Anti-dos attack unmanned aerial vehicle system formation control method and system

Abstract

The application provides an anti-DoS attack UAV system formation control method and system, relates to the technical field of UAV formation control, and comprises the following steps: constructing a dynamic model containing a leading UAV and multiple follower UAVs; constructing a communication topology model according to the communication links between the UAVs, and introducing the time-varying characteristics of DoS attacks based on the communication topology model to construct a dynamic Laplace matrix; fusing the dynamic model and the dynamic Laplace matrix to obtain a distributed state estimator, which is used to estimate the flight state of each UAV, calculate the estimated state deviation and formation tracking deviation of each UAV, and generate control instructions by using a preset distributed state controller based on the estimated state deviation and the formation tracking deviation, so that the real-time flight state of each UAV gradually converges to the expected formation state in the environment of DoS attacks, and the control target of controlling the UAV system to reach the expected formation is achieved.

Description

Technical Field

[0001] This application relates to the field of unmanned aerial vehicle (UAV) formation control technology, and in particular to a method and system for UAV formation control that is resistant to DoS attacks. Background Technology

[0002] With the increasing demand for electricity and the expansion of the power grid, the number of transmission lines consisting of poles, power lines, and other components is constantly increasing, necessitating the use of drones for safety inspections of these lines. The inspection process requires the coordinated operation of multiple drones. For example, one drone can act as a guide drone, while the others act as follower drones. The guide drone and the follower drones conduct inspections according to a preset path and formation, achieving a comprehensive check of the transmission lines and providing technical support for the transmission line inspection of smart grids.

[0003] The process of controlling and guiding a drone and multiple follower drones to conduct inspections according to a preset path and formation is also known as drone formation control. This control requires multiple drones to transmit their status information to each other through a communication link. However, communication links are vulnerable to denial-of-service (DoS) attacks and can be disrupted, causing multiple drones to be unable to share their flight status in a timely manner, thereby undermining formation consensus and causing the inspection mission to fail.

[0004] To overcome the interference of DoS attacks on communication links, existing Chinese patent CN119292057A proposes to construct a "virtual neighbor" using the latest neighbor information received before the attack. The state of the virtual neighbor provides a stable reference target for isolated UAVs, allowing for a passive communication topology switching mechanism. This enables UAVs to automatically switch to a virtual neighbor-dependent mode after a communication link is interrupted, thus maintaining formation control even under DoS attacks. However, this virtual neighbor mechanism based on outdated information is prone to error accumulation in prolonged DoS attacks or highly dynamic environments, leading to significant lag in state estimation and potentially causing formation loss of control. Furthermore, this formation control method idealizes the flight model of multiple UAVs as a linear model, neglecting nonlinear factors such as air resistance and attitude coupling, making it difficult to adapt to complex interference in actual flight.

[0005] Therefore, there is an urgent need to develop a formation control method with strong fault tolerance and anti-interference capabilities to address the challenges of communication link interruptions. Summary of the Invention

[0006] This application provides a method and system for controlling unmanned aerial vehicle (UAV) formations against DoS attacks, aiming to control UAV systems to achieve desired formation control objectives in scenarios where communication links are under DoS attacks. The technical solution is as follows:

[0007] Firstly, a method for swarm control of unmanned aerial vehicle (UAV) systems resistant to DoS attacks is provided, the method comprising:

[0008] Based on the three-degree-of-freedom rotational motion of the UAV, a dynamic model is constructed that includes the guiding UAV and multiple follower UAVs;

[0009] Based on the communication links between the guiding drone and each follower drone, as well as among the follower drones, a communication topology model is constructed;

[0010] Based on the aforementioned communication topology model, the time-varying characteristics of DoS attacks are introduced to construct a dynamic Laplace matrix; wherein, the elements in the dynamic Laplace matrix are dynamically switched according to whether the corresponding communication link is subjected to a DoS attack, including: during the period of a DoS attack, the element corresponding to the communication link represents that the communication link is interrupted; during the period when the DoS attack disappears, the element corresponding to the communication link represents that the communication link is connected.

[0011] By integrating the dynamic model and the dynamic Laplace matrix, a distributed state estimator is designed. The distributed state estimator is used to estimate the flight state of each UAV and calculate the estimated state deviation and formation tracking deviation of each UAV based on the estimated flight state and the expected formation state.

[0012] Based on the estimated state deviation and the formation tracking deviation, a preset distributed state controller is used to generate control commands to drive each UAV to gradually converge its real-time flight state to the desired formation state in a DoS attack environment.

[0013] Secondly, a DoS-resistant drone system formation control system is provided, which includes:

[0014] The first building module is used to construct a dynamic model that includes a guiding drone and multiple follower drones based on the three-degree-of-freedom rotational motion of the drone.

[0015] The second construction module is used to construct a communication topology model based on the communication links between the guiding drone and each following drone, as well as between each following drone;

[0016] The third construction module is used to introduce the time-varying characteristics of DoS attacks based on the communication topology model to construct a dynamic Laplace matrix; wherein, the elements in the dynamic Laplace matrix are dynamically switched according to whether the corresponding communication link is subjected to a DoS attack, including: during the period of a DoS attack, the element corresponding to the communication link represents that the communication link is interrupted; during the period when the DoS attack disappears, the element corresponding to the communication link represents that the communication link is connected.

[0017] The fourth construction module is used to integrate the dynamic model and the dynamic Laplace matrix to design a distributed state estimator. The distributed state estimator is used to estimate the flight state of each UAV and calculate the estimated state deviation and formation tracking deviation of each UAV based on the estimated flight state and the expected formation state.

[0018] The data generation module is used to generate control commands based on the estimated state deviation and the formation tracking deviation using a preset distributed state controller, so as to drive each UAV to gradually converge its real-time flight state to the desired formation state in the DoS attack environment.

[0019] By employing the above technical solutions, this disclosure provides a method and system for anti-DoS attack unmanned aerial vehicle (UAV) formation control. First, a dynamic model is established, including a guide UAV and a follower UAV. This model characterizes the dynamic characteristics of each UAV during its pitch, roll, and yaw three-degree-of-freedom rotational motion, influenced by nonlinear factors such as air resistance, attitude coupling, and actuator saturation. Second, a communication topology model is generated based on the communication relationships between the UAVs. Incorporating the time-varying characteristics of DoS attacks, a dynamic Laplace matrix is ​​constructed. The elements in this matrix dynamically switch according to whether the corresponding communication link is under a DoS attack, thus realistically reflecting the random on / off state of the communication link. Then, by integrating the nonlinear dynamic model and the dynamic Laplace matrix, a distributed state estimator is designed to estimate the flight state of each UAV. Simultaneously, a node and edge event triggering mechanism is introduced. When the triggering conditions are met, the flight state information of each UAV is updated and transmitted, achieving asynchronous, low-communication-frequency collaborative estimation. Finally, utilizing a pre-established distributed state controller, based on the estimated state deviation and formation tracking deviation output by the distributed state estimator, and combined with adaptive coupling weights and compensation signals directly coupled to real-time weight values, dynamic control commands are generated to drive each UAV to gradually converge its real-time flight state to the desired formation state in a DoS attack environment. Furthermore, Lyapunov stability theory is rigorously used to analyze the sufficient conditions for asymptotic convergence of formation errors under quantifiable DoS attack intensity, thereby helping the distributed state controller achieve the control objective of achieving the desired formation for the UAV system in the harsh environment of a DoS attack.

[0020] Therefore, this application not only constructs a cooperative control architecture based on a realistic nonlinear dynamic model and a dynamic communication topology model, but also possesses an inherent distributed fault-tolerant mechanism: when a communication link is interrupted due to a DoS attack, UAVs relying on that communication link suspend the transmission of flight status information and switch to the attack zone, at which point cooperation is achieved through an effective communication link; once the DoS attack disappears and the communication link is restored, the cooperative function is automatically rebuilt. Thus, the control mechanism of this application does not rely on global information, thereby effectively ensuring the strong robustness and high reliability of UAV system formation control in harsh communication environments. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the description of the embodiments of this application will be briefly introduced below. In the drawings:

[0022] Figure 1 This is a flowchart of a method for controlling the formation of unmanned aerial vehicles (UAVs) to resist DoS attacks, according to an embodiment of this application.

[0023] Figure 2 This is an example diagram illustrating the generation and flow of parameters involved in the method embodiments of this application;

[0024] Figure 3 This is a specific application scenario example diagram in the embodiments of the method of this application;

[0025] Figure 4 yes Figure 3 Example diagrams of flight trajectories of various drones in application scenarios;

[0026] Figure 5 yes Figure 3 Example diagram of the response curve of adaptive coupling weights involved in the distributed state controller in the application scenario;

[0027] Figure 6 (a)-6(d) are respectively Figure 3 An example diagram showing four different initial formation tracking deviations set in the application scenario, with the tracking deviations of the four following drones driven by the controller converging to zero over time;

[0028] Figure 7 (a)-7(c) are respectively Figure 3 Example diagram of real-time weight values ​​of edges (1,0), (1,4), (4,1), (3,2), and (2,3) during the period of DoS attack in the application scenario.

[0029] Figure 8 (a) is Figure 3Example diagram of the node event triggering mechanism in application scenarios, showing the triggering time within 0s-10s and the time interval between adjacent triggering times;

[0030] Figure 8 (b)-8(j) are respectively Figure 3 Example diagram of the triggering time and the time interval between adjacent triggering times in the application scenario of the edge event triggering mechanism within 0s-10s;

[0031] Figure 9 This is a block diagram of a drone system formation control system resistant to DoS attacks according to an embodiment of this application;

[0032] Figure 10 This is a structural diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0033] Exemplary embodiments of the present application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present application are shown in the drawings, it should be understood that the present application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this application will be thorough and complete, and will fully convey the scope of the present application to those skilled in the art.

[0034] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such use can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the term "comprising" and its variations should be interpreted as open-ended terms meaning "including but not limited to."

[0035] Typically, a drone system consists of one guide drone and multiple follower drones, which need to collaboratively complete automated inspection tasks in complex communication environments. Specifically, to ensure that each drone in the system can still perform automated power line inspection tasks according to the desired formation configuration even under communication interference from denial-of-service (DoS) attacks, this application provides a DoS-resistant drone system formation control method, such as... Figure 1 As shown, the method mainly includes steps S101 to S105.

[0036] Step S101: Based on the three-degree-of-freedom rotational motion of the UAV, construct a dynamic model that includes the guiding UAV and multiple follower UAVs.

[0037] The dynamics model includes a sub-dynamics model for guiding the UAV and a sub-dynamics model for following the UAV, wherein:

[0038] The sub-dynamic model for guiding the drone is as follows:

[0039] ;

[0040] The sub-dynamics model for following the drone is as follows:

[0041] .

[0042] in, They represent the first The flight status of the drone following and the drone guiding. Represents an m-dimensional real vector. They represent the first Flight observations of drones following and guiding drones. They represent the first Follower drones and guide drones The rate of change of the flight state at any given moment; They represent the first Input variables for following and guiding drones. express 3D real vector; They represent the first Nonlinear factors exist in both follow-up and guide drones. Satisfying the Lipschitz continuity condition, i.e. , Lipschitz coefficient; , , These represent the system matrix, input variable matrix, and observation matrix of the UAV system, respectively.

[0043] Three-degree-of-freedom rotational motion specifically includes pitch, roll, and yaw motions. In actual flight, these motions are affected by nonlinear factors such as changes in air resistance, attitude coupling, and motor saturation. Therefore, in the sub-dynamic models of the guiding and following UAVs constructed in this embodiment, these nonlinear factors are explicitly introduced, i.e., they are incorporated into... This is used to characterize the impact of these nonlinear factors on the two sub-dynamic models. The resulting dynamic model, which includes nonlinear terms, constitutes the nonlinear dynamic model of the UAV system. Compared to the simplified approach in existing formation control methods that often idealize the UAV dynamic model as a linear model, the nonlinear dynamic model established in this embodiment can more realistically and comprehensively reflect the complex disturbances encountered by the UAV in the actual flight environment.

[0044] Step S102: Construct a communication topology model based on the communication links between the guiding drone and each following drone, as well as among the following drones.

[0045] First, an undirected connected graph is used to represent the communication links between the following drones. The undirected connected graph is as follows: Among them, node set Indicates existence A follower drone, Indicates by The local communication topology consists of communication links between the drones following the drone. Indicates the first Follow-up drone and the first The weight value of the communication link between the drone and the aircraft, when hour, ,otherwise, .

[0046] Secondly, the drone will be guided in an undirected connected graph, that is, an undirected connected graph containing a spanning tree, thus obtaining a tree-like communication topology model.

[0047] Based on the obtained tree-like communication topology model, when guiding the UAV with the first When the communication link between the drones is established, the drone is guided to communicate with the first drone. Weight of the communication link between the drones following the drone Conversely, when the two are not connected, the weight value of the communication link between them... .

[0048] Step S103: Based on the communication topology model, the time-varying characteristics of DoS attacks are introduced to construct a dynamic Laplace matrix.

[0049] In a local communication topology excluding the guiding drone, the Laplace matrix is: ;in, , , .

[0050] By incorporating the guiding drone into the local communication topology, i.e., generating a tree-like communication topology model, the corresponding Laplace matrix is: ;in, It is a degree matrix and , , ..., Indicates guiding the drones respectively with The weight value of the communication link between the drone and the drone.

[0051] In actual flight, drones are subject to periodic DoS attacks. During a DoS attack, communication links between drones are interrupted, and when the DoS attack disappears, the communication links between drones are reconnected. Therefore, DoS attacks have time-varying characteristics.

[0052] Based on the time-varying characteristics of DoS attacks, the DoS attack and the set of time periods during which the DoS attack disappears are defined as follows: , Then, the real-time weight value of each communication link in the communication topology model is: .

[0053] Based on the real-time weight value of each communication link Substitute into the degree matrix above and Laplace matrix In this process, the real-time degree function is obtained. and real-time Laplace matrix Then, based on the real-time degree function... and real-time Laplace matrix The dynamic Laplace matrix is ​​obtained as follows: .

[0054] This embodiment introduces a dynamic Laplacian matrix. The core objective is to accurately characterize the changes in flight status information transmitted by each UAV in an unmanned aerial vehicle (UAV) system during DoS attacks and the periods when DoS attacks cease, through a mechanism where the values ​​of its internal elements dynamically change according to the connection and disconnection of the communication link. For example, if the communication link is interrupted, UAVs at both ends of the interrupted link will be unable to transmit their flight status to each other. When the communication link is restored, the UAVs at both ends can continue to transmit their flight status to each other. Compared to the fixed communication topology model relied upon by existing formation control methods, this dynamic approach more realistically reflects the unreliable characteristics of random connection and disconnection of communication links during actual flight, thus laying an accurate model foundation for the subsequent design of a distributed state controller with strong robustness and attack tolerance.

[0055] Step S104: Integrate the dynamic model and the dynamic Laplace matrix to design a distributed state estimator. The distributed state estimator is used to estimate the flight state of each UAV and calculate the estimated state deviation and formation tracking deviation of each UAV based on the estimated flight state and the expected formation state.

[0056] In actual flight, due to sensor limitations, communication constraints, and external interference, it is impossible for each UAV to obtain each other's flight status in real time and accurately. Therefore, this embodiment designs a distributed state estimator by fusing a dynamic model and a dynamic Laplace matrix, specifically as follows:

[0057] ;

[0058] in, For the feedback gain matrix, express 3D real vector; They represent The estimated value.

[0059] Due to the The flight states of the follower drone and the guide drone are respectively The estimated values ​​obtained by using a distributed state estimator are as follows: If we define the expected formation state of the two as Then we get:

[0060] The actual deviation is: ;

[0061] The estimated state deviation is: ;

[0062] Formation tracking deviation is: .

[0063] Furthermore, in order to control the timing of flight state information updates and transmissions in the distributed state estimator, achieve asynchronous communication between UAVs, and reduce communication frequency, this embodiment sets up a node event triggering mechanism for the guiding UAV, and sets up edge event triggering mechanisms for each communication link between the guiding UAV and each following UAV, and between each following UAV, such as... Figure 2 As shown, the specific triggering mechanism is as follows.

[0064] 1) The node event triggering mechanism related to guiding the drone is as follows:

[0065] ;

[0066] in, Indicates guiding the drone Next trigger moment This represents the maximum lower bound of the set. Indicates the node event triggering function and , This indicates the deviation in the predicted state of the guiding drone. express The flight status prediction value of the drone is constantly guided. This indicates taking the norm of a vector or matrix. Indicates the trigger parameter; This represents the threshold for the node event triggering mechanism.

[0067] 2) The side event triggering mechanism related to guiding and following drones is as follows:

[0068] ;

[0069] in, Indicates guiding drones and the first The first communication link between the drones Next trigger moment This represents the maximum lower bound of the set. Indicates the edge event triggering function and , Indicates guiding drones and the first Predicted state deviation between the following drones express Predictive guidance of drones and the first The relative state between the drones following the aircraft Represents the feedback gain matrix. Indicates the predicted tracking deviation. This indicates taking the norm of a vector or matrix. Indicates the trigger parameter, Indicates adaptive coupling weights; This indicates the threshold for the event triggering mechanism of this edge.

[0070] 3) The side event triggering mechanism related to multiple follower drones is as follows:

[0071] ;

[0072] in, Indicates the first Follow-up drone and the first The first communication link between the drones Next trigger moment This represents the maximum lower bound of the set. Indicates the edge event triggering function and , Indicates the first Follow-up drone and the first Predicted state deviation between the following drones express Time of the first Follow-up drone and the first The relative state between the drones following the aircraft Represents the feedback gain matrix. Indicates the predicted tracking deviation. This indicates taking the norm of a vector or matrix. Indicates the trigger parameter, Indicates adaptive coupling weights; This indicates the threshold for the event triggering mechanism of this edge.

[0073] For any of the above triggering mechanisms, when the triggering function exceeds the corresponding threshold, i.e., when the triggering condition of the event triggering mechanism is met, the distributed state estimator is triggered to update the flight state of the corresponding UAV and set the predicted state deviation to 0. Simply put, the event triggering mechanism compares the deviation between the estimated value calculated in real time by the distributed state estimator and the predicted value maintained locally on each communication link. This deviation is the aforementioned predicted state deviation, and its magnitude determines whether the flight state transmission is triggered. When the deviation exceeds the set threshold, the latest estimated value is used to update the corresponding predicted value and sent to neighboring UAVs, thereby achieving asynchronous, low-communication-frequency cooperative control.

[0074] It should be noted that the above event triggering mechanisms are set separately. The threshold parameter directly controls the sensitivity of different event triggering mechanisms. The larger the threshold is set, the lower the corresponding event triggering frequency. This enables asynchronous information transmission between drones and avoids continuous communication between drones, thus saving communication resources.

[0075] Step S105: Based on the estimated state deviation and formation tracking deviation, control commands are generated using a preset distributed state controller to drive each UAV to gradually converge its real-time flight state to the desired formation state in the DoS attack environment.

[0076] To address DoS attacks, this embodiment pre-configures a distributed state controller, specifically as follows:

[0077] ;

[0078] in, Indicates input variables, All represent adaptive coupling weights, which are influenced by the dynamic Laplacian matrix. It will change dynamically with the appearance and disappearance of DoS attacks, so use derivative To update in real time itself, Similarly, using derivative To update in real time itself, This means that when the corresponding communication link is interrupted due to a DoS attack ( or ), and corresponding adaptive coupling weights Stop updating or maintain the current value, thus naturally de-depending on the failed communication link; when the communication link is restored ( or According to the corresponding adaptive coupling weights) Get input variables . This indicates a compensation signal used to extend the desired formation state. The degree of freedom in realizing this allows unmanned aerial vehicle (UAV) systems to form more complex formation configurations.

[0079] The above text appears , , Both represent the feedback gain matrix, and , , , It can be solved using the linear Riccati equation:

[0080] ;

[0081] ;

[0082] in, This represents an identity matrix with dimension p×p.

[0083] During actual flight, the distributed controller receives the estimated state deviation and formation tracking deviation output by the distributed state estimator, and dynamically generates control input variables based on the real-time magnitude of these two types of deviations. This control input is further coordinated via adaptive coupling weights that are directly coupled to the dynamic communication topology model, thereby driving the real-time flight state of each UAV in the UAV system to asymptotically converge to the desired formation state.

[0084] Therefore, the distributed state controller designed in this embodiment is not a fixed controller, but an adaptive controller that can dynamically adjust the control strategy as DoS attacks occur and disappear. Its core working principle is: adaptively coupling weights. Update and real-time weight values ​​of the communication link , Direct coupling. This enables the distributed state controller to sense the status of communication links (connection / disconnection) online and adjust its coordination strategy accordingly. For example, it can make full use of all available communication links for strong coordination when the DoS attack has subsided, and automatically block failed communication links during the DoS attack, relying only on the remaining effective communication links or its own estimation to maintain control. This achieves a distributed control with inherent resilience that matches the dynamic communication environment.

[0085] In order to prove that the control method of this application can ensure that the real-time flight status of each UAV asymptotically converges to the desired formation state under periodic DoS attacks, a rigorous theoretical analysis of the stability of the control method of this application is required. The specific analysis process is as follows.

[0086] 1) Establish a mathematical model for DoS attacks.

[0087] Assuming in A DoS attack exists within the time interval; consider a parameter. Therefore, the mathematical model for a DoS attack is as follows:

[0088] ;

[0089] in, Indicates in The time interval during which a DoS attack occurs within the specified time range. This indicates that the attack time is less than the entire time interval. Indicates in Within the time interval, edge The set of time intervals during which a DoS attack occurs. This indicates the time when the m-th DoS attack occurred. This indicates the duration of the m-th DoS attack. Indicates in The safe interval within the time frame, i.e. the period during which the DoS attack disappears.

[0090] 2) Construct Lyapunov functions.

[0091] The Lyapunov function is:

[0092] ;

[0093] in, , Represents the dynamic Laplace matrix The non-zero eigenvalues ​​are calculated using the above formula to obtain the result. .

[0094] Taking the derivative of the Lyapunov function, we get:

[0095] .

[0096] During the period when the DoS attack disappears (the safe zone), since the UAV system is not affected by the DoS attack, the follower UAV can receive the flight status information of the guide UAV. That is, the communication topology model at this time is a tree-like communication topology model, and the dynamic Laplace matrix... It is a positive definite matrix, that is During the DoS attack period (attack interval), it is assumed that all drones in the drone system are attacked, meaning that all communication links in the communication topology are interrupted at the same time. Therefore, within the attack range, This indicates that the worst-case scenario of an attack is the complete disruption of all communication links.

[0097] 3) Interval-based argumentation.

[0098] Within the safe zone Inside, ;

[0099] In the attack range Inside, .

[0100] Scaling the Lyapunov function using Young's inequality, based on the Lyapunov function within a safe interval. and attack range Different values ​​can be used to define the safe interval. and attack range positive definite function Integrating over time yields the result for a complete DoS attack cycle. :

[0101] ;

[0102] because The above The calculation formula can be simplified as follows:

[0103] .

[0104] As can be seen from the above formula, with the extension of time ( ), due to the exponential decay term and The impact, Combined with the calculation results of the Lyapunov function itself ,therefore, This also proves that the control method of this application can control the target under periodic DoS attacks. It is achievable, meaning that the drone system can be controlled to achieve the desired formation control objective.

[0105] In other words, even when periodic DoS attacks cause random interruptions to communication links, over time, the flight status of each drone in the unmanned aerial vehicle system can still gradually approach the desired formation state, thereby achieving and maintaining the desired formation configuration after a limited time.

[0106] To illustrate the effectiveness of the anti-DoS attack drone system formation control method of this application, the following example uses the control of a drone system consisting of one guide drone and four follower drones.

[0107] like Figure 3 As shown, the guiding drone is represented by UAV#0, and the four following drones are represented by UAV#1, UAV#2, UAV#3, and UAV#4 respectively. Assume the system matrix of the drone system is... Input variable matrix Observation matrix They are respectively:

[0108] , , ;

[0109] At the same time, guide the drone's initial flight state. To guide the initial flight state estimation of the drone ;No. The initial flight state of the follow-up drone , , No. Initial flight state estimate of the follower drone .

[0110] Timing and targets of DoS attacks:

[0111] Let edge (0,1) represent the communication link between the guiding drone and the first following drone. Similarly, let edges (1,3) and (3,1) represent the communication link between the first and third following drones, and edges (2,3) and (3,2) represent the communication link between the second and third following drones. If a DoS attack occurs on edge (0,1) during the time period... The DoS attack occurred on edges (1,3) and (3,1) during the time period. The DoS attack occurred on edges (2,3) and (3,2) during the time period. The remaining edges were not affected by the DoS attack.

[0112] The control parameters are set as follows:

[0113] Input variables , Nonlinear factors , Expected formation state Compensation signal Initial values ​​of adaptive coupling weights Trigger parameters , , , , , , , , , .

[0114] Based on the control parameters set above, the flight trajectories of each UAV can be obtained as follows: Figure 4 As shown, the response curve of the adaptive coupling weight is as follows. Figure 5 As shown, Figure 5 The shaded area in the diagram represents the attack range, denoted by DoS. The formation tracking deviation of the drone system is shown below. Figure 6 As shown, Figure 6 The shaded area in the image also represents the attack area, also denoted by DoS. Figure 7 This shows the values ​​of the elements corresponding to the time period of the DoS attack and the communication link. The time period of the DoS attack is shown in the shaded area. Figure 7 In Chinese, it is also represented by DoS. Figure 8 This displays the moment the event triggering mechanism is activated and the time interval between adjacent activation moments, with the vertical axis showing... The y-axis represents the node event triggering mechanism, with one side having y-axis characteristics. The representation of the edge event triggering mechanism, here Representing an edge ( ).

[0115] from Figure 4 It is clear that at t=15s, the drones have formed the preset formation according to the desired formation state. From Figure 6 The formation tracking deviation shown in the demonstration indicates that, over time, the UAV system's formation tracking deviation eventually reaches zero, demonstrating that under the control of the distributed state controller, the UAV system ultimately achieves the desired formation control objective. From... Figure 8 It is evident that the frequency of flight status updates is significantly reduced after using the event-triggered mechanism. Meanwhile, Figure 8This also indicates that the communication between the drones is asynchronous, which reduces communication resources and network bandwidth.

[0116] It should be noted that the sequence numbers of the steps in the above embodiments do not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application. In practical applications, all the above possible implementation methods can be arbitrarily combined in a combined manner to form possible embodiments of this application, which will not be described in detail here.

[0117] Based on the above embodiments, which provide a method for anti-DoS attack unmanned aerial vehicle (UAV) system formation control, this application also provides an anti-DoS attack unmanned aerial vehicle (UAV) system formation control system based on the same inventive concept.

[0118] Figure 9 This is a block diagram of a drone system formation control system for resisting DoS attacks, provided in an embodiment of this application. Figure 9 As shown, the system may specifically include a first building module, a second building module, a third building module, a fourth building module, and a data generation module. The specific descriptions of each module are as follows.

[0119] The first building module is used to construct a dynamic model that includes a guide drone and multiple follower drones based on the three-degree-of-freedom rotational motion of the drone.

[0120] The second building module is used to construct a communication topology model based on the communication links between the guiding drone and each follower drone, as well as among the follower drones.

[0121] The third building module is used to construct a dynamic Laplace matrix by introducing the time-varying characteristics of DoS attacks based on the communication topology model. The elements in the dynamic Laplace matrix are dynamically switched according to whether the corresponding communication link is subjected to a DoS attack, including: during the period of a DoS attack, the element corresponding to the communication link represents that the communication link is interrupted; during the period when the DoS attack disappears, the element corresponding to the communication link represents that the communication link is connected.

[0122] The fourth building module is used to integrate the dynamic model and the dynamic Laplace matrix to design a distributed state estimator. The distributed state estimator is used to estimate the flight state of each UAV and calculate the estimated state deviation and formation tracking deviation of each UAV based on the estimated flight state and the expected formation state.

[0123] The data generation module is used to generate control commands based on the estimated state deviation and formation tracking deviation using a preset distributed state controller, so as to drive each UAV to gradually converge to the desired formation state in real time under the DoS attack environment.

[0124] In one possible implementation, the fourth building module described above is also used to set up a node event triggering mechanism for the guiding drone, and to set up a side event triggering mechanism for each communication link between the guiding drone and each following drone, and between each following drone; and when the triggering conditions of the node event triggering mechanism or the side event triggering mechanism are met, to control the distributed state estimator to update the estimated values ​​of the flight state of each drone.

[0125] This embodiment provides a UAV system formation control system resistant to DoS attacks, which is used to execute the UAV system formation control method resistant to DoS attacks provided in the above embodiment. Its implementation method and principle are the same. For details of the implementation method of each module, please refer to the relevant description of the above method embodiment, which will not be repeated here.

[0126] Based on the same inventive concept, this application also provides an electronic device, including a processor and a memory, wherein the memory stores a computer program, and the processor is configured to run the computer program to execute a method for anti-DoS attack unmanned aerial vehicle system formation control according to any of the above embodiments.

[0127] In an exemplary embodiment, an electronic device is provided, such as Figure 10 As shown, Figure 10 The illustrated electronic device 1000 includes a processor 1001 and a memory 1003. The processor 1001 and the memory 1003 are connected, for example, via a bus 1002. Optionally, the electronic device 1000 may also include a transceiver 1004. It should be noted that in practical applications, the transceiver 1004 is not limited to one type, and the structure of this electronic device 1000 does not constitute a limitation on the embodiments of this application.

[0128] Processor 1001 may be a CPU (Central Processing Unit), DSP (Digital Signal Processor), ASIC (Application Specific Integrated Circuit), FPGA (Field Programmable Gate Array), or other programmable logic device, transistor logic device, hardware component, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this application. Processor 1001 may also be a combination that implements computational functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0129] Bus 1002 may include a pathway for transmitting information between the aforementioned components. Bus 1002 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Bus 1002 can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 10 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0130] The memory 1003 may be a ROM (Read Only Memory) or other type of static storage device capable of storing static information and instructions, RAM (Random Access Memory) or other type of dynamic storage device capable of storing information and instructions, or an EEPROM (Electrically Erasable Programmable Read Only Memory), CD-ROM (Compact Disc Read Only Memory) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited thereto.

[0131] The memory 1003 stores computer program code that executes the scheme of this application, and its execution is controlled by the processor 1001. The processor 1001 executes the computer program code stored in the memory 1003 to implement the content shown in the foregoing method embodiments.

[0132] Among them, electronic devices include, but are not limited to: mobile terminals such as mobile phones, laptops, digital radio receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), and in-vehicle terminals (such as in-vehicle navigation terminals), as well as fixed terminals such as digital TVs and desktop computers. Figure 10 The electronic device shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments of this application.

[0133] Based on the same inventive concept, this application also provides a storage medium storing a computer program, wherein the computer program is configured to execute, at runtime, a method for anti-DoS attack unmanned aerial vehicle system formation control according to any of the above embodiments.

[0134] Those skilled in the art will clearly understand that the specific working process of the systems, devices, and modules described above can be referred to the corresponding process in the foregoing method embodiments. For the sake of brevity, it will not be repeated here.

[0135] Those skilled in the art will understand that the technical solution of this application, or all or part of it, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several program instructions to cause an electronic device (e.g., a personal computer, server, or network device) to execute all or part of the steps of the methods described in the embodiments of this application when running the program instructions. The aforementioned storage medium includes various media capable of storing program code, such as a USB flash drive, portable hard drive, read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk.

[0136] Alternatively, all or part of the steps of the foregoing method embodiments can be implemented by hardware (such as electronic devices like personal computers, servers, or network devices) associated with program instructions. The program instructions can be stored in a computer-readable storage medium. When the program instructions are executed by the processor of the electronic device, the electronic device executes all or part of the steps of the methods described in the embodiments of this application.

[0137] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that within the spirit and principles of this application, modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein; and these modifications or substitutions do not cause the corresponding technical solutions to leave the protection scope of this application.

Claims

1. A method for formation control of unmanned aerial vehicle (UAV) systems resistant to DoS attacks, characterized in that, include: Based on the three-degree-of-freedom rotational motion of the UAV, a dynamic model is constructed that includes the guiding UAV and multiple follower UAVs; Based on the communication links between the guiding drone and each follower drone, as well as among the follower drones, a communication topology model is constructed; Based on the aforementioned communication topology model, the time-varying characteristics of DoS attacks are introduced to construct a dynamic Laplace matrix; wherein, the elements in the dynamic Laplace matrix are dynamically switched according to whether the corresponding communication link is subjected to a DoS attack, including: during the period of a DoS attack, the element corresponding to the communication link represents that the communication link is interrupted; during the period when the DoS attack disappears, the element corresponding to the communication link represents that the communication link is connected. By integrating the dynamic model and the dynamic Laplace matrix, a distributed state estimator is designed. The distributed state estimator is used to estimate the flight state of each UAV and calculate the estimated state deviation and formation tracking deviation of each UAV based on the estimated flight state and the expected formation state. Based on the estimated state deviation and the formation tracking deviation, a preset distributed state controller is used to generate control commands to drive each UAV to gradually converge its real-time flight state to the desired formation state in the DoS attack environment. The dynamics model includes a sub-dynamics model of the guiding drone and a sub-dynamics model of the following drone; The sub-dynamic model for guiding the UAV is as follows: ； The sub-dynamic model of the following drone is: ； in, They represent the first The flight status of the drone following and the drone guiding. express 3D real vector They represent the first Flight observations of drones following and guiding drones. They represent the first Follower drones and guide drones The rate of change of the flight state at any given moment; They represent the first Input variables for following and guiding drones. express 3D real vector; They represent the first Nonlinear factors exist in both follow-up and guide drones. , , These represent the system matrix, input variable matrix, and observation matrix of the UAV system, respectively. The distributed state estimator is: ； in, This is the feedback gain matrix of the distributed state estimator. express 3D real vector; They represent The estimated value; A node event triggering mechanism is set for the guiding drone, and an edge event triggering mechanism is set for each communication link between the guiding drone and each following drone, and between each following drone; When the triggering conditions of the node event triggering mechanism or the edge event triggering mechanism are met, the distributed state estimator is controlled to update the estimated values ​​of the flight state of each UAV. A node event triggering mechanism is set for the guiding drone, and an edge event triggering mechanism is set for each communication link between the guiding drone and each following drone, and between each following drone; When the triggering conditions of the node event triggering mechanism or the edge event triggering mechanism are met, the distributed state estimator is controlled to update the estimated values ​​of the flight state of each UAV. The node event triggering mechanism is as follows: ； in, Indicates guiding the drone Next trigger time This represents the maximum lower bound of the set. Indicates the node event triggering function and , This indicates the deviation in the predicted state of the guiding drone. express The flight status prediction value of the drone is constantly guided. This indicates taking the norm of a vector or matrix. All represent trigger parameters; Indicates the threshold for the node event triggering mechanism; and / or, ； in, Indicates guiding drones and the first The first communication link between the drones Next trigger time This represents the maximum lower bound of the set. Indicates the edge event triggering function and , Indicates guiding drones and the first Predicted state deviation between the following drones express Predictive guidance of drones and the first The relative state between the drones following the aircraft This represents the feedback gain matrix of the edge event triggering function. Indicates the predicted tracking deviation. This indicates taking the norm of a vector or matrix. Indicates the trigger parameter, Indicates adaptive coupling weights; This indicates the threshold for the event triggering mechanism of this edge; and / or, ； in, Indicates the first Follow-up drone and the first The first communication link between the drones Next trigger time This represents the maximum lower bound of the set. Indicates the edge event triggering function and , Indicates the first Follow-up drone and the first Predicted state deviation between the following drones express Time of the first Follow-up drone and the first The relative state between the drones following the aircraft This represents the feedback gain matrix of the edge event triggering function. Indicates the predicted tracking deviation. This indicates taking the norm of a vector or matrix. Indicates the trigger parameter, Indicates adaptive coupling weights; This represents the threshold for the event triggering mechanism of this edge; The distributed state controller is: ； in, Indicates input variables, Both represent adaptive coupling weights. The derivative is expressed as ,and , express Time of the first Follow-up drone and the first The real-time weight value of the communication link between the drone and the aircraft. Indicates the predicted tracking deviation. , All indicate Time of the first Follow-up drone and the first The relative state between the drones following the aircraft , They represent the first Follow-up drone and the first The predicted flight status of the drone following the aircraft. This is the feedback gain matrix of the adaptive coupling weights, with the superscript T indicating transpose; adaptive coupling weights The derivative is expressed as ,and , express Time of the first The real-time weight value of the communication link between the follower drone and the guide drone. Indicates the predicted tracking deviation. express Constantly guide drones and the first The relative state between the drones following the aircraft express The flight status estimate of the drone is constantly guided; This indicates a compensation signal.

2. The anti-DoS attack unmanned aerial vehicle (UAV) system formation control method according to claim 1, characterized in that, Based on the communication links between the guiding drone and each follower drone, and among the follower drones themselves, a communication topology model is constructed, including: An undirected connected graph is used to represent the communication links between the following UAVs. The undirected connected graph is as follows: ； Among them, node set Indicates existence A follower drone, Indicates by The local communication topology consists of communication links between the drones following the drone. Indicates the first Follow-up drone and the first The weight value of the communication link between the drone and the drone; By adding the guiding drone to the undirected connected graph, a tree-like communication topology model is obtained; Among them, when the guiding drone is with the first When the communication link between the guiding drone and the following drone is established, the guiding drone and the first Weight of the communication link between the drones following the drone .

3. The anti-DoS attack unmanned aerial vehicle (UAV) system formation control method according to claim 2, characterized in that, Based on the aforementioned communication topology model, the time-varying characteristics of DoS attacks are introduced to construct a dynamic Laplace matrix, including: Define the sets of time periods during which a DoS attack occurs and the time periods during which the DoS attack disappears as follows: , ; The real-time weight value of each communication link in the communication topology model is: ; Based on the real-time weight value of each communication link Construct the degree matrix ; Based on the real-time weight value of each communication link in the local communication topology Obtain the initial Laplace matrix , ; According to the degree matrix and the initial Laplace matrix Construct the dynamic Laplace matrix .

4. The anti-DoS attack unmanned aerial vehicle (UAV) system formation control method according to any one of claims 1 to 3, characterized in that, The method further includes: A mathematical model of DoS attack is established, and the DoS attack and the period when the DoS attack disappears are respectively defined as the attack interval and the safe interval through the mathematical model. Construct Lyapunov functions; Based on the different characteristics of the dynamic Laplace matrix in the attack and safe intervals, the changing trend of the Lyapunov function is analyzed, and the changing trend of the Lyapunov function is used to prove that the real-time flight state of each UAV can converge to the desired formation state.

5. A DoS-resistant unmanned aerial vehicle (UAV) formation control system, characterized in that, include: The first building module is used to construct a dynamic model that includes a guiding drone and multiple follower drones based on the three-degree-of-freedom rotational motion of the drone. The second construction module is used to construct a communication topology model based on the communication links between the guiding drone and each following drone, as well as between each following drone; The third construction module is used to introduce the time-varying characteristics of DoS attacks based on the communication topology model to construct a dynamic Laplace matrix; wherein, the elements in the dynamic Laplace matrix are dynamically switched according to whether the corresponding communication link is subjected to a DoS attack, including: during the period of a DoS attack, the element corresponding to the communication link represents that the communication link is interrupted; during the period when the DoS attack disappears, the element corresponding to the communication link represents that the communication link is connected. The fourth construction module is used to integrate the dynamic model and the dynamic Laplace matrix to design a distributed state estimator. The distributed state estimator is used to estimate the flight state of each UAV and calculate the estimated state deviation and formation tracking deviation of each UAV based on the estimated flight state and the expected formation state. The data generation module is used to generate control commands based on the estimated state deviation and the formation tracking deviation using a preset distributed state controller, so as to drive each UAV to gradually converge its real-time flight state to the desired formation state in the DoS attack environment. The dynamics model includes a sub-dynamics model of the guiding drone and a sub-dynamics model of the following drone; The sub-dynamic model for guiding the UAV is as follows: ； The sub-dynamic model of the following drone is: ； in, They represent the first The flight status of the drone following and the drone guiding. express 3D real vector They represent the first Flight observations of drones following and guiding drones. They represent the first Follower drones and guide drones The rate of change of the flight state at any given moment; They represent the first Input variables for following and guiding drones. express 3D real vector; They represent the first Nonlinear factors exist in both follow-up and guide drones. , , These represent the system matrix, input variable matrix, and observation matrix of the UAV system, respectively. The distributed state estimator is: ； in, This is the feedback gain matrix of the distributed state estimator. express 3D real vector; They represent The estimated value; A node event triggering mechanism is set for the guiding drone, and an edge event triggering mechanism is set for each communication link between the guiding drone and each following drone, and between each following drone; When the triggering conditions of the node event triggering mechanism or the edge event triggering mechanism are met, the distributed state estimator is controlled to update the estimated values ​​of the flight state of each UAV. A node event triggering mechanism is set for the guiding drone, and an edge event triggering mechanism is set for each communication link between the guiding drone and each following drone, and between each following drone; When the triggering conditions of the node event triggering mechanism or the edge event triggering mechanism are met, the distributed state estimator is controlled to update the estimated values ​​of the flight state of each UAV. The node event triggering mechanism is as follows: ； in, Indicates guiding the drone Next trigger time This represents the maximum lower bound of the set. Indicates the node event triggering function and , This indicates the deviation in the predicted state of the guiding drone. express The flight status prediction value of the drone is constantly guided. This indicates taking the norm of a vector or matrix. All represent trigger parameters; Indicates the threshold for the node event triggering mechanism; and / or, ； in, Indicates guiding drones and the first The first communication link between the drones Next trigger time This represents the maximum lower bound of the set. Indicates the edge event triggering function and , Indicates guiding drones and the first Predicted state deviation between the following drones express Predictive guidance of drones and the first The relative state between the drones following the aircraft This represents the feedback gain matrix of the edge event triggering function. Indicates the predicted tracking deviation. This indicates taking the norm of a vector or matrix. Indicates the trigger parameter, Indicates adaptive coupling weights; This indicates the threshold for the event triggering mechanism of this edge; and / or, ； in, Indicates the first Follow-up drone and the first The first communication link between the drones Next trigger time This represents the maximum lower bound of the set. Indicates the edge event triggering function and , Indicates the first Follow-up drone and the first Predicted state deviation between the following drones express Time of the first Follow-up drone and the first The relative state between the drones following the aircraft This represents the feedback gain matrix of the edge event triggering function. Indicates the predicted tracking deviation. This indicates taking the norm of a vector or matrix. Indicates the trigger parameter, Indicates adaptive coupling weights; This represents the threshold for the event triggering mechanism of this edge; The distributed state controller is: ； in, Indicates input variables, Both represent adaptive coupling weights. The derivative is expressed as ,and , express Time of the first Follow-up drone and the first The real-time weight value of the communication link between the drone and the aircraft. Indicates the predicted tracking deviation. , All indicate Time of the first Follow-up drone and the first The relative state between the drones following the aircraft , They represent the first Follow-up drone and the first The predicted flight status of the drone following the aircraft. This is the feedback gain matrix of the adaptive coupling weights, with the superscript T indicating transpose; adaptive coupling weights The derivative is expressed as ,and , express Time of the first The real-time weight value of the communication link between the follower drone and the guide drone. Indicates the predicted tracking deviation. express Constantly guide drones and the first The relative state between the drones following the aircraft express The flight status estimate of the drone is constantly guided; This indicates a compensation signal.

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