Unmanned aerial vehicle security compensation control method based on adversarial game under dos attack

Abstract

The application discloses a kind of unmanned aerial vehicle security compensation control methods based on antagonistic game under DoS attack, it is related to the safety control technical field of multi-agent system.Different from the safety control problem of multi-agent system that considers the interaction of attacker unmanned aerial vehicle and defender unmanned aerial vehicle comprehensively without considering the attack or defense as independent, the application establishes the antagonistic game mechanism of multiple participants, simultaneously introduces algebraic graph, respectively expresses the communication network topological relationship between attacker unmanned aerial vehicle, defender unmanned aerial vehicle and attacker unmanned aerial vehicle and defender unmanned aerial vehicle, so as to consider the bidirectional interaction characteristics between attacker unmanned aerial vehicle and defender unmanned aerial vehicle from the perspective of security decision.The application adopts single-judge network architecture, reduces the computing burden, and designs weight updating law through gradient descent method and standardization principle, enhances the adaptability of unmanned aerial vehicle system in real-time control task.

Description

Technical Field

[0001] This invention belongs to the field of security control technology for multi-agent systems, and particularly relates to a security compensation control method for unmanned aerial vehicles (UAVs) based on adversarial game theory under DoS attacks. Background Technology

[0002] In recent years, networked multi-agent systems (MMS) have attracted considerable attention due to their wide applications in intelligent computing, task scheduling, network spectrum allocation, smart grid management, traffic route planning, wireless sensor networks, multi-robot collaboration, and cooperative / non-cooperative game theory. Several new paradigms for MMS control methods have been proposed, such as consensus control, inclusion control, and formation control, providing new insights into MMS control strategies. In particular, with the increasing development of artificial intelligence and cybersecurity, research on safe control methods for unmanned aerial vehicles (UAVs) under malicious cyberattacks has become a research hotspot in the field of complex dynamic system control.

[0003] Networked drones inevitably suffer from malicious cyberattacks during information exchange, which can lead to performance degradation and even system instability. As a typical type of malicious cyberattack, DoS attacks often interrupt data transmission between agents, preventing the target system from continuously receiving valid data. Due to this characteristic, designing a security controller and conducting stability analysis for networked drones subjected to DoS attacks is crucial. Meanwhile, adversarial game theory plays a vital role in simulating and analyzing complex adversarial behaviors between multiple attacker and defender agents in different scenarios. In adversarial games, both attacker and defender agents tend to adopt strategies that maximize their own interests while minimizing control costs, given limited resources and information. Traditional cooperative control paradigms struggle to effectively describe the strategic adversarial behavior between attacker and defender agents. Therefore, researching drone security control based on adversarial game theory under DoS attacks has significant theoretical and practical value. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention proposes a UAV security compensation control method based on adversarial game theory under DoS attacks. Under the established network topology and adversarial game mechanism, system dynamics models of the attacker's UAV and the defender's UAV are modeled. State errors and cost functions are constructed from the perspectives of both the attacker's and defender's UAVs. Adaptive dynamic programming techniques are introduced to design and optimize control laws and single-judgment network weight update laws, thereby achieving the goal of networked UAV security control based on adversarial game theory under DoS attacks.

[0005] The technical solution of this invention is as follows:

[0006] On the one hand, this invention provides a method for security compensation control of unmanned aerial vehicles (UAVs) under DoS attacks based on adversarial game theory, comprising the following steps:

[0007] Establish a nonlinear dynamic model of the motion attitude of the attacker drone and the defender drone, and define the communication network topology between the attacker drone and the defender drone;

[0008] Based on the nonlinear dynamic model of the motion attitude of the attacker drone and the defender drone and the topology of the communication network, the state error and cost function are constructed from the perspectives of the attacker drone and the defender drone, respectively.

[0009] Based on the state errors and cost functions of the attacker's drone and the defender's drone, an adversarial game mechanism with multiple participants is established.

[0010] Based on the established adversarial game mechanism with multiple participants and using the Bellman optimality principle to construct coupled HJB equations to solve the optimal control strategies of the attacker drone and the defender drone, including the optimal control strategy of the attacker drone, the optimal control strategy of the defender drone and the optimal compensation control strategy of the defender drone, so as to realize the control of the attacker drone and the defender drone.

[0011] An adaptive dynamic programming technique is used to construct a single-judgment network to estimate the optimal control strategy of the attacker drone and the optimal control strategy and optimal compensation control strategy of the defender drone for each execution.

[0012] Furthermore, the establishment of a nonlinear dynamic model of the motion attitudes of the attacker drone and the defender drone, and the definition of the communication network topology between the attacker drone and the defender drone, specifically includes:

[0013] A1: Regarding the attacker... Model the motion attitude of the first UAV to obtain the first... A nonlinear dynamic model of the motion attitude of an attacker's drone;

[0014] (1);

[0015] Among them, superscript The drone is referred to as the attacker. , , These represent the attacker's... A drone orbiting the body coordinate system axis, shaft and Moment of inertia in the axial direction, This indicates the attacker's drone's identification number. The drone's coordinate system has its origin at the drone's center of mass, and extends along the drone's longitudinal axis towards the nose. The axis, along the horizontal axis of the fuselage, points towards the right wing of the UAV. Axis, perpendicular to The plane is downward. axis; , , These represent the attacker's... The roll angle, pitch angle, and yaw angle of each drone; , , They represent , and The first derivative; , , They represent , and The second derivative; Indicates the third as the attacker The moment of inertia of the motor blades of a drone. Indicates the third as the attacker Additional perturbations from the drone; , , Indicates the third as the attacker A drone in the body coordinate system axis, shaft and Axial drag coefficient; , , These represent the attacker's... The control parameters of a drone's rotor over roll, pitch, and yaw angles; (The sentence is incomplete and requires more context to translate accurately.) Defined as , Indicates the number of drones acting as attackers;

[0016] Define the attacker as the first The system state variables of a drone And let its state components , , , , , , Indicates transpose, then as the attacker's... The nonlinear dynamic model of the motion attitude of the UAV is further expressed as:

[0017] (2);

[0018] in, express The first derivative, and , , ; ; ;

[0019] A2: Regarding the first as the defender Model the motion attitude of the first UAV to obtain the first... A nonlinear dynamic model of the motion attitude of a defender drone;

[0020] Consider a DoS attack launched by an attacker's drone against the defender's drone's control channel; define... It is a time variable and is defined For the first The instant a DoS attack occurs; definition For the first The time interval of each DoS attack and the time span is ,in, For the first The instant a DoS attack ends ;definition The time interval during which no DoS attack occurred and the time span is [missing information]. ;

[0021] No. The nonlinear dynamic model of the motion attitude of the defender drone is as follows:

[0022] (3);

[0023] Among them, superscript This refers to drones acting as defenders; , , They represent the first as the defender. A drone orbiting the body coordinate system axis, shaft and Moment of inertia in the axial direction, Indicates the number of the defender drone; , , They represent the first as the defender. The roll angle, pitch angle, and yaw angle of each drone; , , They represent , , The first derivative; , , They represent , , The second derivative; Indicating the first as the defender The moment of inertia of the motor blades of a drone. Indicating the first as the defender Additional perturbations from the drone; , , Indicating the first as the defender A drone in the body coordinate system axis, shaft and Axial drag coefficient; , , They represent the first as the defender. The control parameters of a drone's rotor over roll, pitch, and yaw angles; (The sentence is incomplete and requires more context to translate accurately.) Defined as , Indicates the number of drones acting as defenders; , , They represent the first as the defender. The compensating control parameters for roll angle, pitch angle and yaw angle of the rotor of a drone; , , They represent the first as the defender. The rotor compensation control gain of a UAV for roll angle, pitch angle and yaw angle; The coupling gain index; This represents a switching signal used to determine if a DoS attack is in progress; and satisfy , ;

[0024] Define the first as the defender The system state variables of a drone And let its state components , , , , , Then, as the defender, the first The nonlinear dynamic model of the motion attitude of the UAV is further expressed as:

[0025] (4);

[0026] in, express The first derivative, and , , ; ; ; ; ;

[0027] A3: Define the communication network topology between the attacker's drone and the defender's drone;

[0028] Specifically, the communication network topology between the attacker's drones is defined as an undirected graph. ,in, and They are the vertex set and the undirected edge set, respectively. Indicates the third as the attacker Each drone corresponds to a vertex, and each edge represents a communication link between the attacker drones corresponding to that vertex; Define... As vertex The neighborhood group, Indicates the number of the neighboring vertex. Representing neighboring vertices, Represents vertices and The edge between; It is an adjacency matrix. Representing the adjacency matrix The Line 1 Column elements, and satisfying and , Representing the adjacency matrix The Line 1 Column elements; definition For the entry degree array, For the entry degree array The elements on the main diagonal; corresponding to the adjacency matrix. The Laplace matrix is ;

[0029] Define the communication network topology between defender drones as an undirected graph. ,in, and These are the vertex set and the undirected edge set, respectively. Indicates the third as the attacker Each drone corresponds to a vertex, and each edge represents a communication link between the attacker drones corresponding to that vertex; Define... As vertex The neighborhood group, Indicates the number of the neighboring vertex. Representing neighboring vertices, Represents vertices and The edge between; It is an adjacency matrix. Representing the adjacency matrix The Line 1 Column elements, and satisfying and , Representing the adjacency matrix The Line 1 Column elements; definition For the entry degree array, For the entry degree array The elements on the main diagonal; corresponding to the adjacency matrix. The Laplace matrix is ;

[0030] Define the communication network topology between the attacker's drone and the defender's drone as an undirected graph. ,in, , and These are the vertex set, the undirected edge set, and the adjacency matrix, respectively. One attacker drone and The defender drones are located in two different sectors. and All drones exchange information between two different sectors; for those containing A sector of an attacker's drone In other words, if the first The attacker drone was able to capture the first Information about each defender drone, and the connectivity weights between them. ,on the contrary, For those containing A sector of a defender drone In other words, if the first The defender was able to capture the first Information about each attacker, and the connectivity weights between them. ,on the contrary, .

[0031] Furthermore, based on the nonlinear dynamic model of the motion attitude of the attacker drone and the defender drone and the communication network topology, the state error and cost function are constructed from the perspectives of the attacker drone and the defender drone, respectively, specifically including:

[0032] B1: Constructing state errors from the attacker's drone's perspective;

[0033] (5);

[0034] in, This indicates the state error of the attacker's drone's angle. The system state variable representing the attacker's drone corresponding to the neighboring vertex;

[0035] Based on formulas (2) and (5), the state error of the attacker's drone angle The dynamic calculation is as follows:

[0036] (6);

[0037] in, ; express The first derivative;

[0038] B2: Constructing state errors from the perspective of the defender drone;

[0039] (7);

[0040] in, This indicates the state error of the defender drone's angle.

[0041] Based on formulas (4) and (7), the state error of the defender drone angle The dynamic calculation is as follows:

[0042] (8);

[0043] in, ; express The first derivative;

[0044] B3: Based on the state error of the attacker's drone angle State error of the angle of the defender drone Establish the cost function;

[0045] The attacker's drone's attitude response can be characterized by the following cost function:

[0046] (9);

[0047] in, The cost function represents the attacker's drone. This represents the initial value of the attacker's drone's state error. Defined as ; Represents a time variable;

[0048] For the An attacker drone, for:

[0049] (10);

[0050] in, , , , All are positive definite symmetric matrices;

[0051] The attitude response of the defender drone can be characterized by the following cost function:

[0052] (11);

[0053] in, The cost function represents the cost of the defender drone. The initial value of the state error of the defender drone. Defined as ; Defined as , For the first Control inputs for a defender drone;

[0054] For the One Defender drone, for:

[0055] (12);

[0056] in, , , , , All are positive definite symmetric matrices.

[0057] Furthermore, the establishment of an adversarial game mechanism with multiple participants based on the state errors and cost functions of the attacker's drone and the defender's drone specifically includes:

[0058] Based on formula (9), the first is defined The adversarial game value of an attacker's drone for:

[0059] (13);

[0060] Based on formula (11), the first is defined as follows: The adversarial game value of a defender drone for:

[0061] (14);

[0062] Definition of the first The optimized control strategy for the attacker's drone is as follows: , No. The optimized control strategy and optimized compensation control strategy for each defender drone are as follows: and Based on formulas (9) and (11), if the following conditions are met:

[0063] (15);

[0064] (16);

[0065] but , , The Nash equilibrium that constitutes the adversarial game, in which Defined as , Defined as , Defined as .

[0066] Furthermore, the method of constructing coupled HJB equations based on the established adversarial game mechanism with multiple participants and utilizing the Bellman optimality principle to solve the optimal control strategies for the attacker's drone and the defender's drone specifically includes:

[0067] Based on the dynamics of the state error of the attacker's drone angle (6), the first... The Hamiltonian function of the attacker's drone is:

[0068] (17);

[0069] in, Indicates the first Hamiltonian functions of an attacker's drone. Indicates the gradient sign;

[0070] Based on formula (17), the first The optimized control strategy for the attacker's drone is given as follows:

[0071] (18);

[0072] Combining formulas (10), (17), and (18), we obtain the first... The coupled HJB equations for an attacker's drone are shown below:

[0073] (19);

[0074] Based on formula (19) and by solving ,get The specific form is as follows:

[0075] (20);

[0076] Based on the dynamics of the state error of the defender drone angle (8), the first... The Hamiltonian function for a defender drone is:

[0077] (twenty one);

[0078] in, Indicates the first Hamiltonian function for a defender drone;

[0079] Based on equation (21), the first The optimized control strategy and optimized compensation control strategy for the defender drone are given as follows:

[0080] (twenty two);

[0081] (twenty three);

[0082] when At that time, according to formulas (12), (21), (22), and (23), we obtain the first... The coupled HJB equations for a single defender drone are shown below:

[0083] (twenty four);

[0084] Based on formula (24) and by solving ,get The specific form is as follows:

[0085] (25);

[0086] in, It is a positive definite symmetric matrix The inverse matrix;

[0087] Based on formula (24) and by solving ,get The specific form is as follows:

[0088] (26);

[0089] in, It is a positive definite symmetric matrix The inverse matrix;

[0090] when At that time, it can be known Further, we can obtain At this point, simply optimizing the compensation control strategy is sufficient. It takes effect; according to formulas (12), (21), (22), and (23), the following can be obtained: The coupled HJB equations for a single defender drone are as follows:

[0091] (27);

[0092] Based on formula (27) and by solving ,available The specific form is shown in formula (26).

[0093] Furthermore, the adoption of adaptive dynamic programming technology to construct a single-evaluation network estimates the optimal control strategy of the attacker's drone and the optimal control strategy and optimal compensation control strategy of the defender's drone for each execution, specifically including:

[0094] The game values ​​are approximated by implementing a single-judge neural network. and ,get:

[0095] (28);

[0096] (29);

[0097] in, , , For the first Weights, activation function, and approximation error of a single-judge neural network for an attacker's drone. The number of neural nodes; , , For the first Weights, activation function, and approximation error of a single-judge neural network for a defender drone;

[0098] Based on formulas (28) and (29), and The gradient is expressed as follows:

[0099] (30);

[0100] (31);

[0101] in, , , They are respectively , and The gradient; , , They are respectively , and The gradient;

[0102] Substituting formula (30) into formula (20), we get:

[0103] (32);

[0104] in, ,and It is norm-bounded, meaning there exists a positive constant. Make ;

[0105] when Substituting formula (31) into formulas (25) and (26) respectively, we get:

[0106] (33);

[0107] (34);

[0108] in, ,and satisfy , It is a positive constant; ,and It is norm-bounded, meaning there exists a positive constant. Make ;

[0109] when At that time, only the compensation control strategy is optimized. It takes effect; at this point, one can obtain... The specific form is the same as that of formula (34);

[0110] Based on formulas (30) and (31), and It is estimated as follows:

[0111] (35);

[0112] (36);

[0113] in, , , , They are respectively , , and The estimate;

[0114] Based on formulas (32) and (35), It is estimated as follows:

[0115] (37);

[0116] in, for The estimate;

[0117] Based on formula (37), the first The ultimate control law of the attacker's drone It is designed as follows:

[0118] (38);

[0119] when At that time, based on formulas (33), (34) and (36), and It is estimated as follows:

[0120] (39);

[0121] (40);

[0122] in, , for and The estimate;

[0123] Based on formulas (39) and (40), the first The ultimate security control law for the defender drone and It is designed as follows:

[0124] (41);

[0125] (42);

[0126] when At that time, only the compensation control law It takes effect; at this point, one can obtain... The specific form is the same as that of formula (42);

[0127] Based on formulas (10), (17), and (35), the first The estimates of the Hamiltonian function of the attacker's drone are given below:

[0128] (43);

[0129] in, Indicates the first Hamiltonian function of an attacker's drone The estimate; Defined as ; ,and ;

[0130] Based on formulas (12), (21), and (36), the first The estimates of the Hamiltonian function for the defender drone are given below:

[0131] (44);

[0132] in, ; ; ; ;

[0133] Based on formulas (19) and (43), the first is defined as follows: The Bellman residual function of the attacker's drone is shown below:

[0134] (45);

[0135] in, For the first Bellman residual function of an attacker's drone;

[0136] Based on formulas (24), (27), and (44), the first is defined as follows: The Bellman residual function of the Defender UAV is shown below:

[0137] (46);

[0138] in, For the first Bellman residuals of a defender drone;

[0139] Based on formula (45) and using gradient descent and standardization principles, the single evaluation network weight update law for the attacker's drone is designed as follows:

[0140] (47);

[0141] in, Indicates the first Single-evaluation network weight update law for an attacker's drone; For update rate; It was used for standardization;

[0142] Based on formula (46) and using gradient descent and standardization principles, the single evaluation network weight update law for the defender drone is designed as follows:

[0143] (48);

[0144] in, Indicates the first Single-evaluation network weight update law for a single defender drone; and All are update rates; and It was used for standardization.

[0145] Secondly, this application proposes an electronic device, including: one or more processors, and a memory, the memory being used to store instructions, which, when executed by the one or more processors, cause the one or more processors to execute the aforementioned anti-DoS attack-based drone security compensation control method.

[0146] Thirdly, this application proposes a computer-readable storage medium storing executable instructions, which, when executed, cause a processor to perform the aforementioned drone security compensation control method based on adversarial game theory under DoS attacks.

[0147] Fourthly, this application proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the aforementioned method for drone security compensation control based on adversarial game theory under DoS attacks.

[0148] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0149] To address the security control problem of multi-agent systems containing multiple attacker and defender drones, this invention proposes a drone security compensation control method based on adversarial game theory under DoS attacks, ensuring the stability of the system even under DoS attacks. Furthermore, unlike multi-agent system security control problems that treat attacks and defenses as independent entities without fully considering the interaction between attacker and defender drones, this invention establishes an adversarial game mechanism with multiple participants and introduces three algebraic graphs to represent the communication network topology relationships between attacker drones, between defender drones, and between attacker and defender drones, respectively. This allows for consideration of the bidirectional interaction characteristics between attacker and defender drones from a security decision-making perspective. Compared to adaptive dynamic programming methods using an actor-critic network architecture, this invention employs a single-critic network architecture, reducing computational burden, and designs a weight update law using gradient descent and standardization principles to enhance the adaptability of the drone system in real-time control tasks. Attached Figure Description

[0150] Figure 1 This is a flowchart of a networked drone security control method based on adversarial game theory under a DoS attack, as described in this embodiment of the invention.

[0151] Figure 2 This is an undirected topological graph showing the relationship between the attacker's drone and the defender's drone in a simulation of an embodiment of the present invention.

[0152] Figure 3 This is a switching signal response diagram used in the simulation of this embodiment of the invention to determine whether a DoS attack exists;

[0153] Figure 4 This is a system state variable response curve of the attacker's drone in the simulation of an embodiment of the present invention;

[0154] Among them, (a) is the response curve of the three state components in the system state variables of the first attacker drone; (b) is the response curve of the three state components in the system state variables of the second attacker drone; (c) is the response curve of the three state components in the system state variables of the third attacker drone; and (d) is the response curve of the three state components in the system state variables of the fourth attacker drone.

[0155] Figure 5 This is a system state variable response curve of the defender drone under a DoS attack in a simulation of an embodiment of the present invention;

[0156] Among them, (a) is the response curve of the three state components in the system state variables of the first defender drone under a DoS attack; (b) is the response curve of the three state components in the system state variables of the second defender drone under a DoS attack; (c) is the response curve of the three state components in the system state variables of the third defender drone under a DoS attack; and (d) is the response curve of the three state components in the system state variables of the fourth defender drone under a DoS attack.

[0157] Figure 6 This is a control law response curve of the attacker's drone in a simulation of an embodiment of the present invention;

[0158] Among them, (a) is the response curve of the roll angle, pitch angle and yaw angle control of the first attacker UAV; (b) is the response curve of the roll angle, pitch angle and yaw angle control of the second attacker UAV; (c) is the response curve of the roll angle, pitch angle and yaw angle control of the third attacker UAV; and (d) is the response curve of the roll angle, pitch angle and yaw angle control of the fourth attacker UAV.

[0159] Figure 7 This is a response curve of the compensated control quantity of the defender drone under a DoS attack in a simulation of an embodiment of the present invention;

[0160] Among them, (a) is the compensation control response curve of the first defender drone under DoS attack for the roll, pitch and yaw angles; (b) is the compensation control response curve of the second defender drone under DoS attack for the roll, pitch and yaw angles; (c) is the compensation control response curve of the third defender drone under DoS attack for the roll, pitch and yaw angles; and (d) is the compensation control response curve of the fourth defender drone under DoS attack for the roll, pitch and yaw angles. Detailed Implementation

[0161] To enable those skilled in the art to better understand the present invention, the technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. However, it should be understood that, without further description, the present invention can be advantageously incorporated into other embodiments.

[0162] Example 1:

[0163] like Figure 1 As shown, this invention provides a drone security compensation control method based on adversarial game theory under DoS attacks, including the following steps:

[0164] S1: Establish a nonlinear dynamic model of the motion attitude of the attacker drone and the defender drone, and define the communication network topology between the attacker drone and the defender drone;

[0165] The specific steps include:

[0166] S1.1: Regarding the attacker's actions... Model the motion attitude of the first UAV to obtain the first... A nonlinear dynamic model of the motion attitude of an attacker's drone;

[0167] (1);

[0168] Among them, superscript The drone is referred to as the attacker. , , These represent the attacker's... A drone orbiting the body coordinate system axis, shaft and Moment of inertia in the axial direction, This indicates the attacker's drone's identification number. The drone's coordinate system has its origin at the drone's center of mass, and extends along the drone's longitudinal axis towards the nose. The axis, along the horizontal axis of the fuselage, points towards the right wing of the UAV. Axis, perpendicular to The plane is downward. axis; , , These represent the attacker's... The roll angle, pitch angle, and yaw angle of each drone; , , They represent , and The first derivative; , , They represent , and The second derivative; Indicates the third as the attacker The moment of inertia of the motor blades of a drone. Indicates the third as the attacker Additional perturbations from the drone; , , Indicates the third as the attacker A drone in the body coordinate system axis, shaft and Axial drag coefficient; , , These represent the attacker's... The control parameters of a drone's rotor over roll, pitch, and yaw angles; (The sentence is incomplete and requires more context to translate accurately.) Defined as , Indicates the number of drones acting as attackers;

[0169] Define the attacker as the first The system state variables of a drone And let its state components , , , , , , Indicates transpose, then as the attacker's... The nonlinear dynamic model of the motion attitude of the UAV is further expressed as:

[0170] (2);

[0171] in, express The first derivative, and , , ; ; ;

[0172] S1.2: For the defender Model the motion attitude of the first UAV to obtain the first... A nonlinear dynamic model of the motion attitude of a defender drone;

[0173] Consider a DoS attack launched by an attacker's drone against the defender's drone's control channel; define... It is a time variable and is defined For the first The instant a DoS attack occurs; definition For the first The time interval of each DoS attack and the time span is ,in, For the first The instant a DoS attack ends ;definition The time interval during which no DoS attack occurred and the time span is [missing information]. ;

[0174] The first The nonlinear dynamic model of the motion attitude of the defender drone is as follows:

[0175] (3);

[0176] Among them, superscript This refers to drones acting as defenders; , , They represent the first as the defender. A drone orbiting the body coordinate system axis, shaft and Moment of inertia in the axial direction, Indicates the number of the defender drone; , , They represent the first as the defender. The roll angle, pitch angle, and yaw angle of each drone; , , They represent , , The first derivative; , , They represent , , The second derivative; Indicating the first as the defender The moment of inertia of the motor blades of a drone. Indicating the first as the defender Additional perturbations from the drone; , , Indicating the first as the defender A drone in the body coordinate system axis, shaft and Axial drag coefficient; , , They represent the first as the defender. The control parameters of a drone's rotor over roll, pitch, and yaw angles; (The sentence is incomplete and requires more context to translate accurately.) Defined as , Indicates the number of drones acting as defenders; , , They represent the first as the defender. The compensating control parameters for roll angle, pitch angle and yaw angle of the rotor of a drone; , , They represent the first as the defender. The rotor compensation control gain of a UAV for roll angle, pitch angle and yaw angle; The coupling gain index; This represents a switching signal used to determine if a DoS attack is in progress; and satisfy , ;

[0177] Define the first as the defender The system state variables of a drone And let its state components , , , , , Then, as the defender, the first The nonlinear dynamic model of the motion attitude of the UAV is further expressed as:

[0178] (4);

[0179] in, express The first derivative, and , , ; ; ; ; ;

[0180] S1.3: Define the communication network topology between the attacker's drone and the defender's drone;

[0181] Specifically, the communication network topology between the attacker's drones is defined as an undirected graph. ,in, and They are the vertex set and the undirected edge set, respectively. Indicates the third as the attacker Each drone corresponds to a vertex, and each edge represents a communication link between the attacker drones corresponding to that vertex; Define... As vertex The neighborhood group, Indicates the number of the neighboring vertex. Representing neighboring vertices, Represents vertices and The edge between; It is an adjacency matrix. Representing the adjacency matrix The Line 1 Column elements, and satisfying and , Representing the adjacency matrix The Line 1 Column elements; definition For the entry degree array, For the entry degree array The elements on the main diagonal; corresponding to the adjacency matrix. The Laplace matrix is ;

[0182] Define the communication network topology between defender drones as an undirected graph. ,in, and These are the vertex set and the undirected edge set, respectively. Indicates the third as the attacker Each drone corresponds to a vertex, and each edge represents a communication link between the attacker drones corresponding to that vertex; Define... As vertex The neighborhood group, Indicates the number of the neighboring vertex. Representing neighboring vertices, Represents vertices and The edge between; It is an adjacency matrix. Representing the adjacency matrix The Line 1 Column elements, and satisfying and , Representing the adjacency matrix The Line 1 Column elements; definition For the entry degree array, For the entry degree array The elements on the main diagonal; corresponding to the adjacency matrix. The Laplace matrix is ;

[0183] Define the communication network topology between the attacker's drone and the defender's drone as an undirected graph. ,in, , and These are the vertex set, the undirected edge set, and the adjacency matrix, respectively. One attacker drone and The defender drones are located in two different sectors. and All drones exchange information between two different sectors; for those containing A sector of an attacker's drone In other words, if the first The attacker drone was able to capture the first Information about each defender drone, and the connectivity weights between them. ,on the contrary, For those containing A sector of a defender drone In other words, if the first The defender was able to capture the first Information about each attacker, and the connectivity weights between them. ,on the contrary, ;

[0184] S2: Based on the nonlinear dynamic model of the motion attitude of the attacker drone and the defender drone and the topology of the communication network, construct the state error and cost function from the perspectives of the attacker drone and the defender drone respectively.

[0185] The specific steps include:

[0186] S2.1: Construct state errors from the perspective of the attacker's drone;

[0187] (5);

[0188] in, This indicates the state error of the attacker's drone's angle. The system state variable representing the attacker's drone corresponding to the neighboring vertex;

[0189] Based on formulas (2) and (5), the state error of the attacker's drone angle The dynamic calculation is as follows:

[0190] (6);

[0191] in, ; express The first derivative;

[0192] S2.2: Construct state errors from the perspective of the defender drone;

[0193] (7);

[0194] in, This indicates the state error of the defender drone's angle.

[0195] Based on formulas (4) and (7), the state error of the defender drone angle The dynamic calculation is as follows:

[0196] (8);

[0197] in, ; express The first derivative;

[0198] S2.3: State error based on the attacker's drone angle State error of the angle of the defender drone Establish the cost function;

[0199] The attacker's drone's attitude response can be characterized by the following cost function:

[0200] (9);

[0201] in, The cost function represents the attacker's drone. This represents the initial value of the attacker's drone's state error. Defined as ; Represents a time variable;

[0202] For the An attacker drone, for:

[0203] (10);

[0204] in, , , , All are positive definite symmetric matrices;

[0205] The attitude response of the defender drone can be characterized by the following cost function:

[0206] (11);

[0207] in, The cost function represents the cost of the defender drone. The initial value of the state error of the defender drone. Defined as ; Defined as , For the first Control inputs for a defender drone;

[0208] For the One Defender drone, for:

[0209] (12);

[0210] in, , , , , All are positive definite symmetric matrices;

[0211] S3: Based on the state error and cost function between the attacker's drone and the defender's drone, establish an adversarial game mechanism with multiple participants;

[0212] Based on formula (9), the first is defined The adversarial game value of an attacker's drone for:

[0213] (13);

[0214] Based on formula (11), the first is defined as follows: The adversarial game value of a defender drone for:

[0215] (14);

[0216] Definition of the first The optimized control strategy for the attacker's drone is as follows: , No. The optimized control strategy and optimized compensation control strategy for each defender drone are as follows: and Based on formulas (9) and (11), if the following conditions are met:

[0217] (15);

[0218] (16);

[0219] but , , The Nash equilibrium that constitutes the adversarial game, in which Defined as , Defined as , Defined as ;

[0220] S4: Based on the established adversarial game mechanism with multiple participants and using the Bellman optimality principle, construct coupled HJB equations to solve the optimal control strategies of the attacker drone and the defender drone, including the optimal control strategy of the attacker drone, the optimal control strategy of the defender drone, and the optimal compensation control strategy of the defender drone, so as to realize the control of the attacker drone and the defender drone.

[0221] The specific steps are as follows:

[0222] Based on the dynamics of the state error of the attacker's drone angle (6), the first... The Hamiltonian function of the attacker's drone is:

[0223] (17);

[0224] in, Indicates the first Hamiltonian functions of an attacker's drone. Indicates the gradient sign;

[0225] Based on formula (17), the first The optimized control strategy for the attacker's drone is given as follows:

[0226] (18);

[0227] Combining formulas (10), (17), and (18), we obtain the first... The coupled HJB equations for an attacker's drone are shown below:

[0228] (19);

[0229] Based on formula (19) and by solving ,get The specific form is as follows:

[0230] (20);

[0231] Based on the dynamics of the state error of the defender drone angle (8), the first... The Hamiltonian function for a defender drone is:

[0232] (twenty one);

[0233] in, Indicates the first Hamiltonian function for a defender drone;

[0234] Based on equation (21), the first The optimized control strategy and optimized compensation control strategy for the defender drone are given as follows:

[0235] (twenty two);

[0236] (twenty three);

[0237] when At that time, according to formulas (12), (21), (22), and (23), we obtain the first... The coupled HJB equations for a single defender drone are shown below:

[0238] (twenty four);

[0239] Based on formula (24) and by solving ,get The specific form is as follows:

[0240] (25);

[0241] in, It is a positive definite symmetric matrix The inverse matrix;

[0242] Similarly, based on formula (24) and by solving... ,get The specific form is as follows:

[0243] (26);

[0244] in, It is a positive definite symmetric matrix The inverse matrix;

[0245] when At that time, it can be known Further, we can obtain At this point, simply optimizing the compensation control strategy is sufficient. It takes effect; according to formulas (12), (21), (22), and (23), the following can be obtained: The coupled HJB equations for a single defender drone are as follows:

[0246] (27);

[0247] Based on formula (27) and by solving ,available The specific form is shown in formula (26);

[0248] S5: Since the optimal control strategy to be solved is not explicit, an adaptive dynamic programming technique is used to construct a single-evaluation network to estimate the optimal control strategy of the attacker drone and the optimal control strategy and optimal compensation control strategy of the defender drone for each execution.

[0249] The specific steps are as follows:

[0250] The game values ​​are approximated by implementing a single-judge neural network. and ,get:

[0251] (28);

[0252] (29);

[0253] in, , , For the first Weights, activation function, and approximation error of a single-judge neural network for an attacker's drone. The number of neural nodes; , , For the first Weights, activation function, and approximation error of a single-judge neural network for a defender drone;

[0254] Based on formulas (28) and (29), and The gradient is expressed as follows:

[0255] (30);

[0256] (31);

[0257] in, , , They are respectively , and The gradient; , , They are respectively , and The gradient;

[0258] Substituting formula (30) into formula (20), we get:

[0259] (32);

[0260] in, ,and It is norm-bounded, meaning there exists a positive constant. Make ;

[0261] when Substituting formula (31) into formulas (25) and (26) respectively, we get:

[0262] (33);

[0263] (34);

[0264] in, ,and satisfy , It is a positive constant; ,and It is norm-bounded, meaning there exists a positive constant. Make ;

[0265] when At that time, only the compensation control strategy is optimized. It takes effect; at this point, one can obtain... The specific form is the same as that of formula (34);

[0266] Based on formulas (30) and (31), and It is estimated as follows:

[0267] (35);

[0268] (36);

[0269] in, , , , They are respectively , , and The estimate;

[0270] Based on formulas (32) and (35), It is estimated as follows:

[0271] (37);

[0272] in, for The estimate;

[0273] Based on formula (37), the first The ultimate control law of the attacker's drone It is designed as follows:

[0274] (38);

[0275] when At that time, based on formulas (33), (34) and (36), and It is estimated as follows:

[0276] (39);

[0277] (40);

[0278] in, , for and The estimate;

[0279] Based on formulas (39) and (40), the first The ultimate security control law for the defender drone and It is designed as follows:

[0280] (41);

[0281] (42);

[0282] when At that time, only the compensation control law It takes effect; at this point, one can obtain... The specific form is the same as that of formula (42);

[0283] Based on formulas (10), (17), and (35), the first The estimates of the Hamiltonian function of the attacker's drone are given below:

[0284] (43);

[0285] in, Indicates the first Hamiltonian function of an attacker's drone The estimate; Defined as ; ,and

[0286] ;

[0287] Based on formulas (12), (21), and (36), the first The estimates of the Hamiltonian function for the defender drone are given below:

[0288] (44);

[0289] in, ;

[0290] ; ;

[0291] ;

[0292] Based on formulas (19) and (43), the first is defined as follows: The Bellman residual function of the attacker's drone is shown below:

[0293] (45);

[0294] in, For the first Bellman residual function of an attacker's drone;

[0295] Based on formulas (24), (27), and (44), the first is defined as follows: The Bellman residual function of the Defender UAV is shown below:

[0296] (46);

[0297] in, For the first Bellman residuals of a defender drone;

[0298] Based on formula (45) and using gradient descent and standardization principles, the single evaluation network weight update law for the attacker's drone is designed as follows:

[0299] (47);

[0300] in, Indicates the first Single-evaluation network weight update law for an attacker's drone; For update rate; It was used for standardization;

[0301] Based on formula (46) and using gradient descent and standardization principles, the single evaluation network weight update law for the defender drone is designed as follows:

[0302] (48);

[0303] in, Indicates the first Single-evaluation network weight update law for a single defender drone; and All are update rates; and It was used for standardization.

[0304] To verify the effectiveness of the control method of this invention, four attacker drones and four defender drones were selected for simulation verification in the embodiment. The undirected graph topology between them is as follows: Figure 2 As shown, the following adjacency matrix and Laplace matrix can be obtained:

[0305] , ;

[0306] Select the first The system state variables of the attacker's drone are: , And let the state components , , The initial values ​​for the state variables of the four attacker drones are given as follows: , , , Four attacker drones orbiting the aircraft's coordinate system axis, shaft and The moment of inertia in the axial direction is , , The moment of inertia of the propeller blades of the four attacker drones is... , , , The additional perturbations of the four attacker drones are , , , Four attacker drones in the body coordinate system axis, shaft and The drag coefficient in the axial direction is , , .

[0307] Select the first The system state variables of the defender drone are: , And let the state components , , The initial values ​​for the state variables of the four defender drones are given as follows: , , , Four Defender drones orbiting the aircraft's coordinate system. axis, shaft and The moment of inertia in the axial direction is , , The moment of inertia of the propeller blades of the four defender drones is... , , , The additional perturbations of the four defender drones are , , , Four Defender drones in the body coordinate system axis, shaft and The drag coefficient in the axial direction is , , The compensatory control gains for roll, pitch, and yaw angles of the four Defender UAV rotors are: , , ;

[0308] The update rates of the single-evaluation network weight update laws for the four attacker drones are respectively chosen as follows: , , and For the four defender drones, when When, the update rate of the single-evaluation network weight update law is selected as respectively. , , , ,when When, the update rate of the single-evaluation network weight update law is selected as respectively. , , and The switching signal for determining the presence of a DoS attack is selected as... .

[0309] Simulation results are as follows Figures 3-7 As shown. Figure 3 This is a switching signal response diagram used in the simulation of this embodiment of the invention to determine whether a DoS attack exists. It can be seen that the union of the time intervals in which the DoS attack occurs is... . Figure 4 The figure shows the system state variable response curves of the attacker's drone in the simulation of the embodiment of the present invention. It can be seen that the oscillations are large at the beginning and then tend to stabilize. Figure 5 The figure shows the system state variable response curve of the defender drone under a DoS attack in the simulation of the embodiment of the present invention. It can be seen that the system state is still stable even under the DoS attack. Figure 6 The diagram shows the control law response curves of the attacker's drone in the simulation of this embodiment of the invention. It can be seen that they converge to the small neighborhood of zero within a finite time. Figure 7 The graph shows the response curve of the compensation control quantity of the defender drone under a DoS attack in the simulation of the embodiment of the present invention. It can be seen that even under the DoS attack, the compensation control quantity of the defender drone will still converge to the zero-point small neighborhood.

[0310] Example 2:

[0311] This embodiment proposes an electronic device, including: one or more processors, and a memory, wherein the memory is used to store instructions, and when the instructions are executed by the one or more processors, the one or more processors execute the aforementioned drone security compensation control method based on adversarial game theory under DoS attack.

[0312] The electronic device can be a mobile phone, computer, or tablet computer, etc., and includes a memory and a processor. The memory stores a computer program, which, when executed by the processor, implements the UAV security compensation control method based on adversarial game theory under DoS attacks as described in the embodiment. It is understood that the electronic device may also include input / output (I / O) interfaces and communication components.

[0313] The processor is used to execute all or part of the steps in the adversarial game-based drone security compensation control method under DoS attacks as described in the above embodiments. The memory is used to store various types of data, which may include, for example, instructions for any application or method in the electronic device, as well as application-related data.

[0314] The processor can be implemented as an Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic components, and is used to execute the UAV security compensation control method based on adversarial game theory under DoS attack described in the above embodiments.

[0315] Example 3:

[0316] This embodiment proposes a computer-readable storage medium that stores executable instructions. When these instructions are executed, if they are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium.

[0317] The computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the anti-DoS attack-based drone security compensation control method described in the various embodiments of this application.

[0318] The aforementioned storage media include: flash memory, hard disks, multimedia cards, card-type memory (e.g., SD (Secure Digital Memory Card) or DX (Memory Data Register, MDR) memory), random access memory (RAM), static random-access memory (SRAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), programmable read-only memory (PROM), magnetic storage, disks, optical discs, servers, APP (Application) app stores, and other media capable of storing program verification codes. These media store computer programs, which, when executed by a processor, can implement the various steps of the aforementioned DoS attack-based adversarial game-theoretic drone security compensation control method.

[0319] Example 4:

[0320] This embodiment proposes a computer program product, including a computer program or instructions, which, when executed by a processor, implements the aforementioned method for drone security compensation control based on adversarial game theory under DoS attacks.

[0321] Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or part of the technical solution, can be embodied in the form of a computer program product.

[0322] The various embodiments in this application are described in a progressive manner. The same or similar parts between the various embodiments can be referred to each other. Each embodiment focuses on describing the differences from other embodiments.

[0323] The scope of protection of this application is not limited to the embodiments described above. Obviously, those skilled in the art can make various modifications and variations to this disclosure without departing from the scope and spirit of this disclosure. If such modifications and variations fall within the scope of this disclosure and its equivalents, then the intent of this disclosure also includes these modifications and variations.

Claims

1. A method for security compensation control of unmanned aerial vehicles (UAVs) under DoS attacks based on adversarial game theory, characterized in that, Includes the following steps: Establish a nonlinear dynamic model of the motion attitude of the attacker drone and the defender drone, and define the communication network topology between the attacker drone and the defender drone; Based on the nonlinear dynamic model of the motion attitude of the attacker drone and the defender drone and the topology of the communication network, the state error and cost function are constructed from the perspectives of the attacker drone and the defender drone, respectively. Based on the state errors and cost functions of the attacker's drone and the defender's drone, an adversarial game mechanism with multiple participants is established. Based on the established adversarial game mechanism with multiple participants and using the Bellman optimality principle to construct coupled HJB equations to solve the optimal control strategies of the attacker drone and the defender drone, including the optimal control strategy of the attacker drone, the optimal control strategy of the defender drone and the optimal compensation control strategy of the defender drone, so as to realize the control of the attacker drone and the defender drone. An adaptive dynamic programming technique is used to construct a single-judgment network to estimate the optimal control strategy of the attacker drone and the optimal control strategy and optimal compensation control strategy of the defender drone for each execution.

2. The method for drone security compensation control based on adversarial game theory under DoS attack as described in claim 1, characterized in that, The establishment of a nonlinear dynamic model of the motion attitude of the attacker drone and the defender drone, and the definition of the communication network topology between the attacker drone and the defender drone, specifically includes: A1: Regarding the attacker... Model the motion attitude of the first UAV to obtain the first... A nonlinear dynamic model of the motion attitude of an attacker's drone; (1)； Among them, superscript The drone is referred to as the attacker. , , These represent the attacker's... A drone orbiting the body coordinate system axis, shaft and Moment of inertia in the axial direction, This indicates the attacker's drone's identification number. The drone's coordinate system has its origin at the drone's center of mass, and extends along the drone's longitudinal axis towards the nose. The axis, along the horizontal axis of the fuselage, points towards the right wing of the UAV. Axis, perpendicular to The plane is downward. axis; , , These represent the attacker's... The roll angle, pitch angle, and yaw angle of each drone; , , They represent , and The first derivative; , , They represent , and The second derivative; Indicates the third as the attacker The moment of inertia of the motor blades of a drone. Indicates the third as the attacker Additional perturbations from the drone; , , Indicates the third as the attacker A drone in the body coordinate system axis, shaft and Axial drag coefficient; , , These represent the attacker's... The control parameters of a drone's rotor over roll, pitch, and yaw angles; (The sentence is incomplete and requires more context to translate accurately.) Defined as , Indicates the number of drones acting as attackers; Define the attacker as the first The system state variables of a drone And let its state components , , , , , , Indicates transpose, then as the attacker's... The nonlinear dynamic model of the motion attitude of the UAV is further expressed as: (2)； in, express The first derivative, and , , ; ; ; A2: Regarding the first as the defender Model the motion attitude of the first UAV to obtain the first... A nonlinear dynamic model of the motion attitude of a defender drone; Consider a DoS attack launched by an attacker's drone against the defender's drone's control channel; define... It is a time variable and is defined For the first The instant a DoS attack occurs; definition For the first The time interval of each DoS attack and the time span is ,in, For the first The instant a DoS attack ends ;definition The time interval during which no DoS attack occurred and the time span is [missing information]. ; No. The nonlinear dynamic model of the motion attitude of the defender drone is as follows: (3)； Among them, superscript This refers to drones acting as defenders; , , They represent the first as the defender. A drone orbiting the body coordinate system axis, shaft and Moment of inertia in the axial direction, Indicates the number of the defender drone; , , They represent the first as the defender. The roll angle, pitch angle, and yaw angle of each drone; , , They represent , , The first derivative; , , They represent , , The second derivative; Indicating the first as the defender The moment of inertia of the motor blades of a drone. Indicating the first as the defender Additional perturbations from the drone; , , Indicating the first as the defender A drone in the body coordinate system axis, shaft and Axial drag coefficient; , , They represent the first as the defender. The control parameters of a drone's rotor over roll, pitch, and yaw angles; (The sentence is incomplete and requires more context to translate accurately.) Defined as , Indicates the number of drones acting as defenders; , , They represent the first as the defender. The compensating control parameters for roll angle, pitch angle and yaw angle of the rotor of a drone; , , They represent the first as the defender. The rotor compensation control gain of a UAV for roll angle, pitch angle and yaw angle; The coupling gain index; This represents a switching signal used to determine if a DoS attack is in progress; and satisfy , ; Define the first as the defender The system state variables of a drone And let its state components , , , , , Then, as the defender, the first The nonlinear dynamic model of the motion attitude of the UAV is further expressed as: (4)； in, express The first derivative, and , , ; ; ; ; ; A3: Define the communication network topology between the attacker's drone and the defender's drone; Specifically, the communication network topology between the attacker's drones is defined as an undirected graph. ,in, and They are the vertex set and the undirected edge set, respectively. Indicates the third as the attacker Each drone corresponds to a vertex, and each edge represents a communication link between the attacker drones corresponding to that vertex; Define... As vertex The neighborhood group, Indicates the number of the neighboring vertex. Representing neighboring vertices, Represents vertices and The edge between; It is an adjacency matrix. Representing the adjacency matrix The Line 1 Column elements, and satisfy and , Representing the adjacency matrix The Line 1 Column elements; definition For the entry degree array, For the entry degree array The elements on the main diagonal; corresponding to the adjacency matrix. The Laplace matrix is ; Define the communication network topology between defender drones as an undirected graph. ,in, and These are the vertex set and the undirected edge set, respectively. Indicates the third as the attacker Each drone corresponds to a vertex, and each edge represents a communication link between the attacker drones corresponding to that vertex; Define... As vertex The neighborhood group, Indicates the number of the neighboring vertex. Representing neighboring vertices, Represents vertices and The edge between; It is an adjacency matrix. Representing the adjacency matrix The Line 1 Column elements, and satisfy and , Representing the adjacency matrix The Line 1 Column elements; definition For the entry degree array, For the entry degree array The elements on the main diagonal; corresponding to the adjacency matrix. The Laplace matrix is ; Define the communication network topology between the attacker's drone and the defender's drone as an undirected graph. ,in, , and These are the vertex set, the undirected edge set, and the adjacency matrix, respectively. One attacker drone and The defender drones are located in two different sectors. and All drones exchange information between two different sectors; for those containing A sector of an attacker's drone In other words, if the first The attacker drone was able to capture the first Information about each defender drone, and the connectivity weights between them. ,on the contrary, For those containing A sector of a defender drone In other words, if the first The defender was able to capture the first Information about each attacker, and the connectivity weights between them. ,on the contrary, .

3. The method for drone security compensation control based on adversarial game theory under DoS attack as described in claim 1, characterized in that, Based on the nonlinear dynamic model of the motion attitude of the attacker's drone and the defender's drone and the communication network topology, the state error and cost function are constructed from the perspectives of the attacker's drone and the defender's drone, respectively, specifically including: B1: Constructing state errors from the attacker's drone's perspective; (5)； in, This indicates the state error of the attacker's drone's angle. The system state variable representing the attacker's drone corresponding to the neighboring vertex; Based on formulas (2) and (5), the state error of the attacker's drone angle The dynamic calculation is as follows: (6)； in, ; express The first derivative; B2: Constructing state errors from the perspective of the defender drone; (7)； in, This indicates the state error of the defender drone's angle. Based on formulas (4) and (7), the state error of the defender drone angle The dynamic calculation is as follows: (8)； in, ; express The first derivative; B3: Based on the state error of the attacker's drone angle State error of the angle of the defender drone Establish the cost function; The attitude response of the attacker's drone is characterized by the following cost function: (9)； in, The cost function represents the attacker's drone. This represents the initial value of the attacker's drone's state error. Defined as ; Represents a time variable; For the An attacker drone, for: (10)； in, , , , All are positive definite symmetric matrices; The attitude response of the defender drone is characterized by the following cost function: (11)； in, The cost function represents the cost of the defender drone. The initial value of the state error of the defender drone. Defined as ; Defined as , For the first Control inputs for a defender drone; For the One Defender drone, for: (12)； in, , , , , All are positive definite symmetric matrices.

4. The method for security compensation control of unmanned aerial vehicles under DoS attacks based on adversarial game theory as described in claim 1, characterized in that, The aforementioned method establishes an adversarial game mechanism with multiple participants based on the state errors and cost functions of the attacker's drone and the defender's drone, specifically including: Based on formula (9), the first... The adversarial game value of an attacker's drone for: (13)； Based on formula (11), the first is defined as follows: The adversarial game value of a defender drone for: (14)； Definition of the first The optimized control strategy for the attacker's drone is as follows: , No. The optimized control strategy and optimized compensation control strategy for each defender drone are as follows: and Based on formulas (9) and (11), if the following conditions are met: (15)； (16)； but , , The Nash equilibrium that constitutes the adversarial game, in which Defined as , Defined as , Defined as .

5. The method for drone security compensation control based on adversarial game theory under DoS attack as described in claim 1, characterized in that, The method for constructing coupled HJB equations based on the established adversarial game mechanism with multiple participants and utilizing the Bellman optimality principle to solve the optimal control strategies for the attacker's drone and the defender's drone specifically includes: Based on the dynamics of the state error of the attacker's drone angle (6), the first... The Hamiltonian function of the attacker's drone is: (17)； in, Indicates the first Hamiltonian functions of an attacker's drone. Indicates the gradient sign; Based on formula (17), the first The optimized control strategy for the attacker's drone is given as follows: (18)； Combining formulas (10), (17), and (18), we obtain the first... The coupled HJB equations for an attacker's drone are shown below: (19)； Based on formula (19) and by solving ,get The specific form is as follows: (20)； Based on the dynamics of the state error of the defender drone angle (8), the first... The Hamiltonian function for a defender drone is: (21)； in, Indicates the first Hamiltonian function for a defender drone; Based on equation (21), the first The optimized control strategy and optimized compensation control strategy for the defender drone are given as follows: (22)； (23)； when At that time, according to formulas (12), (21), (22), and (23), we obtain the first... The coupled HJB equations for a single defender drone are shown below: (24)； Based on formula (24) and by solving ,get The specific form is as follows: (25)； in, It is a positive definite symmetric matrix The inverse matrix; Based on formula (24) and by solving ,get The specific form is as follows: (26)； in, It is a positive definite symmetric matrix The inverse matrix; when hour, Further obtained At this point, simply optimizing the compensation control strategy is sufficient. It takes effect; according to formulas (12), (21), (22), and (23), we obtain the first... The coupled HJB equations for a single defender drone are as follows: (27)； Based on formula (27) and by solving ,get The specific form is shown in formula (26).

6. The method for drone security compensation control based on adversarial game theory under DoS attack as described in claim 1, characterized in that, The method employs adaptive dynamic programming to construct a single-evaluation network to estimate the optimal control strategy of the attacker's drone and the optimal control strategy and optimal compensation control strategy of the defender's drone for each execution. Specifically, this includes: The game values ​​are approximated by implementing a single-judge neural network. and ,get: (28)； (29)； in, , , For the first Weights, activation function, and approximation error of a single-judge neural network for an attacker's drone. The number of neural nodes; , , For the first Weights, activation function, and approximation error of a single-judge neural network for a defender drone; Based on formulas (28) and (29), and The gradient is expressed as follows: (30)； (31)； in, , , They are respectively , and The gradient; , , They are respectively , and The gradient; Substituting formula (30) into formula (20), we get: (32)； in, ,and It is norm-bounded, meaning there exists a positive constant. Make ; when Substituting formula (31) into formulas (25) and (26) respectively, we get: (33)； (34)； in, ,and satisfy , It is a positive constant; ,and It is norm-bounded, meaning there exists a positive constant. Make ; when At that time, only the compensation control strategy is optimized. It takes effect; at this time, one obtains The specific form is the same as that of formula (34); Based on formulas (30) and (31), and It is estimated as follows: (35)； (36)； in, , , , They are respectively , , and The estimate; Based on formulas (32) and (35), It is estimated as follows: (37)； in, for The estimate; Based on formula (37), the first The ultimate control law of the attacker's drone It is designed as follows: (38)； when At that time, based on formulas (33), (34) and (36), and It is estimated as follows: (39)； (40)； in, , for and The estimate; Based on formulas (39) and (40), the first The ultimate security control law for the defender drone and It is designed as follows: (41)； (42)； when At that time, only the compensation control law It takes effect; at this time, one obtains The specific form is the same as that of formula (42); Based on formulas (10), (17), and (35), the first The estimates of the Hamiltonian function of the attacker's drone are given below: (43)； in, Indicates the first Hamiltonian function of an attacker's drone The estimate; Defined as ; ,and ; Based on formulas (12), (21), and (36), the first The estimates of the Hamiltonian function for the defender drone are given below: (44)； in, ; ; ; ; Based on formulas (19) and (43), the first is defined as follows: The Bellman residual function of the attacker's drone is shown below: (45)； in, For the first Bellman residual function of an attacker drone; Based on formulas (24), (27), and (44), the first is defined as follows: The Bellman residual function of the Defender UAV is shown below: (46)； in, For the first Bellman residuals of a defender drone; Based on formula (45) and using gradient descent and standardization principles, the single evaluation network weight update law for the attacker's drone is designed as follows: (47)； in, Indicates the first Single-evaluation network weight update law for an attacker's drone; For update rate; It was used for standardization; Based on formula (46) and using gradient descent and standardization principles, the single evaluation network weight update law for the defender drone is designed as follows: (48)； in, Indicates the first Single-evaluation network weight update law for a single defender drone; and All are update rates; and It was used for standardization.

7. An electronic device, comprising: One or more processors, characterized in that, and a memory for storing instructions, which, when executed by the one or more processors, cause the one or more processors to perform the UAV security compensation control method based on adversarial game theory under DoS attack as described in any one of claims 1-6.

8. A computer-readable storage medium, characterized in that, It stores executable instructions that, when executed, cause the processor to perform the anti-DDoS attack-based drone security compensation control method according to any one of claims 1-6.

9. A computer program product, characterized in that, Includes a computer program or instructions that, when executed by a processor, implement the UAV security compensation control method based on adversarial game theory under DoS attacks as described in any one of claims 1-6.

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