A method and device for elastic and secure formation of drone swarms under network attacks

Abstract

The present application provides a method and device for elastic and secure formation of drone clusters under network attacks, relating to the fields of drone formation control and network security. The method includes: establishing a drone cluster dynamics model that takes data deception attacks into consideration; determining a formation mission objective based on the following state of the follower drones, the state of the leader drone, and the expected time-varying formation vector in the drone cluster dynamics model that takes data deception attacks into consideration; determining a elastic control protocol for the drone cluster based on the formation mission objective and the drone cluster dynamics model; determining control instructions for each follower drone based on the drone cluster elastic control protocol; the control instructions are used to control the flight trajectory of the follower drones, so that each follower drone can still complete a preset formation even if it suffers a data deception attack.

Description

Technical Field

[0001] The present application relates to the fields of drone formation control and network security, and in particular to a method and related devices for elastic and secure formation of drone clusters under network attacks. Background Art

[0002] With the advancement of science and technology, drone technology is gradually improving and gaining widespread application in various fields. In the military, drone swarm warfare, as a new combat method, can perform multiple missions, including reconnaissance, jamming, and strikes, establishing a comprehensive, multi-layered strike capability against the enemy, effectively countering the enemy's complex air defense and combat systems. As a new combat method characterized by high autonomy, strong coordination, and outstanding combat capabilities, drone swarm warfare has become a focus of research and development in various countries. In future wars, drone swarm warfare will play an increasingly important role and become a vital component of the military forces of various countries.

[0003] When drone swarms are performing missions, they must ensure they maintain their pre-defined formation. This means that coordinated control of the drone swarm system is crucial. Currently, coordinated control of drone swarm systems relies on distributed control protocols, which assume that each drone in the swarm can accurately, continuously, and stably receive and send information from its neighbors. In practical applications, the group communication signals of drone swarms are often attacked by hostile forces. Consequently, control against cyberattacks (also known as resilience control) has been widely researched over the past decade.

[0004] Generally speaking, network attacks are categorized into two main types: denial of service (DoS) attacks and data spoofing (false data injection) attacks. If a drone swarm's network control system is attacked by a DoS attack, system resources become unavailable, preventing drones from exchanging formation tracking information with their neighbors. To combat DoS attacks, intermittent communication strategies can be employed to address the secure formation of drone swarms. However, if a drone swarm's network control system is attacked by a data spoofing attack, data packets transmitted in the communication link can be tampered with, formation tracking can be interrupted, and the overall performance of the drone swarm formation can be severely impacted. Currently, there is no effective response strategy to data spoofing attacks on drone swarm systems. Summary of the Invention

[0005] The purpose of this application is to provide a method and related devices for elastic and secure formation of drone clusters under network attacks, which can effectively resist data deception attacks on drone cluster systems.

[0006] To achieve the above objectives, this application provides the following solutions:

[0007] In a first aspect, the present application provides a method for elastic and secure formation of drone swarms under network attacks, comprising:

[0008] A drone cluster dynamics model considering data deception attacks is established; the drone cluster dynamics model includes dynamics models of multiple follower drones and dynamics models of multiple leader drones; the parameters in the dynamics model of the follower drones include the following state of the follower drones, the controller output of the follower drones, the deception data disturbance input to the follower drone controllers, the following output of the follower drones and the deception data disturbance input to the follower drone sensors or links; the parameters in the dynamics model of the leader drone include the state of the leader drone and the output of the leader drone.

[0009] According to the following status of the follower drones, the status of the leader drone and the expected time-varying formation vector, a drone cluster elastic formation mission objective is constructed.

[0010] Determine elastic control protocol expressions for multiple follower drones based on the drone swarm elastic formation mission objective and the drone swarm dynamics model considering data deception attacks;

[0011] Solving the unknown quantities in the elastic control protocol expressions of the multiple follower drones to obtain the elastic control protocols of the multiple follower drones; the unknown quantities in the elastic control protocol of the follower drones include the local formation neighbor estimation error of the follower drones, the estimation error between the follower drones and all leader drones, the attack estimation of the follower drone controller, the first controller gain of the follower drones, the second controller gain of the follower drones, and the formation compensation value of the follower drones;

[0012] The elastic control protocols of multiple follower drones are combined to obtain an elastic control protocol for a drone cluster.

[0013] According to the UAV cluster elastic control protocol, a control instruction for each follower UAV is determined; the control instruction is used to control the flight trajectory of the follower UAV.

[0014] In a second aspect, the present application provides a computer device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of a method for elastic and secure formation of a drone cluster under a network attack as described in the first aspect.

[0015] According to the specific embodiments provided in this application, this application discloses the following technical effects:

[0016] The present application provides a method and device for elastic and secure formation of drone clusters under network attacks. The method for elastic and secure formation of drone clusters under network attacks includes: establishing a drone cluster dynamics model that takes into account data deception attacks; determining a formation mission objective based on the following state of the follower drones, the state of the leader drone, and the expected time-varying formation vector in the drone cluster dynamics model that takes into account data deception attacks; determining a flexible control protocol for the drone cluster based on the formation mission objective and the drone cluster dynamics model; determining control instructions for each follower drone based on the drone cluster flexible control protocol; the control instructions are used to control the flight trajectory of the follower drones, so that each follower drone can still complete a preset formation even if it suffers a data deception attack. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0018] Figure 1 This is an application environment diagram of a method for flexible and secure formation of drone clusters under network attacks in one embodiment of the present application;

[0019] Figure 2 A flowchart of a method for elastically and securely forming a drone swarm under network attack provided by one embodiment of the present application;

[0020] Figure 3 A schematic diagram of a drone swarm network model considering data spoofing attacks provided in one embodiment of the present application;

[0021] Figure 4 A schematic diagram of attack estimation for a drone swarm provided in one embodiment of the present application;

[0022] Figure 5 A state transition diagram of a drone cluster provided in one embodiment of the present application;

[0023] Figure 6 A graph showing the formation error of a drone cluster over time according to an embodiment of the present application;

[0024] Figure 7 A flowchart of a method for elastically and securely forming a drone swarm under a network attack, provided in another embodiment of the present application;

[0025] Figure 8 A graph showing the relationship between the triggering and timing of the control signals for each follower drone in the drone cluster;

[0026] Figure 9 A schematic diagram of the structure of a computer device provided in one embodiment of the present application. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0028] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0029] The embodiment of the present application provides a method for the flexible and secure formation of drone clusters under network attacks, which can be applied to Figure 1 In the application environment shown, the ground control station 102 communicates with the drone cluster 101 via a network. The drone cluster includes a data storage system that can store data that the drone cluster 101 needs to process. The ground control station 102 can send a desired formation signal to the drone cluster 101. After receiving the desired formation signal, the drone cluster 101 determines the control instructions for each follower drone according to the drone cluster elastic control protocol. The control instructions are used to control the flight trajectory of the follower drones, allowing the drone cluster 101 to complete the desired formation. The drone cluster 101 can also feedback the current formation signal to the ground control station 102.

[0030] In an exemplary embodiment, Figure 2 As shown, a method for elastic and secure formation of drone clusters under network attacks is provided. In the embodiment of the present application, the method is applied to Figure 1 Taking the drone cluster 101 in FIG. 1 as an example, the method includes the following steps 201 to 208. Among them:

[0031] Step 201: Establish a drone swarm dynamics model that takes data deception attacks into consideration.

[0032] Among them, the UAV cluster dynamics model includes the dynamics models of multiple follower UAVs and the dynamics models of multiple leader UAVs; the parameters in the dynamics model of the follower UAV include the following state of the follower UAV, the controller output of the follower UAV, the deception data disturbance input to the follower UAV controller, the following output of the follower UAV and the deception data disturbance input to the follower UAV sensor or link; the parameters in the dynamics model of the leader UAV include the state of the leader UAV and the output of the leader UAV.

[0033] The dynamic model of the follower UAV is:

[0034]

[0035] y i (t) = Cx i (t)+Cψ xi ;

[0036] in, is the following state of follower drone i, is the controller output of follower UAV i, ψ ui is the deception data perturbation input to the follower drone i controller; is the follower output of the follower drone i, is the system state matrix of follower UAV i, is the system interference matrix of follower UAV i, represents the system state matrix of follower UAV i, ψ xi is the deceptive data perturbation input to the follower drone i’s sensor or link;

[0037] The dynamic model of the leader UAV is:

[0038]

[0039] y m (t) = Cx m (t);

[0040] in, is the status of the leader drone m, is the output of the leader drone m.

[0041] As an optional implementation, Figure 3 A schematic diagram of a drone swarm dynamics model considering data deception attacks is given. Figure 3 There are six follower drones i (i=1,2,...,6) and three leader drones m (m=7,8,9). The figure shows three different models of controller attack, sensor attack and link attack.

[0042] Step 202 : constructing a flexible formation mission objective for the drone swarm based on the following status of the follower drones, the status of the leader drone, and the desired time-varying formation vector.

[0043] The specific objectives of the UAV swarm flexible formation mission are:

[0044] In the UAV swarm formation, the following state of each follower UAV i satisfies:

[0045]

[0046] in, is the time-varying formation vector expected by follower UAV i, and the time-varying formation vector expected by follower UAV i is piecewise continuously differentiable; c m is a set of constants satisfying N is the total number of drones in the drone cluster, the first M are follower drones, and the last NM are leader drones.

[0047] Step 203 : Determine elastic control protocol expressions for multiple follower drones based on the drone cluster elastic formation mission objective and the drone cluster dynamics model considering data deception attacks.

[0048] The elastic control protocol expression of the follower UAV is:

[0049]

[0050] Among them, u ci (t) is the elastic control protocol of follower UAV i; is the local formation neighbor estimation error of follower UAV i; is the estimation error between follower UAV i and leader UAV; is the attack estimation of the follower UAV i controller; G ei is the first controller gain of follower UAV i; G ui is the second controller gain of follower UAV i; v i (t) is the formation compensation value of follower UAV i.

[0051] Step 204 : Solve the unknown variables in the elastic control protocol expressions of the multiple follower UAVs to obtain the elastic control protocols of the multiple follower UAVs.

[0052] Among them, the unknown quantities in the elastic control protocol of the follower UAV include the local formation neighbor estimation error of the follower UAV, the estimation error between the follower UAV and all leader UAVs, the attack estimation of the follower UAV controller, the first controller gain of the follower UAV, the second controller gain of the follower UAV and the formation compensation value of the follower UAV.

[0053] As an optional implementation, the calculation formula for the local formation neighbor estimation error of the follower drone i is:

[0054]

[0055] in, is the set of UAVs that directly communicate with UAV i in the communication topology. Figure 3 Taking follower drone 3 (node ​​3) in the example, the drones that directly communicate with it are 6, 7, 8, and 9. To calculate the local formation neighbor estimation error for follower drone 3, the estimation errors of the four neighbor drones need to be calculated and then summed. It should be noted that neighbor drone j can be both a follower drone and a leader drone.

[0056] The topological adjacency matrix of the UAV cluster communication is: , N is the number of drones in the drone cluster. ij is the element in row i and column j of the communication topology adjacency matrix; a ij =1 means that follower UAV i has communication connection with UAV j, a ij =0 means that follower UAV i has no communication connection with UAV j.

[0057] The calculation formula of the estimated error between the follower UAV i and the leader UAV is:

[0058]

[0059] Among them, a im is the element in the i-th row and m-th column of the communication topology adjacency matrix; a im =1 means that the follower UAV i has a communication connection with the leader UAV m; im =0 means that follower drone i has no communication connection with leader drone m.

[0060] refer to Figure 3 For example, for follower UAV 5, when calculating the estimation error between follower UAV 5 and leader UAV, it is necessary to calculate the estimation errors between follower UAV 5 and leader UAV 7, leader UAV 8 and leader UAV 9 respectively, and then sum them up.

[0061] in addition, and The corresponding actual error can be expressed by the following formula:

[0062]

[0063]

[0064] As an optional implementation, the attack estimation of the follower UAV i controller The determination process is:

[0065] Design the state estimator of follower UAV i, the expression of the state estimator of follower UAV i is:

[0066] in, represents the state estimation of follower UAV i, Tx i (t), ψ ui , ψ xi The estimation of , G, J, T, R are the preset estimator matrices.

[0067] The determination process of G, J, T, and R is as follows:

[0068] Defining the estimation error For ε i (t) Taking the derivative we get:

[0069]

[0070] Wherein, matrix G, matrix T, matrix J, and matrix R satisfy TA-GT-RC=0, and TB-J=0; matrix G is a Hurwitz matrix;

[0071] Then we can get in

[0072] Substitute the determined matrix G, matrix T, matrix J and matrix R into the state estimation expression of follower drone i to obtain the attack estimation of the controller of follower drone i and attack estimation of follower drone i sensor or link

[0073] Obviously, if data deception can be correctly detected, then when t→∞, ε ui (t) = ε xi (t) = 0, ε i (t) = 0. Further, we can set , thus Written in compact form, we get:

[0074]

[0075] in,

[0076] As an optional implementation, the formation compensation value v of the follower UAV i is i (t) Must meet the following requirements:

[0077]

[0078] Among them, v i The specific process of determining (t) is as follows: Let z i (t) = x i (t)-h i (t), then the expression of “substituting the elastic control protocol expression of the follower UAV into the dynamic model of the follower UAV” (this expression can refer to step 205) can be further written as:

[0079]

[0080] make Then we have:

[0081]

[0082] in,

[0083] Define v i (t) Satisfy the conditions Then the first-order derivative of ξ(t) can be written as:

[0084]

[0085] In the process of designing attack estimation and control gain, this application is completed with the help of stability analysis function, which is:

[0086]

[0087] in, P is The solution, and Q are both positive definite matrices. and Substitute into V(t), let G ui =-I p , then the first-order derivative of V(t) is expressed as:

[0088]

[0089] if The controller design is considered to satisfy stability, and the controller gain is then designed and proved.

[0090] As an optional implementation, the first controller gain of the follower UAV i is G ui =-I p ; The second controller gain of follower drone i is G ei =ω e R -1 B T P -1 ; Among them, ω e ≤-1 / 2λ M <0;λ M is the communication topology Laplace matrix L a The maximum eigenvalue of .

[0091] Where P is The solution, and Q are both positive definite matrices; I p represents the p×p dimensional identity matrix; ω e For the control gain coefficient, the control gain coefficient is designable.

[0092] Therefore, the first few items of stability analysis are:

[0093]

[0094] in matrix Meet U T L a1 U=J a1 , J a1 =diag{λ1,...,λ M},γ0=λ1λ min (QP -2 )>0.

[0095] According to Young's inequality, the third and fourth terms of the stability analysis can be determined as:

[0096]

[0097] in,

[0098] Next, the attack estimate is designed so that the fifth, sixth, and seventh terms of the stability analysis are zero, that is, the attack estimate is designed so that

[0099] Therefore, we can further obtain

[0100] Similarly, the last few items are also designed to be zero,

[0101] From this we can get

[0102] According to the above analysis process of the stability analysis function, we can get:

[0103]

[0104] based on e i (t) and r i The definition of (t) can be obtained:

[0105]

[0106] in,

[0107] According to Young's inequality and The expression of By deduction, we can get the stability analysis results:

[0108]

[0109] in,

[0110] right and By integrating, we can get the specific design of the estimation of data deception attack by drone clusters:

[0111]

[0112]

[0113] in,

[0114] As an optional implementation, Figure 4 The attack estimation of drone swarm is given. Figure 4 a means Figure 3 The estimation of the controller attack on follower drone 1; Figure 4 b means Figure 3 The estimation of sensor attack on follower drone 6; Figure 4 c represents the estimation of the link attack suffered by follower UAV 3; Figure 4 d represents the estimation of the link attack suffered by follower UAV 5.

[0115] Step 205: Combining the elastic control protocols of multiple follower drones to obtain an elastic control protocol for the drone cluster. The elastic control protocols of multiple follower drones are combined to obtain an elastic control protocol for the drone cluster, specifically including:

[0116] Substituting the elastic control protocol expression of the follower UAV into the dynamic model of the follower UAV, we can obtain:

[0117]

[0118] y i (t) = Cx i (t)+Cψ xi .

[0119] Will and y i (t) can be written in compact form as:

[0120]

[0121]

[0122] Similarly, in the dynamic model of leader m and y m (t) can be written in compact form:

[0123]

[0124]

[0125] in,

[0126]

[0127]

[0128] G e =diag{G e1 ,...,G eM}, G u =diag{G u1 ,...,G uM}, L a is the Laplace matrix form of the UAV cluster communication topology, L a =[L a1 L a2 ;00], is the follower communication topology matrix, is the follower-leader communication topology matrix. a1The eigenvalues ​​of are {λ1,...,λ M}, where λ1 is the smallest, λ M maximum.

[0129] It should be noted that the compact form mentioned above refers to expanding the expression of a single drone to the expression of the entire drone cluster.

[0130] Step 206: Determine the control instructions for each follower drone according to the drone cluster elastic control protocol; the control instructions are used to control the flight trajectory of the follower drone.

[0131] As an optional implementation, Figure 5 The state transition diagram of the drone cluster is given, where the three red five-pointed stars represent the three drone leaders and the six blue quadrilaterals represent the six follower drones. Figure 5 a represents the initial state of the drone cluster (t=0s), and a random value is used here. Figure 5 b represents the UAV cluster completing the desired formation when it is not subjected to data deception attack (t = 15s). Figure 5 c represents the state of the drone cluster when it suffers a data spoofing attack (t = 20s). Figure 5 d represents the state of the drone cluster completing the desired formation after being attacked by data spoofing (t = 30s). Figure 5 e and Figure 5 f represents the state when the UAV cluster stably maintains the desired formation (t = 40s and t = 50s).

[0132] It should be noted that to achieve the desired formation goal, only the follower drones need to maintain the desired formation, and the relative positions of the leader drones do not need to be considered. In other words, the leader drone only assists the follower drones in positioning; the leader drone itself is not part of the desired formation.

[0133] Further, Figure 6 A curve chart showing the formation error of the UAV cluster changing over time is given. Figure 5 and Figure 6 It can be seen that at time 0, the drone cluster is in the initial state and the formation error is the largest; around 15 seconds, the formation error is close to 0, and the drones complete the desired formation; around 20 seconds, the drone cluster suffers a data deception attack, and the formation error suddenly increases; at 30 seconds, the formation error is almost reduced to 0, indicating that after suffering a data deception attack, the drone cluster only needs 10 seconds of adjustment time to complete the desired formation.

[0134] By implementing the above steps 201 to 206, each follower drone can still complete the preset formation even if it is attacked by data spoofing.

[0135] In another exemplary embodiment, Figure 6 As shown, the method for elastic and secure formation of drone clusters under network attacks also includes:

[0136] Step 207: Determine the event triggering condition of the elastic control protocol of the follower drone i and the minimum communication interval of the elastic control protocol of the follower drone i.

[0137] Figure 8 The relationship between the triggering and time of the control signal of each follower UAV in the UAV cluster is given. Figure 8 It can be seen that the data in follower drone 1 is the most dense, this is because Figure 3 The number of neighbor drones that directly communicate with follower drone 1 (node ​​1) is the largest, and the communication is more frequent.

[0138] As an optional implementation, the event triggering condition for follower UAV i to receive communication from its neighbor UAV j can be designed as follows:

[0139]

[0140]

[0141] in, is the state estimate of neighbor UAV j received by follower UAV i at time t, It is the estimated state value of follower UAV i after making an abnormal estimation of neighbor UAV j at time t. The meaning is: when the event is triggered, the follower UAV i and its neighbor UAV j communicate and exchange state information. At this time, the state estimation value Directly assign to

[0142] Defining prediction error And according to and It can be seen that Since this is an ever-increasing estimation error term, and considering the event triggering mechanism, the designed event triggering condition needs to be smaller than the overall formation error, that is, satisfying

[0143] Therefore, the event triggering conditions for designing the elastic control protocol of follower UAV i are:

[0144]

[0145] in, is the state estimation value after follower UAV i makes anomaly estimation on neighbor UAV j.

[0146] The minimum communication interval of the flexible control protocol of the follower UAV i is:

[0147]

[0148] in,

[0149]

[0150] in, These are all predetermined parameters;

[0151] M is the number of follower drones.

[0152] Further, The specific process of determining is as follows:

[0153] The drones are divided into two equal parts based on their most recent communication time, namely F1(t) and F2(t). The most recent communication time of the drones in F1(t) is less than that in F2(t). Define μ1+μ2=μ<1, where μ1∈(0,1), μ2∈(0,1), μ1≤μ2, and we can get the following two inequalities:

[0154]

[0155]

[0156] According to the event triggering conditions of the elastic control protocol of the follower UAV i, the sufficient conditions of the above inequality are further derived:

[0157]

[0158] in,

[0159] Continuing the derivation of the inequality, we can get in,

[0160] Let ε ei (t) = ε xi (t)-ε pi (t),||ε ei (t)|| / ||ξ(t)|| can be further derived as:

[0161]

[0162] in, γ5=max{γ3,γ4};

[0163] for From 0 to The lower bound of , from which we can get:

[0164]

[0165] The present application also provides an application scenario, which applies the above-mentioned method for elastic and secure formation of drone clusters under network attacks. Specifically: The method for elastic and secure formation of drone clusters under network attacks provided in this embodiment can be applied to scenarios where drone clusters are subjected to network attacks while performing tasks. The network attacks suffered by drone clusters are mainly divided into two categories: DOS attacks and data deception attacks. The method provided by the present application solves the problem that drone clusters are difficult to maintain a preset formation when subjected to data deception attacks, thereby improving the robustness of drone cluster formations.

[0166] In an exemplary embodiment, a computer device is provided. The computer device may be a server or a terminal. The internal structure diagram thereof may be as follows: Figure 9 As shown. The computer device includes a processor, a memory, an input / output interface (Input / Output, abbreviated as I / O) and a communication interface. The processor, memory and input / output interface are connected through a system bus, and the communication interface is connected to the system bus through the input / output interface. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The database of the computer device is used to store a drone cluster dynamics model that takes into account data deception attacks. The input / output interface of the computer device is used to exchange information between the processor and an external device. The communication interface of the computer device is used to communicate with an external terminal through a network connection. When the computer program is executed by the processor, a method for elastic and secure formation of drone clusters under network attacks is implemented.

[0167] Those skilled in the art will understand that Figure 9 The structure shown in the figure is only a block diagram of a part of the structure related to the solution of the present application, and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components than shown in the figure, or combine certain components, or have a different component arrangement.

[0168] In an exemplary embodiment, a computer device is further provided, including a memory and a processor. The memory stores a computer program, and the processor implements the steps in the above method embodiments when executing the computer program.

[0169] In an exemplary embodiment, a computer-readable storage medium is provided, storing a computer program. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0170] In an exemplary embodiment, a computer program product is provided, including a computer program. When the computer program is executed by a processor, the steps in the above method embodiments are implemented.

[0171] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of relevant data must comply with relevant regulations.

[0172] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, database or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory may include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0173] The databases involved in the various embodiments provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchains. The processors involved in the various embodiments provided herein may include, but are not limited to, general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic units, data processing logic units based on quantum computing, and the like.

[0174] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0175] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A method for flexible and secure formation of drone swarms under network attacks, characterized by: The method for elastic and secure formation of drone swarms under network attacks includes: Establish a UAV swarm dynamics model that takes into account data deception attacks; the UAV swarm dynamics model includes dynamics models of multiple follower UAVs and dynamics models of multiple leader UAVs; the parameters in the dynamics model of the follower UAVs include the following state of the follower UAVs, the controller output of the follower UAVs, the deception data perturbation input to the follower UAV controller, the following output of the follower UAVs, and the deception data perturbation input to the follower UAV sensor or link; the parameters in the dynamics model of the leader UAV include the state of the leader UAV and the output of the leader UAV; Constructing a UAV swarm flexible formation mission objective based on the following status of the follower UAV, the status of the leader UAV, and the desired time-varying formation vector; Determine elastic control protocol expressions for multiple follower drones based on the drone swarm elastic formation mission objective and the drone swarm dynamics model considering data deception attacks; Solving the unknown quantities in the elastic control protocol expressions of the multiple follower drones to obtain the elastic control protocols of the multiple follower drones; the unknown quantities in the elastic control protocol of the follower drones include the local formation neighbor estimation error of the follower drones, the estimation error between the follower drones and all leader drones, the attack estimation of the follower drone controller, the first controller gain of the follower drones, the second controller gain of the follower drones, and the formation compensation value of the follower drones; Combining the elastic control protocols of the plurality of follower drones to obtain an elastic control protocol for a drone cluster; According to the UAV cluster elastic control protocol, a control instruction for each follower UAV is determined; the control instruction is used to control the flight trajectory of the follower UAV.

2. The method for flexible and secure formation of drone swarms under network attacks according to claim 1 is characterized in that: The dynamic model of the follower UAV is: y i (t)=Cx i (t)+Cψ xi ; in, is the following state of follower drone i, is the controller output of follower UAV i, ψ ui is the deception data perturbation input to the follower drone i controller; is the follower output of the follower drone i, is the system state matrix of follower UAV i, is the system interference matrix of follower UAV i, represents the system state matrix of follower UAV i, ψ xi is the deceptive data perturbation input to the follower drone i’s sensor or link; The dynamic model of the leader UAV is: y m (t)=Cx m (t); in, is the status of the leader drone m, is the output of the leader drone m.

3. The method for flexible and secure formation of drone swarms under network attacks according to claim 2 is characterized in that: The specific objectives of the UAV swarm flexible formation mission are: In the UAV swarm formation, the following state of each follower UAV i satisfies: in, is the time-varying formation vector expected by follower UAV i, and the time-varying formation vector expected by follower UAV i is piecewise continuously differentiable; c m is a set of constants satisfying N is the total number of drones in the drone cluster, the first M are follower drones, and the last NM are leader drones.

4. The method for flexible and secure formation of drone swarms under network attacks according to claim 3 is characterized in that: The elastic control protocol expression of the follower UAV is: Among them, u ci (t) is the elastic control protocol of follower UAV i; is the local formation neighbor estimation error of follower UAV i; is the estimation error between follower UAV i and leader UAV; is the attack estimation of the follower UAV i controller; G ei is the first controller gain of follower UAV i; G ui is the second controller gain of follower UAV i; v i (t) is the formation compensation value of follower UAV i.

5. The method for flexible and secure formation of drone swarms under network attacks according to claim 4 is characterized in that: The calculation formula of the local formation neighbor estimation error of the follower UAV i is: in, is the set of UAVs that directly communicate with follower UAV i in the communication topology; a ij is the element in row i and column j of the communication topology adjacency matrix; a ij =1 means that follower UAV i has communication connection with UAV j, a ij =0 means that follower UAV i has no communication connection with UAV j; The calculation formula of the estimated error between the follower UAV i and the leader UAV is: Among them, a im is the element in the i-th row and m-th column of the communication topology adjacency matrix; a im =1 means that the follower UAV i has a communication connection with the leader UAV m; im =0 means that follower drone i has no communication connection with leader drone m.

6. The method for flexible and secure formation of drone swarms under network attacks according to claim 4 is characterized in that: Attack Estimation of Follower UAV i-Controller The determination process is: Design the state estimator of follower UAV i, the expression of the state estimator of follower UAV i is: in, represents the state estimation of follower UAV i, Tx i (t), ψ ui , ψ xi The estimation of , G, J, T, R are the preset estimator matrices; The determination process of G, J, T, and R is as follows: Defining the estimation error For ε i (t) Taking the derivative we get: Wherein, matrix G, matrix T, matrix J, and matrix R satisfy TA-GT-RC=0, and TB-J=0; matrix G is a Hurwitz matrix; Then we can get in Substitute the determined matrix G, matrix T, matrix J and matrix R into the state estimation expression of follower drone i to obtain the attack estimation of the controller of follower drone i and attack estimation of follower drone i sensor or link 7. The method for flexible and secure formation of drone swarms under network attacks according to claim 4 is characterized in that: The formation compensation value v of the follower drone i i (t) Must meet the following requirements: The first controller gain of the follower UAV i is G ui =-I p ; The second controller gain of the follower drone i is G ei =ω e R -1 B T P -1 ; Among them, ω e ≤-1 / 2λ M <0;λ M is the communication topology Laplace matrix L a The maximum eigenvalue of The solution, and Q are both positive definite matrices; I p represents the p×p dimensional identity matrix; ω e is the control gain coefficient.

8. The method for flexible and secure formation of drone swarms under network attacks according to claim 4 is characterized in that: The method for elastic and secure formation of drone swarms under network attacks also includes: Determine an event triggering condition of the elastic control protocol of the follower drone i and a minimum communication interval of the elastic control protocol of the follower drone i.

9. The method for flexible and secure formation of drone swarms under network attacks according to claim 8, characterized in that: The event triggering conditions of the elastic control protocol of the follower UAV i are: in, 0<α i <1; is the state estimation value after follower UAV i makes anomaly estimation on neighbor UAV j; The minimum communication interval of the flexible control protocol of the follower UAV i is: in, in, γ5 are all predetermined parameters; 10. A computer device comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor executes the computer program to implement a method for elastic and secure formation of drone clusters under network attacks as described in any one of claims 1-9.

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