effect, the method requires less attack information, does not need to know the specific form, and is easy to implement in engineering.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of satellite control, and relates to a control method and system for anti-spoofing attack satellite formation. BACKGROUND

[0002] As a shining pearl of modern science and technology, space technology has provided unprecedented possibilities for human exploration of space with its rapid development. However, with the increasing frequency of space activities, a series of technical challenges and safety issues have gradually emerged. In particular, in spacecraft formation flight, how to ensure the coordinated work among formation members and maintain stable control performance in the face of various disturbances and attacks has become a key problem that needs to be solved.

[0003] Among them, the research on anti-spoofing control method is particularly urgent. In the space environment, satellite sensors may have abnormal measurement results due to various reasons, such as sensor itself out of control, external environment mutation, and malicious network attack, etc. These abnormal conditions will directly lead to the decrease of the accuracy of sensor measurement data, and even produce completely wrong information. These inaccurate measurement data will directly affect the formulation and execution of control strategy, and further affect the control performance of the entire spacecraft formation. The existence of interference factors is a challenge that cannot be ignored in spacecraft formation control. These disturbances may come from natural changes in the space environment, such as solar wind, cosmic rays, etc., or from human factors, such as network attacks, malicious interference, etc. These disturbances will destroy the accuracy of spacecraft sensor measurement data, making the control strategy difficult to achieve the expected effect. SUMMARY

[0004] The purpose of the present application is to solve the problem that the external interference and attack in the prior art affect the measurement results of the satellite sensor, destroy the accuracy of the spacecraft sensor measurement data, and make the control strategy difficult to achieve the expected effect, and to provide a control method and system for anti-spoofing attack satellite formation.

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

[0006] A control method for anti-spoofing attack satellite formation, comprising the following steps:

[0007] Constructing a satellite motion model based on discrete time, the satellite motion model including a target function and a disturbance of each satellite;

[0008] Designing a distributed state observer based on the satellite motion model, the distributed state observer estimating the state error of the satellite;

[0009] Designing an anti-spoofing attack controller for the multi-satellite network based on the satellite motion model, and optimizing the control ability of the satellite based on the anti-spoofing attack controller.

[0010] Further improvement of the present application is:

[0011] The constructed satellite motion model is:

[0012]

[0013] Wherein, x i,k+1 represents the state of the i-th satellite at the k+1 step; x i,k represents the state of the i-th satellite at the k step; v i,k+1 represents the speed of the i-th satellite at the k+1 step; v i,k represents the speed of the i-th satellite at the k step; h represents the sampling time, which is a constant value in the present application; represents the control input of the i-th satellite at the k step; d i,k represents the disturbance received by the i-th satellite at the k step.

[0014] The distributed state observer is:

[0015]

[0016] Wherein represents the state estimation of satellite i to satellite j at the k+1 step, φ i,j represents the gain of the state observer, represents the state mean value transmitted by satellite j to satellite l after being attacked by a deception attack.

[0017] State mean value is defined as:

[0018]

[0019] Wherein, ò represents a small amount greater than 0, α i,l,k is a Bernoulli random variable satisfying; represents the state quantity transmitted by satellite j to satellite i after being affected by the interference signal at the k step.

[0020] The anti-deception attack controller is:

[0021]

[0022] Wherein β 1,i and β 2,i are control gains greater than 0.

[0023] The constraint conditions of the distributed state observer and the anti-deception attack controller are set as:

[0024] The distributed state observer error is defined as Substitute the distributed state observer into it, and get:

[0025]

[0026] Wherein,

[0027] Further rewritten as:

[0028]

[0029] Wherein Define the error between the satellite state and the equilibrium point as

[0030] The convergence condition of the acquisition system includes:

[0031] When there is an observation parameter Θ and a positive definite matrix P = diag{p, p} that makes the following inequality hold,

[0032]

[0033] Then, the Nash search strategy converges to the equilibrium point x * , and the error limit is:

[0034]

[0035] A control system for anti-spoofing attack satellite formation, comprising:

[0036] A satellite motion model construction module for constructing a discrete-time-based satellite motion model, the satellite motion model including a target function and a disturbance of each satellite;

[0037] A distributed state observer construction module for designing a distributed state observer based on the satellite motion model, the distributed state observer estimating the state error of the satellite;

[0038] A Nash search game strategy construction module for designing an anti-spoofing attack controller for a multi-satellite network based on the satellite motion model, the anti-spoofing attack controller for optimizing the control ability of the satellite.

[0039] A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the steps of the method of any one of the present application.

[0040] A computer-readable storage medium, the computer-readable storage medium stores a computer program, the computer program is executed by a processor to implement the steps of the method of any one of the present application.

[0041] Compared with the prior art, the present application has the following beneficial effects:

[0042] The application discloses a control method for an anti-spoofing attack satellite formation. BRIEF DESCRIPTION OF DRAWINGS

[0043] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings needed to be used in the embodiments will be briefly introduced as follows, and it should be understood that the following drawings only show some of the embodiments of the present application, and therefore should not be regarded as a limitation to the scope, and other related drawings can also be obtained by those of ordinary skill in the art without creative labor on the premise of the drawings.

[0044] Figure 1 The flow chart of the present application;

[0045] Figure 2 The satellite position change over time diagram of the present application. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solutions and advantages of the embodiments of the present application more clear, the technical solutions 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 some of the embodiments of the present application, but not all of the embodiments. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0047] Therefore, the following detailed description of the embodiments of the present application provided in the drawings 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 of ordinary skill in the art without creative labor are within the scope of the present application.

[0048] It should be noted that like reference numerals and letters refer to like items in the several views, and that no further definitions and explanations of a certain item are required in the subsequent drawings once the item has been defined in one of the drawings.

[0049] In the description of the embodiments of the present application, it should be noted that the orientation or position relationship indicated by the terms "upper", "lower", "horizontal", "inner" and the like is based on the orientation or position relationship shown in the drawings or the orientation or position relationship in which the product of the present application is usually placed, and is only for the convenience of describing the present application and simplifying the description, and does not 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 present 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.

[0050] 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.

[0051] In the description of the embodiments of the present application, it should 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, they can be fixedly connected, or can be detachably connected, or integrally connected; can be mechanically connected, or can be electrically connected; can be directly connected, or can be indirectly connected through an intermediate medium; 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.

[0052] The present application will be described in further detail below in conjunction with the accompanying drawings:

[0053] Referring to Figure 1 The embodiments of the present application disclose a control method for anti-spoofing attack satellite formation, which can realize estimation and offset of unknown attacks and disturbances, and finally realize better control performance, including the following steps:

[0054] Step 1: constructing a satellite motion model based on discrete time, the satellite motion model including a target function and a disturbance of each satellite;

[0055] Constructing a satellite motion model:

[0056] Where x 0i ,y 0i ,z 0i are the coordinates of the satellite in the Euler-Hill reference frame, is the control input quantity, and is defined and the sampling time h, which can be rewritten as:

[0057]

[0058] definition Rewrite the system as:

[0059]

[0060] Among them, x i,k+1 represents the state of the i-th satellite at the k+1th step; x i,k represents the state of the i-th satellite at the k-th step; v i,k+1 represents the speed of the i-th satellite at the k+1th step; v i,k represents the speed of the i-th satellite at the k-th step; h represents the sampling time, which is a constant value in the present invention; represents the control input of the i-th satellite at the k-th step; d i,k represents the disturbance received by the i-th satellite at the k-th step.

[0061] in,

[0062]

[0063] d i,k Satisfy f i,k =(d i,k+1 -d i,k ) / h is bounded, that is:

[0064]

[0065] ||f i,k || represents f i,k 2-norm of , N represents the set of all satellites, that is,

[0066] Furthermore, the cost function of each satellite is defined as J i (x i ,x -i ),in

[0067] Furthermore, the state set of all satellites is defined as

[0068] Furthermore, the multi-satellite game is defined as G = {N, J i ,Ω i}.

[0069] Assumption 1: Cost function J i For x i ,x -i C 2 Continuous convex function

[0070] Under this assumption, there exists a Nash equilibrium strategy equilibrium point such that:

[0071]

[0072] where,

[0073]

[0074] called the pseudo-gradient of the cost function of satellite i, is defined The pseudo-gradient of all satellites is obtained as:

[0075]

[0076] Assumption 2: F(x) satisfies strong monotonicity, i.e., for all There exists such that:

[0077]

[0078] Assumption 3: F(x) satisfies Lipschitz continuity, i.e., for all There exists θ > 0 such that:

[0079] ||F(a)-F(b)||≤θ||a-b|| (9)

[0080] Definition 1: For a game G = {N, J i , Ω i}, for all x i ∈ Ω i satisfies:

[0081]

[0082] Equilibrium point is called an ò-Nash equilibrium equilibrium point. ò is a small positive number.

[0083] Therefore, the goal of satellite i can be described as:

[0084]

[0085] And the Nash equilibrium in the game satisfies:

[0086]

[0087] Step 2: Design a distributed state observer based on the satellite motion model, which estimates the state error of the satellite;

[0088] The state observer can realize accurate estimation of unknown disturbance and attack and provide a feedforward compensation term to offset the disturbance, while having good dynamic response. The invention first needs to establish the extended state equation of the satellite:

[0089]

[0090] The anti-wild value observer for the extended state equation of the satellite is designed as follows:

[0091]

[0092] Wherein, represents the estimation of satellite i on x i,k ,v i,k ,d i,k at the kth step;

[0093] Definition Scalar k 1,i ,k 2,i ,k 3,i represents the gain of the state observer, and the nonlinear equation in formula (14) is defined as:

[0094]

[0095] ρ satisfies:

[0096]

[0097] Where 0≤δ i <1 and r i >0;

[0098] Definition

[0099] Further, the error equation of the satellite system is obtained:

[0100]

[0101] Definition

[0102] Further, the distributed state observation is designed as:

[0103]

[0104] Wherein represents the estimation of satellite i on the state of satellite j at the k+1 step, φ i,j represents the gain of the state observer, represents the mean value of the state transmitted by satellite j to satellite l after being attacked by deception, is defined as:

[0105]

[0106] wherein, o represents a small amount greater than 0, a l,k is a Bernoulli random variable satisfying:

[0107]

[0108] represents the probability of being attacked;

[0109] represents the state quantity of satellite j transmitted to satellite i after being affected by the interference signal at the kth step, and is defined as

[0110]

[0111] wherein, a j,k is a Bernoulli random variable satisfying:

[0112]

[0113] Step 3: Design an anti-spoofing attack controller for the multi-satellite network based on the satellite motion model, wherein the anti-spoofing attack controller is used to optimize the control ability of the satellite;

[0114] The designed anti-spoofing attack controller is:

[0115]

[0116] wherein, b 1,i and b 2,i are control gains greater than 0.

[0117] Step 4: Set the constraint conditions of the distributed state observer and the anti-spoofing attack controller, optimize the model parameters, estimate and offset the attacks and errors, and obtain the convergence conditions of the system

[0118] Define the observer error as

[0119] Substitute formula (18) into the observer error to obtain:

[0120]

[0121] wherein, Define the error between the satellite state and the equilibrium point as wherein, the state equation of satellite i is:

[0122]

[0123] Further define:

[0124]

[0125] where

[0126] Further, for all satellites, rewrite equation (24) as:

[0127]

[0128] Further, rewrite the satellite system, equation (2) as:

[0129]

[0130] where Let Then:

[0131]

[0132] where:

[0133]

[0134] Since Then:

[0135]

[0136] Further, optimize the controller parameters, solve the system convergence condition:

[0137] Select Lyapunov function p is a positive definite matrix, and its difference is:

[0138]

[0139] Further, based on assumption 3, we have:

[0140]

[0141] Definition:

[0142]

[0143] where:

[0144]

[0145] Let, combine equations (32), (33) and (34) to get:

[0146]

[0147] Select Lyapunov function Based on assumption 2, its difference is:

[0148]

[0149] Select Lyapunov function Its difference is:

[0150]

[0151] Where,

[0152]

[0153] And

[0154] In summary, for ΔV k = ΔV 1,k + ΔV 2,k + ΔV 3,k , we have:

[0155]

[0156] Where,

[0157] When the formula (40) of Φ satisfies Φ < -εdiag{p, I, I, 0} + τdiag{0, 0, 0, I}, 0 < ε < 1, τ > 0, that is:

[0158]

[0159] Further, we have:

[0160]

[0161] That is,

[0162] In summary, when there is an observation parameter Θ and a positive definite matrix P = diag{p, p} that makes the inequality

[0163]

[0164] hold, then the Nash search strategy converges to the equilibrium point x * , and the error limit is:

[0165]

[0166] Where,

[0167]

[0168] In order to verify the correctness and effectiveness of the theory, the present application considers the interference occurring in the satellite system, each satellite is affected by unknown disturbance, and the expression of the disturbance is as follows:

[0169]

[0170] The initial position is randomly selected in [-5, 5], and the initial speed is randomly selected in [-1, 1].

[0171] The formation position is set as:

[0172]

[0173] The data transmission rate is The upper bound of the deception attack is

[0174] From the results Figure 2 , the position of the satellite gradually converges to the equilibrium point, and the speed of the satellite gradually converges to 0, and the satellite reaches the equilibrium point at about 10s, only with a small fluctuation, which is caused by network attack and external interference.

[0175] The present application designs a controller design method which can guarantee the consistency of the formation of the satellite formation system under the condition of link destruction caused by deception attack. The implementation of the algorithm is distributed, and the satellite formation system is autonomously tended to the predetermined formation configuration through real-time interaction of link information. The distributed implementation method improves the reliability of the system to a certain extent, and the failure of a single satellite node does not affect the task execution of the overall system. In addition, by designing the controller parameters for each satellite node, the system can have a certain ability to resist the influence of attacks when subjected to network deception attacks. The method requires less attack information and does not need to know the specific form, and is easy to implement in engineering.

[0176] The present application also discloses a control system for anti-deception attack satellite formation, comprising:

[0177] A satellite motion model construction module is configured to construct a satellite motion model based on discrete time, wherein the satellite motion model comprises a target function and a disturbance of each satellite;

[0178] A distributed state observer construction module is configured to design a distributed state observer based on the satellite motion model, wherein the distributed state observer is configured to estimate the state error of the satellite;

[0179] A Nash search game strategy construction module is configured to design an anti-deception attack controller of a multi-satellite network based on the satellite motion model, wherein the anti-deception attack controller is configured to optimize the control ability of the satellite.

[0180] 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 executable on the processor. The processor implements the steps in each of the method embodiments above when executing the computer program. Alternatively, the processor implements the functions of each module / unit in each of the device embodiments above when executing the computer program.

[0181] 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.

[0182] The terminal device can be a desktop computer, a notebook computer, a palm computer, a cloud server, and the like. The terminal device can include, but is not limited to, a processor and a memory.

[0183] 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 devices, discrete gate or transistor logic devices, discrete hardware components, and the like.

[0184] The memory can be used to store the computer program and / or modules. The processor implements various functions of the terminal device by running or executing the computer program and / or modules stored in the memory, and calling data stored in the memory.

[0185] 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 implemented. The computer program includes computer program code, which can be in the form of source code, object code, executable files or some intermediate forms, etc. 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 content included in the computer readable medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction, for example, in some jurisdictions, according to legislation and patent practice, the computer readable medium does not include electrical carrier signals and telecommunication signals.

[0186] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. The present application can have various modifications and changes for those skilled in the art. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A control method for satellite formations to resist deception attacks, characterized in that: The following steps are involved: Constructing a discrete-time satellite motion model, wherein the satellite motion model includes an objective function and a disturbance for each satellite; Designing a distributed state observer based on a satellite motion model, wherein the distributed state observer estimates the state error of the satellite; Design a multi-satellite network anti-spoofing attack controller based on the satellite motion model, and optimize the control capability of the satellite based on the anti-spoofing attack controller; Set constraints for the distributed state observer and anti-cheating attack controller, optimize model parameters, and obtain the convergence conditions of the system; The constructed satellite motion model is: in, Indicates the Satellite in the The status of the step; Indicates the Satellite in the The status of the step; Indicates the Satellite in the Step speed; Indicates the Satellite in the Step speed; Indicates the sampling time, which is a constant value in the present invention; Indicates the Satellite in the Step control input; Indicates the Satellite in the The disturbance received by the step; The distributed state observer is: in Indicates the Time-stepping satellite Satellite The state estimation, represents the gain of the state observer, After being spoofed, the satellite Transmit to satellite The state mean of State mean Defined as: in, Represents a small amount greater than 0, is a Bernoulli random variable satisfying; Indicates that after being affected by the interference signal at step k, the satellite Transmit to satellite The state quantity of The anti-spoofing attack controller is: in is a control gain greater than 0; The constraints for setting the distributed state observer and the anti-cheating attack controller include: Define the distributed state observer error as , substituting the distributed state observer into it, we get: in, ; Further rewritten as: in , the error between the satellite state and the equilibrium point is defined as ; The convergence conditions of the acquisition system include: When there are observation parameters With positive definite matrix When the following inequality holds true, Then, the Nash search strategy converges to the equilibrium point , and the error limit is:

2. A control system for a satellite formation to resist deception attacks, which implements the method of claim 1, characterized in that: include: A satellite motion model building module is used to build a satellite motion model based on discrete time, wherein the satellite motion model includes an objective function and a disturbance of each satellite; A distributed state observer building module is used to design a distributed state observer based on a satellite motion model, wherein the distributed state observer estimates the state error of the satellite; A Nash search game strategy building module for designing a multi-satellite network anti-spoofing attack controller based on a satellite motion model. The anti-spoofing attack controller is used to optimize the control capabilities of the satellites. The control parameter determination module is used to set the constraints of the distributed state observer and the anti-cheating attack controller, optimize the model parameters, and obtain the convergence conditions of the system.

3. A terminal device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the steps of the method according to claim 1 are implemented.

4. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the method according to claim 1 are implemented.

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