Information physical cross-layer game three-party satellite confrontation method and system

Abstract

The invention discloses an information physical cross-layer game three-party satellite confrontation method and system, and the method comprises the steps: constructing a motion model and a communication interference model of a maneuver-limited attacker-defender-communicator three-party non-cooperative satellite, and constructing a three-party optimal control problem; in consideration of energy consumption of three parties, communication interference efficiency of an information layer and pursuit behaviors of a physical layer, an optimal control problem of an attacker, a defender and a communicator is converted into a round system game problem and is decomposed into a series of simpler unilateral optimization sub-problems, a multi-targeting method is adopted to solve an optimal strategy, and the optimal control problem of the attacker, the defender and the communicator is solved on the premise of meeting a safe distance. In order to realize efficient solving of a cross-layer three-party strategy, an information-physics coupling system is constructed, a Stackelberg game idea and a multiple targeting method are adopted, a three-party differential game problem is converted into a turn system game problem, and then a large-scale nonlinear problem is solved, so that efficient solving of the cross-layer three-party strategy is realized. And the interference survival capability of attackers, the accurate interception capability of defenders and the anti-interference communication capability of communicators are improved.

Description

Technical Field

[0001] This invention belongs to the field of satellite communication and satellite control technology, and relates to a cyber-physical cross-layer game three-party satellite confrontation method and system. Background Technology

[0002] With the rapid increase in the number of spacecraft and the rapid development of satellite communication technology, the complexity and adversarial nature of space activities have significantly increased. Satellites in orbit face diverse space threats, and space security issues in complex scenarios have attracted high attention from all countries. To effectively address these diverse threats, the issue of spacecraft competition and adversarial activities has received close attention from the space and military communities of various countries.

[0003] The adversarial problem can manifest as tracking and escape at the physical level, or as interference and anti-interference at the network level. At the physical level, adversarial challenges mainly involve spacecraft orbit planning, attitude control, and propulsion system optimization, with a typical scenario being a chase-escape game, a dynamic confrontation between the "tracker" and the "escapee." At the network level, adversarial challenges focus on the stability and security of communication links, involving technologies such as electromagnetic interference, signal encryption, and communication countermeasures. The defender needs to maintain link stability by optimizing orbital maneuvers and communication strategies, while the attacker aims to reduce the target's communication capabilities, affecting its decision-making and actions. Although some technologies involve satellite-based game-based adversarial challenges, most are limited to two-party games or layered independent optimization problems, and have not yet coupled physical-layer chase-escape and network-layer interference strategies. This makes it difficult to achieve collaborative optimization in cross-layer three-party game scenarios, resulting in problems such as weak attacker survivability, low interception efficiency of interceptors, and poor communication quality of communicators. It is difficult to generate a three-party collaborative Nash equilibrium strategy in real time while satisfying satellite dynamic constraints. Summary of the Invention

[0004] The purpose of this invention is to address the problems of disconnect between physical layer pursuit and network layer communication interference, and the lack of cross-layer optimization capabilities in existing three-way game techniques. Specifically, for non-cooperative three-way game scenarios involving attackers, defenders, and communicators, this invention provides a cyber-physical cross-layer game three-way satellite adversarial method and system. To achieve the above objective, this invention employs the following technical solution:

[0005] A cyber-physical cross-layer game-theoretic three-party satellite adversarial method includes the following steps:

[0006] Construct a motion model and a communication jamming model for a non-cooperative three-party satellite with limited mobility, consisting of an attacker, a defender, and a communicator;

[0007] Based on the motion model and communication interference model of the three non-cooperative satellites of attacker, defender and communicator, the performance indicators of attacker, defender and communicator are established respectively, and the optimal control objectives of attacker, defender and communicator are obtained according to the performance indicators;

[0008] Construct a three-party game problem based on the optimal control objectives of the attacker, defender, and communicator, decompose the three-party game problem into a series of unilateral optimization subproblems, solve the unilateral optimization subproblems using the multiple shooting method, and combine the safety distance constraint to obtain the Nash equilibrium control strategies of the attacker, defender, and communicator respectively.

[0009] A further improvement of the present invention lies in:

[0010] The performance index of the attacker is defined as:

[0011] [[ID=1十一]]

[0012] Among them, ‖p , , C , , ,

[0021] ,

[0020] , , , <00​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​

[0025] The process of obtaining the Nash equilibrium control strategies for the attacker, defender, and communicator includes:

[0026] By employing the Stackelberg game theory approach and the multiple-targeting method, the three-party differential game problem is transformed into a series of one-sided optimization subproblems, which are then used to solve the nonlinear problem.

[0027] Initialize parameters to determine the number of target points N and the termination time t in the turn-based game problem. f The initial value of the state variable x(0) and the tolerance error ε;

[0028] Based on the current state information of the attacker, defender, and communicator, the initial trajectory states of the attacker, defender, and communicator are calculated respectively based on the attack-defender-communicator satellite maneuver-limited motion model, and the state variables of the attacker, defender, and communicator are obtained.

[0029] The state variables of the attacker, defender, and communicator are stored in the auxiliary vector s as the initial state value of each target point, and the initial control value c is set.

[0030] The three-way coupling problem is decomposed into three subproblems that can be solved sequentially. Each of the attacker, defender, and communicator optimizes its own state variables and control variables independently based on the state variables of the other two parties using the multiple-shot method, and obtains the performance indexes of the attacker, defender, and communicator at this time. The updated state variables of the attacker, defender, and communicator are stored in the auxiliary vector s, and the control variables are stored in the auxiliary vector c, which serve as the initial state and control values ​​for the next shot point.

[0031] Repeat this step until the difference between the performance metrics output by two consecutive iterations is less than the set tolerance error ε, then stop the iteration and output the current state variables, control variables, and channel capacity.

[0032] The constructed non-cooperative satellite motion model involving a limited-maneuver attacker, defender, and communicator includes:

[0033] A motion model with limited maneuverability for the attacker-defender-communicator satellite is described using the CW equation:

[0034]

[0035] in, μ is the gravitational constant, a0 is the reference orbital radius, and T represents the upper limit of thrust per unit mass.

[0036] Transform the above equations into state equations:

[0037]

[0038] in, Represents the satellite's state vector; u = [u x u y u z ] T Indicates the control input of the satellite;

[0039] in,

[0040]

[0041] The communication interference model is as follows:

[0042]

[0043] in, The communication power at which the space station sends signals to the communicator, ||p C ‖ represents the distance between the space station and the communicator. The jamming power emitted by the attacker is used to disrupt the communication link between the space station and the communicator, ||p A -p C ‖ represents the distance between the attacker and the communicator, α is the signal attenuation coefficient with distance, and σ 2 This refers to the environmental noise level.

[0044] A cyber-physical cross-layer game-theoretic three-party satellite adversarial system includes:

[0045] The model building module is used to construct a non-cooperative satellite motion model and a communication jamming model involving a limited-maneuverability attacker-defender-communicator tripartite;

[0046] The game problem description module is used to establish performance indicators for the attacker, defender, and communicator based on a non-cooperative satellite motion model and a communication interference model with limited maneuverability, and to obtain the optimal control problem for the attacker, defender, and communicator based on the performance indicators.

[0047] The game theory problem-solving module is used to transform the optimal control problem of attackers, defenders and communicators into a turn-based game problem based on the Stackelberg game theory concept. It decomposes the problem into a series of simpler one-sided optimization subproblems and uses the multi-shot method to solve for the optimal strategy. Under the premise of satisfying the safe distance, it obtains the Nash equilibrium control strategies of attackers, defenders and communicators respectively.

[0048] 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.

[0049] 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.

[0050] Compared with the prior art, the present invention has the following beneficial effects:

[0051] This invention discloses a cyber-physical cross-layer game-theoretic three-party satellite adversarial method. It constructs a motion model and a communication interference model for a non-cooperative three-party satellite with limited maneuverability (attacker, defender, and communicator). When constructing the optimal control objectives for the attacker, defender, and communicator, it simultaneously considers the energy consumption of all three parties, the effectiveness of information-layer communication interference, and the pursuit behavior at the physical layer. The optimal control problem for the attacker, defender, and communicator is transformed into a turn-based game problem, decomposed into a series of simpler unilateral optimization subproblems. A multi-targeting method is used to solve for the optimal strategy. Under the premise of strictly satisfying satellite dynamic constraints and safe distances, it achieves efficient solution of cross-layer three-party strategies, which differs from existing research that only considers… Unlike two-party game methods that consider electromagnetic interference countermeasures at the network layer or only physical layer pursuit and escape countermeasures, this invention constructs an "information-physics" coupled system. By adopting the Stackelberg game theory and multiple target shooting method, the three-party differential game problem is transformed into a turn-based game problem, and then a large-scale nonlinear problem is solved. This ensures that the decisions of each satellite require dynamic consideration of its own position, velocity, and communication link quality, ensuring the accuracy and reliability of the information. This significantly improves the attacker's interference survivability, the defender's precise interception capability, and the communicator's anti-interference communication capability, solving the intelligent decision-making problem of three-party cross-layer attack and defense in complex space confrontation scenarios. Attached Figure Description

[0052] 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.

[0053] Figure 1 This is a flowchart of the method of the present invention;

[0054] Figure 2 This is a diagram illustrating a three-party cross-layer game scenario in an embodiment of the present invention;

[0055] Figure 3The following is a simulation result of the three-way game between the attacker, communicator, and defender in an embodiment of the present invention (where a represents the three-dimensional trajectory diagram of the attacker-communicator-defender; b represents the channel capacity change diagram);

[0056] Figure 4 This is a schematic diagram illustrating the impact of the attacker's mobility on the simulation in an embodiment of the invention. Figure 1 (Where, a represents a three-dimensional view of each satellite trajectory; b is a distance relationship diagram between attacker and defender; c is a distance relationship diagram between attacker and communicator; d is a channel capacity variation diagram);

[0057] Figure 5 This is a schematic diagram illustrating the impact of the attacker's mobility on the simulation in an embodiment of the invention. Figure 2 (Where, a represents a three-dimensional view of each satellite trajectory; b is a distance relationship diagram between attacker and defender; c is a distance relationship diagram between attacker and communicator; and d is a channel capacity variation diagram.) Detailed Implementation

[0058] 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.

[0059] 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.

[0060] 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.

[0061] 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.

[0062] 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.

[0063] 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.

[0064] The present invention will now be described in further detail with reference to the accompanying drawings:

[0065] See Figure 1 This invention, based on a three-way adversarial scenario, addresses both the physical-level pursuit-escape game problem and the network-level communication game problem. It discloses a cyber-physical cross-layer game-themed three-way satellite adversarial method. This method can provide a Nash equilibrium solution to the problem in a cross-layer game-themed adversarial scenario involving communication satellites, escort defense satellites, and jamming satellites at both the physical and network levels. Simulation results are also provided under different maneuvering capabilities and different jamming weights. The method includes the following steps:

[0066] Step 1: Establish a satellite motion model with limited maneuverability and a communication interference model:

[0067] Establish an LVLH reference coordinate system. In this coordinate system, the CW equations are used to describe the motion of the attacker-defender-communicator satellite when its motion is constrained.

[0068]

[0069] in, μ is the gravitational constant, and a0 is the reference orbital radius. The maneuverability of each participant is restricted, and T represents the upper limit of thrust per unit mass.

[0070] The above equations can be expressed in the form of state equations. u = [u x u y u z ] T Let the satellite's state vector and control input be represented respectively, then:

[0071]

[0072] in,

[0073]

[0074] For ease of analysis, we take the position vector. Where the superscripts i = A, D, C, A represents the attacker, D represents the interceptor, and C represents the communicator; the upper limit of thrust per unit mass is taken as T. i ,i=A,D,C.

[0075] Assume the relative distance between the transmitter and receiver is d, and the transmitter operates at power P. T If transmitted, the received signal power P R for:

[0076] P R =P T d -α (3)

[0077] The signal-to-noise ratio (SINR) is given by the following formula:

[0078]

[0079] Among them, P I σ represents the electromagnetic interference signal generated by other interference sources and perceived by the receiver. 2 It refers to the level of ambient noise.

[0080] Channel capacity C t It is given by the following formula:

[0081]

[0082] Therefore, the channel capacity between the communication satellite and the space station can be obtained as follows:

[0083]

[0084] in, The communication power at which the space station sends signals to the communicator, ||p C ‖ represents the distance between the space station and the communicator. The jamming power emitted by the attacker is used to disrupt the communication link between the space station and the communicator, ||p A -p C ‖ represents the distance between the attacker and the communicator, α is the signal attenuation coefficient with distance, and σ 2 This refers to the environmental noise level.

[0085] Step 2: Establish performance indicators for each satellite:

[0086] For the attacker, its goal is to minimize its own energy consumption while maximizing the communication interference to the enemy, that is, to minimize the channel capacity of the enemy. At the same time, it has to avoid the interception of the defender, that is, to maximize the distance from the defender. Therefore, the performance index of the attacker can be defined as:

[0087]

[0088] where, ‖p D -p A 0‖ represents the distance between the attacker and the defender, u A represents the control vector of the attacker, k1 is the communication interference weight factor, reflecting the tendency of the attacker to implement communication interference behavior; k2 is the avoidance weight factor, reflecting the tendency of the attacker to avoid the interception of the defender in the game; the strategy preference of the attacker is dynamically adjusted through the weight factor. When k1>k2, it indicates that the attacker is more eager to enhance the communication interference to the communicator; when k1<k2, it indicates that the attacker is more eager to increase the distance from the defender.

[0089] Therefore, the optimal control objective of the attacker can be defined as:

[0090]

[0091] That is, to find the admissible control u A such that the performance index J A reaches the minimum.

[0092] For the defender, its goal is to minimize its own energy consumption while intercepting the attacker, that is, to minimize the distance from the attacker. Therefore, the performance index of the defender can be defined as:

[0093]

[0094] where, u D represents the control vector of the communicator.

[0095] Therefore, the optimal control objective of the defender can be defined as:

[0096]

[0097] That is, to find the admissible control u D such that the performance index J D reaches the minimum.

[0098] For the communicator, its goal is to minimize its own energy consumption while maintaining communication with the space station as much as possible, that is, to maximize its own channel capacity. Therefore, the objective function of the communicator can be defined as: <000​

[0100] Among them, u C Represents the control vector of the communicator.

[0101] Therefore, the optimal control objective of the communicator can be defined as:

[0102]

[0103] That is, to find permissible control u C This makes the performance index J C To reach the minimum.

[0104] In the aforementioned non-cooperative game, the strategy combination {u A* ,u D* ,u C*} is a Nash equilibrium strategy if and only if for any feasible strategy {u A ,u D ,u C},satisfy

[0105]

[0106] Among them, J A J D and J C Performance metric functions for attackers, defenders, and communicators, respectively, u A ,u D ,u C Control strategies for attackers, defenders, and communicators.

[0107] The proof of the existence of Nash equilibrium is as follows:

[0108] Proof: According to the above definition, {u A}、{u D} and {u C All of these are compact metric spaces. The objective function J in (7), (9), and (11) is... A J D and J C It is continuous and bounded, and can be calculated as follows:

[0109]

[0110] From formulas (14)-(16), we can see that J A For u A There exists a minimum value, J D For u D There exists a minimum value, J C For u C There exists a minimum value. Therefore, for the above differential game, there exists a pure strategy Nash equilibrium.

[0111] Step 3, the solution method is as follows:

[0112] As shown in formula (2), each participant has 6 state variables, so there are a total of 18 state variables in the entire three-party adversarial game. Since the function used to measure the quality of communication is a nonlinear function, the performance index cannot be designed as a quadratic performance index. Under such circumstances, the two-point boundary value problem generally cannot be solved analytically and must be solved numerically. The multi-shot method can transform the original problem into a nonlinear programming (NLP) problem to solve, and reach the optimal solution through iteration. The multi-shot method is mainly applicable to unilateral optimization problems and cannot directly solve multi-party game problems. Therefore, the Stackelberg game idea is introduced to first transform the three-party differential game problem into a round-based game problem, decompose it into a series of simpler unilateral optimization problems, and then perform subsequent processing. That is, the Stackelberg game idea is combined with the multi-shot method idea, specifically including:

[0113] First, without considering the decisions of other participants, all participants calculate their own state trajectories based on the current state information using the CW equation, i.e., making preliminary decisions without external control.

[0114] Next, each participant adjusts their decisions based on the behavior of the other two parties in order to minimize their own performance metrics.

[0115] Subsequently, each participant continues to optimize their decision based on the behavior of the other two parties in the previous stage, so that their performance indicators are as close to the minimum as possible.

[0116] Through this iterative process, an equilibrium state is eventually reached, where neither party has an incentive to change its decision, because any change would lead to a decrease in its own gains.

[0117] The challenge of using the multiple-target method to solve problems lies in finding and accurately fitting basis functions. To address this challenge, this invention utilizes the CasADi toolkit. CasADi is a gradient-based general-purpose numerical optimization tool whose interface includes various NLP solvers. One of the most commonly used solvers is IPOPT, an open-source primitive bivariate interior-point method solver. In this invention, the IPOPT solver will be invoked to find and fit basis functions, thereby solving the NLP problem.

[0118] Building effective NLP problem models:

[0119] This invention combines the multi-target attack method with the Stackelberg game theory to solve the three-way adversarial problem between the attacker, defender, and communicator. The specific algorithm steps are as follows:

[0120] Step 1: Determine the number of target points N and the termination time t in the game problem. f Initialize the system parameters by setting the initial values ​​of the state variables x(0) and the tolerance error ε.

[0121] Step 2: Without considering other participants, each participant calculates the initial state trajectory based on the current state information and without applying control, using the CW equation. The obtained state variables are stored in the auxiliary vector s as the initial state value of each shooting point, and the initial control value c is set according to the problem model.

[0122] Step 3: Decompose the three-way coupling problem into three sequentially solvable subproblems. Each participant optimizes its current state variables and control variables independently using a multi-target attack method based on the state information of the other two parties, and outputs the attacker's performance index J at this time. A Defender performance index J D Communicator performance index J C The current state variable is stored in the auxiliary vector s, and the current control variable is stored in the auxiliary vector c, which serve as the initial state and control values ​​for the next target point.

[0123] Step 4: Repeat step 3 until the difference between the performance indicators output by two consecutive iterations is less than the tolerance error. Stop the iteration, output the state variables, control variables and channel capacity at this time, and obtain the control strategies of each party.

[0124] It is important to note that, since this invention is applied in outer space, the safe distance between spacecraft and the space station must be considered. Therefore, to avoid collisions, in addition to satisfying the continuity boundary conditions and control variable magnitude constraints when applying the multiple target method to solve the optimal control problem, an important safety constraint is added: the relative distance between all spacecraft and the space station must always be no less than 1 km.

[0125] This invention studies the game theory problem among communication satellites, escort defense satellites, and jamming satellites. Based on a pursuit-escape game model between attackers and defenders, and a communication jamming game model between attackers and communicators, it optimizes the control strategies of the three parties by combining Stackelberg game theory with a multi-targeting approach. Unlike existing studies that only consider network-layer electromagnetic interference countermeasures or physical-layer pursuit-escape countermeasures, this invention constructs an "information-physics" coupled system, transforming the three-party differential game problem into a turn-based game problem, and then performing large-scale nonlinear problem solving. This requires each satellite to dynamically weigh its own position, velocity, and communication link quality in its decision-making, ensuring the accuracy and reliability of the information obtained. This significantly improves the attacker's jamming survivability, the defender's precise interception capability, and the communicator's anti-jamming communication capability, solving the intelligent decision-making problem of three-party cross-layer attack and defense in complex space confrontation scenarios. It significantly improves the attacker's jamming survivability, the interceptor's precise interception capability, and the communicator's anti-jamming capability, solving the cross-layer space game problem integrating attack and defense. Parts of this invention not described in detail are common knowledge to those skilled in the art.

[0126] Experimental Example

[0127] To verify the correctness and effectiveness of this theory, this invention considers a real-world attack-defense game scenario in a three-party cross-layer adversarial system. (See the diagram for the three-party cross-layer game scenario.) Figure 2 .

[0128] Earth's gravitational constant μ = 3.986 × 10⁻⁶ 14 m 3 / s 2 Reference orbital radius a0 = 8 × 10 3 If km, then n0 = 8.8234 × 10 -4 rad / s. Take α=3.75, σ=0.5, t f =50, N=100. The safe distance between spacecraft during the game is set to 0.01km. Assume the maximum thrust per unit mass of the attacker, defender, and communicator are T, T, and T, respectively. A =0.03g, T D =0.03g and T C =0.01g, interference weighting factor k1=1, evasion weighting factor k2=1, transmission power of information transmitted by the space station jamming power emitted by the attacker The initial positions and velocities of the attacker, defender, and communicator are shown in the table below, with stars representing the final positions of each spacecraft.

[0129] Table 1 Initial positions and velocities of the attacker, defender, and communicator

[0130] State parameters attacker Defender communicator x(km) 22 8 8 y(km) 22 8 8 z(km) 1 2 1 <![CDATA[v x (km·s -1 )]]> 0 0 0 <![CDATA[v y (km·s -1 )]]> 0 0 0 <![CDATA[v z (km·s -1 )]]> 0 0 0

[0131] The program can output the integral value of the channel capacity over the entire simulation period as: C t =77.308667.

[0132] from Figure 3 The motion characteristics of the three spacecraft can be observed: the communicator shows a continuous tendency to move closer to the origin (space station). This is because shortening the communication distance with the space station effectively improves the signal-to-noise ratio of the received signal, thereby optimizing channel capacity and ultimately enhancing communication capabilities. The defender adopts a strategy of actively approaching the attacker, forcing the attacker to maintain a safe distance from the communicator, fully demonstrating its defensive intent to protect the communication link and prevent potential communication interference. Although the attacker attempts to approach the communicator, its maneuverability is significantly restricted under the continuous interception and suppression of the defender, making it difficult to achieve the expected approach trajectory. Analysis of the images shows that the defense strategy of this invention has achieved the expected results, successfully preventing the attacker from approaching the communicator.

[0133] from Figure 3 As can be seen from b, the channel capacity increases significantly as the communicator gradually approaches the space station. Since this invention sets a constraint that the relative distance between each satellite and the space station is not less than 1km, in the later stages of the game, the communicator moves slightly around the space station, causing the channel capacity to fluctuate slightly.

[0134] To illustrate the impact of different maneuverability of the attacker and defender on the outcome, the maximum thrust per unit mass of the attacker and defender is selected as T. A =0.05g, T D =0.03g and T A =0.03g, T D A comparative experiment was conducted with a value of 0.05g. The program can output the integral value of the channel capacity over the entire simulation period as C. t =3.187232 and C t =77.302547. Simulation results are shown in the figure below. Figure 4 and Figure 5 As shown, Figure 4 The maximum thrust per unit mass for both attacker and defender is T. A =0.05g, T D A schematic diagram of 0.03g. Figure 5 The maximum thrust per unit mass for both attacker and defender is T. A =0.03g, T D The diagram of 0.05g shows that, through analysis and comparison, it can be found that enhancing the attacker's mobility can effectively interfere with the communicator's communication link and weaken the performance of the communication system.

[0135] This embodiment also discloses a cyber-physical cross-layer game three-party satellite adversarial system, including:

[0136] The model building module is used to construct a non-cooperative satellite motion model and a communication interference model for a three-party system with limited maneuverability, consisting of attacker, defender, and communicator. The game problem description module is used to establish performance indicators for the attacker, defender, and communicator based on the non-cooperative satellite motion model and the communication interference model with limited maneuverability, and to obtain the optimal control problem for the attacker, defender, and communicator based on the performance indicators.

[0137] The game theory problem-solving module is used to transform the optimal control problem of attackers, defenders and communicators into a turn-based game problem based on the Stackelberg game theory concept. It decomposes the problem into a series of simpler one-sided optimization subproblems and uses the multi-shot method to solve for the optimal strategy. Under the premise of satisfying the safe distance, it obtains the Nash equilibrium control strategies of attackers, defenders and communicators respectively.

[0138] 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.

[0139] 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.

[0140] 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.

[0141] The optimal choice for the processor is a multi-core high-speed central processing unit (CPU).

[0142] 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.

[0143] 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.

[0144] 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 cyber-physical cross-layer game three-party satellite adversarial method, characterized in that, Includes the following steps: Construct a motion model and a communication jamming model for a non-cooperative three-party satellite with limited mobility, consisting of an attacker, a defender, and a communicator; Based on the motion model and communication interference model of the three non-cooperative satellites of attacker, defender and communicator, the performance indicators of attacker, defender and communicator are established respectively, and the optimal control objectives of attacker, defender and communicator are obtained according to the performance indicators; A three-way game problem is constructed based on the optimal control objectives of the attacker, defender, and communicator. The three-way game problem is decomposed into a series of one-sided optimization subproblems. The one-sided optimization subproblems are solved using the multiple-shot method. Combined with the safety distance constraint, the Nash equilibrium control strategies of the attacker, defender, and communicator are obtained.

2. The cyber-physical cross-layer game three-party satellite adversarial method according to claim 1, characterized in that, The attacker's performance metrics are defined as follows: where, ‖p D - p A ‖ represents the distance between the attacker and the defender. k1 is the communication interference weight factor, reflecting the tendency of the attacker to perform communication interference behavior; k2 is the weight factor for avoiding capture, reflecting the tendency of the attacker to avoid interception by the defense party in the game. The strategy preference of the attacker is dynamically adjusted through the weight factor. When k1 > k2, it indicates that the attacker expects to enhance the communication interference on the communicator more; when k1 < k2, it indicates that the attacker expects to increase the distance from the defender more; u A represents the control vector of the attacker; C t represents the channel capacity between the communication satellite and the space station; The attacker's optimal control objective is defined as follows:

3. The cyber-physical cross-layer game three-party satellite adversarial method according to claim 2, characterized in that, The performance metrics of the defender are defined as follows: Among them, u D Represents the control vector of the communicator; The defender's optimal control objective is defined as:

4. The cyber-physical cross-layer game three-party satellite adversarial method according to claim 3, characterized in that, The performance metrics of the communicator are defined as follows: Among them, u C Represents the control vector of the communicator; The optimal control objective of the communicator is defined as follows:

5. A cyber-physical cross-layer game three-party satellite adversarial method according to claim 1, characterized in that, The process of obtaining the Nash equilibrium control strategies for the attacker, defender, and communicator includes: By employing the Stackelberg game theory approach and the multiple-targeting method, the three-party differential game problem is transformed into a series of one-sided optimization subproblems, which are then used to solve the nonlinear problem. Initialize parameters to determine the number of target points N and the termination time t in the turn-based game problem. f The initial value of the state variable x(0) and the tolerance error ε; Based on the current state information of the attacker, defender, and communicator, the initial trajectory states of the attacker, defender, and communicator are calculated respectively based on the attack-defender-communicator satellite maneuver-limited motion model, and the state variables of the attacker, defender, and communicator are obtained. The state variables of the attacker, defender, and communicator are stored in the auxiliary vector s as the initial state value of each target point, and the initial control value c is set. The three-way coupling problem is decomposed into three subproblems that can be solved sequentially. Each of the attacker, defender, and communicator optimizes its own state variables and control variables independently based on the state variables of the other two parties using the multiple-shot method, and obtains the performance indexes of the attacker, defender, and communicator at this time. The updated state variables of the attacker, defender, and communicator are stored in the auxiliary vector s, and the control variables are stored in the auxiliary vector c, which serve as the initial state and control values ​​for the next shot. Repeat this step until the difference between the performance metrics output by two consecutive iterations is less than the set tolerance error ε, then stop the iteration and output the current state variables, control variables, and channel capacity.

6. A cyber-physical cross-layer game three-party satellite adversarial method according to claim 1, characterized in that, The constructed non-cooperative satellite motion model involving a limited-maneuver attacker, defender, and communicator includes: A motion model with limited maneuverability for the attacker-defender-communicator satellite is described using the CW equation: in, μ is the gravitational constant, a0 is the reference orbital radius, and T represents the upper limit of thrust per unit mass. Transform the above equations into state equations: in, Represents the satellite's state vector; u = [u x u y u z ] T Indicates the control input of the satellite; in, 7. A cyber-physical cross-layer game three-party satellite adversarial method according to claim 6, characterized in that, The communication interference model is as follows: in, The communication power at which the space station sends signals to the communicator, ||p C ‖ represents the distance between the space station and the communicator. The jamming power emitted by the attacker is used to disrupt the communication link between the space station and the communicator, ||p A -p C ‖ represents the distance between the attacker and the communicator, α is the signal attenuation coefficient with distance, and σ 2 This refers to the environmental noise level.

8. A cyber-physical cross-layer game-theoretic three-party satellite adversarial system, characterized in that, include: The model building module is used to construct a non-cooperative satellite motion model and a communication jamming model involving a limited-maneuverability attacker-defender-communicator tripartite; The game problem description module is used to establish performance indicators for the attacker, defender, and communicator based on a non-cooperative satellite motion model and a communication interference model with limited maneuverability, and to obtain the optimal control problem for the attacker, defender, and communicator based on the performance indicators. The game theory problem-solving module is used to transform the optimal control problem of attackers, defenders and communicators into a turn-based game problem based on the Stackelberg game theory concept. It decomposes the problem into a series of simpler one-sided optimization subproblems and uses the multi-shot method to solve for the optimal strategy. Under the premise of satisfying the safe distance, it obtains the Nash equilibrium control strategies of attackers, defenders and communicators respectively.

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, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1-7.

10. 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 1-7.

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