An event-triggered state estimation method for a drone coordination system under asynchronous denial-of-service attacks

Abstract

The present application belongs to the field of unmanned aerial vehicle cluster control, and relates to an event-triggered state estimation method for an unmanned aerial vehicle cooperative system under asynchronous denial of service attack, comprising: establishing a linear unmanned aerial vehicle cooperative system model; constructing an asynchronous denial of service attack model, dividing a time interval into multiple subintervals of the same state according to the network state between unmanned aerial vehicles, and establishing a switching vector; constructing a state observer for the unmanned aerial vehicle cooperative system; constructing a dynamic event-triggered mechanism under asynchronous denial of service attack; based on Lyapunov stability theory and switching system ideas, using a linear matrix inequality tool, obtaining sufficient conditions for state estimation error stability of the unmanned aerial vehicle cooperative system under asynchronous denial of service attack, an observation matrix of the state observer, and a symmetric positive definite matrix of the trigger function. The present application solves the consistency problem and the communication resource shortage problem of the unmanned aerial vehicle cooperative system under asynchronous DoS attack by designing a dynamic event-triggered mechanism.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of unmanned aerial vehicle cluster control, and particularly relates to an event-triggered state estimation method for a cooperative unmanned aerial vehicle system under asynchronous denial-of-service attacks. BACKGROUND

[0002] Thanks to the development of communication technology and control technology, unmanned aerial vehicle cooperative systems have been widely applied. In the military field, unmanned aerial vehicle cooperative systems can be applied to tactical reconnaissance tasks. Multiple unmanned aerial vehicles can work cooperatively to conduct all-around reconnaissance of a target area from different angles and heights, obtaining comprehensive and detailed intelligence information, and their coverage range and information richness far exceed that of single unmanned aerial vehicles. Unmanned aerial vehicle cooperative systems also perform excellently in target attack tasks. Multiple attack unmanned aerial vehicles can simultaneously attack a target from different directions, improving the hit rate and lethality of attacks, and can also attack multiple targets simultaneously, effectively breaking through enemy air defense systems. At the same time, unmanned aerial vehicle cooperative systems have been widely applied in disaster rescue, logistics transportation, environmental monitoring, and agricultural plant protection due to their high efficiency, flexibility, adaptability to complex environments, and excellent functional expandability.

[0003] State estimation design can obtain real-time and accurate state information such as the position, speed, and attitude of each unmanned aerial vehicle. In the cooperative formation flight of unmanned aerial vehicles, through accurate state estimation, each unmanned aerial vehicle can fly according to the predetermined formation and path based on its own and other unmanned aerial vehicles' states, maintain appropriate spacing and relative positions, and avoid collisions. At the same time, excellent state estimation design can improve the ability of the entire system to cope with complex environments and autonomous decision-making.

[0004] Unmanned aerial vehicle cooperative systems highly depend on communication networks to achieve information sharing, task coordination, and cooperative control. Network communication brings many conveniences to unmanned aerial vehicle cooperative systems, but also poses a hidden danger of being attacked. Once attacked, the communication link may be disturbed, interrupted, or tampered with, causing unmanned aerial vehicles to be unable to timely and accurately transmit information, leading to system out-of-control, and further affecting real tasks, which may cause incalculable losses. At present, there are many researches on unmanned aerial vehicle cooperative systems coping with various network attacks such as denial-of-service attacks and deception attacks. However, as attackers become more and more intelligent, attackers can attack one or more communication links in the unmanned aerial vehicle cooperative system at any time, and previous research results often fail when facing such asynchronous attacks. SUMMARY

[0005] To solve the above technical problems, the purpose of the present application is to provide an event-triggered state estimation method for a UAV cooperative system under asynchronous denial of service attack, which solves the consistency problem and the problem of tight communication resources of the UAV cooperative system under asynchronous DoS attack through a dynamic event-triggering mechanism.

[0006] The present application provides an event-triggered state estimation method for a UAV cooperative system under asynchronous denial of service attack, comprising:

[0007] Step 1: Establish a linear leaderless UAV cooperative system model;

[0008] Step 2: Build an asynchronous denial of service attack model, divide the time interval into multiple subintervals of the same state according to the network state between UAVs, and establish a switching vector;

[0009] Step 3: Build a state observer for the UAV cooperative system;

[0010] Step 4: Build a dynamic event-triggering mechanism under asynchronous denial of service attack;

[0011] Step 5. Based on Lyapunov stability theory and switching system idea, using linear matrix inequality tool, obtain the sufficient condition of state estimation error stability of the UAV cooperative system under asynchronous denial of service attack, the observation matrix of the state observer and the symmetric positive definite matrix of the trigger function.

[0012] The event-triggered state estimation method for a UAV cooperative system under asynchronous denial of service attack of the present application has the following advantages:

[0013] 1. The present application fully applies graph theory and set knowledge, and visually expresses the network topology relationship formed between individuals of the UAV cooperative system.

[0014] 2. The present application applies denial of service attack to the UAV cooperative system, solves the problem that UAVs cannot transmit information between each other when the communication network of the system is attacked, and considers the problem that multiple transmission channels bear asynchronous denial of service attack due to the wide geographical distribution of large UAV cooperative systems, which is more consistent with general practical applications.

[0015] 3. The present application designs an event-triggered state estimation method suitable for the UAV cooperative system, which ensures more effective signal transmission between UAVs and reduces the dependence on factual state in the system control process.

[0016] 4、The application obtains the relationship between the estimation error stability and the denial of service attack intensity through the equivalent attenuation rate method, and in actual production, the design parameters can be adjusted to balance the work efficiency and system flexibility to meet the production demand and efficiency demand.

[0017] 5、The application proposes a sufficient condition for state estimation stability of a UAV cooperative system subjected to denial of service attacks, provides a judgment standard for realizing fixed-time consensus of the system, and gives a design method of an event-triggered scheme for a class of asynchronous denial of service attacks. BRIEF DESCRIPTION OF DRAWINGS

[0018] Figure 1 A flowchart of an event-triggered state estimation method of a UAV cooperative system under asynchronous denial of service attacks. DETAILED DESCRIPTION

[0019] In order to better understand the purpose, structure and function of the application, the application will be further described in detail below in combination with the drawings.

[0020] As shown in the drawings, Figure 1 The event-triggered state estimation method of a UAV cooperative system under asynchronous denial of service attacks of the application comprises:

[0021] Step 1: Establish a linear leaderless UAV cooperative system model, specifically:

[0022] Step 1.1: Let v represent the speed of the UAV, R represent the distance between the UAV and the origin of the coordinate system, and establish a ground coordinate system Under the coordinate system, according to the basic theorem of dynamics and the dynamic model of the aircraft, the dynamic equation of the UAV is as follows:

[0023]

[0024] Where g is the acceleration of gravity, is the tangential overload, is the net thrust, m is the mass of the UAV, is the pitch angle, is the roll angle, is the yaw angle, is the normal overload, is the net lift.

[0025] When the UAV is in stable flight, it receives four forces: thrust T, drag D, lift F and gravity G.

[0026] (1) The thrust T is calculated as follows:

[0027] , , , ,in, is the throttle size, , is the maximum thrust of the engine, is the gravity of the drone, Thrust-to-weight ratio of the UAV.

[0028] (2) The lift force F is calculated as follows:

[0029] , ,in is the flight medium density, For speed, is the wing area, is the lift coefficient, is the maximum lift coefficient, is the scale factor, .

[0030] (3) The resistance D is calculated as follows:

[0031] , , ,in is the drag coefficient, which can be obtained from the lift coefficient and lift-to-drag ratio Calculated.

[0032] Therefore, the net thrust and net lift as follows:

[0033] ,

[0034] .

[0035] Step 1.2: Establish the kinematic equations of the drone as follows:

[0036]

[0037] in, 、 、 They are Coordinates of three directions in the coordinate plane.

[0038] Step 1.3: Establish a state space model and let the state vector , the state space model is as follows:

[0039]

[0040] in, is the drone number, and N is the number of drones in the drone collaborative system; For the The state of a drone, whose dimensions are related to the type of real drone, usually includes parameter variables such as position, speed, angular velocity, acceleration, etc. For the The input of a drone, For the The output of each UAV, A, B, and C are the system matrix, input matrix, and output matrix respectively.

[0041] Step 1.4: Create a topology diagram of the UAV collaborative system:

[0042] The topological structure of UAV cooperative system express, ,in , represents the set of drones, represents the set of edges; let is the weighted adjacency matrix, represents the edge between the i-th UAV and the j-th UAV in the UAV system, if , that is, the i-th UAV and the j-th UAV can communicate, then ;if , that is, the i-th UAV and the j-th UAV cannot communicate, then ; Let the Laplace matrix of the topological graph be ,if ,but ,if ,but .

[0043] Step 2: Build an asynchronous denial of service attack model. Based on the network status between drones (safe state and attacked state), divide the time interval into multiple sub-intervals with the same state and establish switching vectors. Specifically,

[0044] Step 2.1: Considering that asynchronous denial of service attacks can cause transmission channel congestion, resulting in signal transmission failure. Considering the limited energy of network attackers, an asynchronous denial of service attack model with limited attack duration is established:

[0045]

[0046] in, For the time interval The sum of the DoS attack durations on the transmission channels of the i-th UAV and the j-th UAV, is the regularization coefficient, For the attack intensity coefficient, it can be seen from the attack model that, The smaller, the longer the attack duration, the practical meaning of this model is that the total time of DoS attack existence must not exceed the overall time.

[0047] Step 2.2: Under the asynchronous denial of service attack, the switching vector is described as:

[0048]

[0049] Wherein, Denotes the time interval in which the DoS attack does not exist in the time interval ; Represents the time interval set divided by , and different As the switching vector;

[0050]

[0051] Wherein, Is the set of transmission channels in the denial of service attack interval at time t.

[0052] Step 3: Construct the state observer of the UAV cooperative system, specifically:

[0053] Step 3.1: Rewrite the state space model as:

[0054]

[0055] Wherein, Is the relative measurement value of the output of the UAV, , Denotes the number of UAVs that can communicate with the ith UAV, Is the Order unit matrix, and:

[0056]

[0057] Wherein, Is the state of the adjacent neighbor jth UAV of the ith UAV, and .

[0058] Step 3.2: Based on the rewritten state space model, the state observer of the UAV cooperative system is constructed:

[0059]

[0060] Wherein, Is the observation value of , Is the observation value of the i-th UAV at the k-th time, is the observation matrix to be designed, is the observation value of the i-th UAV at the k-th time, is the observation value of the i-th UAV at the k-th time, and satisfies:

[0061]

[0062] wherein, is the observation value of the i-th UAV at the k-th time, is the observation value of the i-th UAV at the k-th time.

[0063] Step 4: Construct a dynamic event triggering mechanism under asynchronous denial of service attack.

[0064] The present application introduces a dynamic event triggering mechanism to alleviate the communication resource constraint and control the problem of dependence on real-time state information.

[0065] In the implementation, the trigger function of the dynamic event triggering mechanism is:

[0066]

[0067]

[0068]

[0069] wherein, represents the time of the i-th UAV triggered at the k-th time, inf represents the lower limit of the set, that is, the minimum value in all results satisfying the set condition, is the left limit of the i-th UAV at the k-th time; , h is the sampling period of the system, is a dynamic variable related to the internal information of the dynamic event triggering mechanism and the system, is the observation error of the state observer, is the error weight coefficient, is the dynamic variable weight coefficient, is the dynamic variable time-varying coefficient, is a symmetric positive definite matrix.

[0070] The actual meaning of the trigger function is:

[0071] First, it is judged whether the current time is in the attack interval of DoS, if there is no DoS attack at the current time, it is judged whether the current system parameter value satisfies , if yes, the triggering is successful, and the i-th UAV needs to exchange data with the adjacent UAVs, ​If not, the data exchange is not needed. If the current time is in the DoS attack interval, the ith UAV takes the sampling period as the data transmission period, and attempts to transmit data to the neighbor UAVs at regular intervals until the attempt is successful, to ensure that data exchange can be performed as soon as possible after the DoS attack, so as to ensure the stable operation of the entire UAV cooperative system.

[0072] Step 5: Based on Lyapunov stability theory and switching system idea, the linear matrix inequality tool is used to obtain the sufficient condition for the state estimation error stability of the UAV cooperative system under asynchronous denial of service attack, the observation matrix of the state observer and the symmetric positive definite matrix of the trigger function, specifically:

[0073] Step 5.1: Based on the event-triggered mechanism, the UAV cooperative system tracking error model is constructed, and the consistency problem is converted into a stability problem.

[0074] Let , Each UAV uses a state feedback controller , The observation error is brought into the state space model of step 1 to obtain the switching system model of the UAV cooperative system:

[0075]

[0076] , is the Laplacian matrix determined in step 2.2, when takes different values, it switches to different subsystems, is the control matrix, and L is the Laplacian matrix of the topological graph.

[0077] Let the tracking error be described as:

[0078]

[0079] , is an N-order identity matrix, , , is the average value of the instantaneous state of each UAV at time , , , is the dimension of the state vector.

[0080] The tracking error is brought into the switching system model of the UAV cooperative system to obtain the following tracking error model:

[0081]

[0082] Step 5.2: Based on Lyapunov stability theory, the decay rate of each subsystem of the UAV cooperative system under event-triggered mechanism and asynchronous DoS attack is obtained, and the observation matrix of the state observer is obtained.

[0083] The Lyapunov function is constructed as follows:

[0084]

[0085] Wherein, , is a positive definite matrix.

[0086] The derivative of the Lyapunov function is obtained by taking the derivative of and respectively.

[0087]

[0088]

[0089] Using Young's inequality, the scaling is performed for , and the following is obtained:

[0090]

[0091] According to the event-triggered condition, , so

[0092]

[0093] From the above, the derivative of the Lyapunov function is obtained as follows:

[0094]

[0095] Wherein, , , , .

[0096] Based on the quadratic form theory, it is known that when the following linear matrix inequality is satisfied:

[0097] , and the observation matrix of the state estimator , then holds.

[0098]

[0099]

[0100]

[0101] the matrix represents the transpose of is a matrix with as the diagonal line, is the switching vector of the subsystems' decay rate.

[0102] By solving the above linear matrix inequality, the optimal solution P, , the decay rate of each subsystem and the observation matrix H of the state estimator can be obtained.

[0103] Step 5.3: Based on the decay rate of the subsystem in step 5.2 The dynamic performance of a single UAV cannot be accurately matched, and to more accurately describe the internal relationship between network attacks and design parameters, the equivalent decay rate method is proposed to obtain the decay rate of each UAV, and the sufficient condition for the stability of the UAV cooperative system is obtained.

[0104] For step 5.2, , the integral is performed at each subsystem switching time, and the recursive idea is used to convert the integral from the subsystem switching time to the entire time interval:

[0105]

[0106] where, , ; denotes the time of system switching, and k denotes the number of triggers.

[0107] Let denote the equivalent decay rate of the i-th UAV under the j-th UAV, , represent the equivalent decay rate of the i-th UAV when the transmission channel between the i-th UAV and the j-th UAV is in a safe state; represent the equivalent decay rate of the i-th UAV when the transmission channel between the i-th UAV and the j-th UAV is in an attacked state.

[0108] From the definition of the equivalent decay rate, the relationship between the equivalent decay rate and the subsystem decay rate can be obtained as:

[0109]

[0110] Then, when holds, the value range of is obtained as:

[0111] ; ​

[0112] Considering the asynchronous DoS attack model described in step 2, we have:

[0113] ;

[0114]

[0115]

[0116] Based on, , , when , by Lyapunov stability theorem, the entire UAV system observation error tends to be stable.

[0117] From the above, if the equivalent decay rate of each UAV in the safe environment and the DoS attack environment satisfies and , and the maximum attack strength of the denial of service attack satisfies , then the entire UAV system observation error tends to be stable, that is, the designed state observer meets the performance requirements.

[0118] The present application relates to the field of UAV cooperative system control and the field of malicious network attack defense, and specifically is an event-triggered state estimation method for large-scale UAV cooperative systems under asynchronous denial of service (DoS) attacks and communication resource shortage. In particular, the present application considers the case where the signal transmission channel in the UAV cooperative system is subjected to asynchronous DoS attacks, and proposes a signal transmission strategy based on a dynamic event-triggered mechanism, which saves communication resources while ensuring system performance requirements. A safety mechanism based on a state observer is designed to complete distributed state estimation for multi-agent systems under DoS attacks with an event-triggered strategy. A switching method based on network attack timing is designed, which uses the idea of switching systems and Lyapunov stability theory to obtain sufficient conditions for the decay rate of each subsystem and the consistency of UAVs in the UAV system under asynchronous DoS attacks. An equivalent decay rate method is designed, which reveals the relationship between the maximum attack strength that the UAV system can withstand and the parameters in the event-triggered mechanism, which allows the present application to balance the response speed and control objectives of the system by adjusting the parameters of the event-triggered mechanism according to the actual network attack environment in practical applications.

[0119] The above only describes the preferred embodiments of the present application and does not limit the idea of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application should be included in the protection scope of the present application.

Claims

1. An event-triggered state estimation method for a UAV cooperative system under asynchronous denial-of-service attacks, characterized in that: include: Step 1: Establish a linear UAV collaborative system model; Step 2: Build an asynchronous denial of service attack model. Based on the network status between drones, divide the time interval into multiple subintervals with the same status and establish a switching vector. Step 3: Construct a state observer for the UAV collaborative system, specifically: Step 3.1: Rewrite the state-space model as: in, is the relative measurement value of the UAV’s output, represents the number of drones that can communicate with the i-th drone. N i The identity matrix is ​​of order, and: Among them, x i,j (t) is the state of the jth neighboring UAV of the i-th UAV, and j∈N i ; i∈N is the drone number, N is the number of drones in the drone collaborative system, x i (t) is the state of the i-th drone, u i (t) is the input of the i-th UAV, y i (t) is the output of the i-th UAV, A, B, and C are the system matrix, input matrix, and output matrix respectively; Step 3.2: Construct the state observer of the UAV cooperative system based on the rewritten state space model: in, is x i The observed value of (t), for The observation value, H is the observation matrix to be designed, is Δχ i (t) and satisfies: in, for Observed values ​​of Step 4: Build a dynamic event triggering mechanism under asynchronous denial of service attacks; Step 5: Based on Lyapunov stability theory and the idea of ​​switching systems, use linear matrix inequality tools to obtain sufficient conditions for the stability of the state estimation error of the UAV cooperative system under asynchronous denial of service attacks, the observation matrix of the state observer, and the symmetric positive definite matrix of the trigger function.

2. The event-triggered state estimation method for a UAV cooperative system under an asynchronous denial-of-service attack according to claim 1 is characterized in that: The step 1 is specifically as follows: Step 1.1: Let v represent the speed of the drone, R represent the distance between the drone and the coordinate origin, and establish the ground coordinate system O xyz In this coordinate system, according to the basic theorem of dynamics and the dynamic model of the aircraft, the dynamic equation of the UAV is given as follows: Where g is the acceleration due to gravity, is tangential overload, T net is the net thrust, m is the mass of the drone, φ is the pitch angle, γ is the roll angle, ψ is the yaw angle, is the normal overload, F net is the net lift; Step 1.2: Establish the kinematic equations of the drone as follows: Among them, x o 、y o 、z o O xyz Coordinates of three directions in the coordinate plane; Step 1.3: Establish a state space model and let the state vector x T =[x o T y o T z o T ] T , the state space model is as follows: Among them, i∈N is the drone number, N is the number of drones in the drone cooperative system, x i (t) is the state of the i-th drone, u i (t) is the input of the i-th UAV, y i (t) is the output of the i-th UAV, A, B, and C are the system matrix, input matrix, and output matrix respectively; Step 1.4: Create a topology diagram of the UAV collaborative system: The topological structure of the UAV cooperative system is represented by Π, Π={V,ε}, where V={v1,...,v N }, represents the set of drones, represents the set of edges; let is a weighted adjacency matrix, (i, j) represents the edge between the i-th UAV and the j-th UAV in the UAV system. If (i, j)∈ε, that is, the i-th UAV and the j-th UAV can communicate, then a ij >0; if That is, the i-th UAV and the j-th UAV cannot communicate, then a ij =0; let the Laplace matrix of the topological graph be L=[l ij ], if i=j, then If i≠j, then l ij =-a ij .

3. The event-triggered state estimation method for a UAV cooperative system under an asynchronous denial-of-service attack according to claim 1 is characterized in that: The step 2 is specifically as follows: Step 2.1: Considering the limited energy of network attackers, establish an asynchronous denial of service attack model with limited attack duration: Among them, |D ij (t1, t2)| is the sum of the DoS attack durations on the transmission channels of the i-th UAV and the j-th UAV in the time interval (t1, t2), is the regularization coefficient, μ ij ∈(0,1) is the attack strength coefficient; Step 2.2: Under asynchronous denial of service attack, the switching vector is described as: in, Indicates the time interval (t1, t2) during which DoS attack does not exist; E Γ(t) (t1, t2) represents the set of time intervals divided by Γ(t), which are divided by different E Γ(t) (t1, t2) as the switching vector; Γ(t)={(i,j)∈ε|t∈D ij (0,∞)} Among them, Γ(t) is the set of transmission channels in the denial of service attack interval at time t.

4. The event-triggered state estimation method for a UAV cooperative system under an asynchronous denial-of-service attack according to claim 1 is characterized in that: The trigger function of the dynamic event trigger mechanism is: in, represents the time when the i-th drone is triggered for the kth time, inf is the infimum of the representative set, that is, the minimum value of all results that meet the set conditions, t - is the left limit of t; r∈N, h is the sampling period of the system, η i (t) is a dynamic variable related to the dynamic event triggering mechanism and the system internal information, is the observation error of the state observer, ξ i >0 is the error weight coefficient, ρ i >0 is the dynamic variable weight coefficient, θ i >0 is the time-varying coefficient of dynamic variables, Φ i is a symmetric positive definite matrix.

5. The event-triggered state estimation method for a UAV cooperative system under an asynchronous denial of service attack according to claim 1 is characterized in that: The step 5 is specifically as follows: Step 5.1: Based on the dynamic event triggering mechanism, a tracking error model of the UAV cooperative system is constructed to transform the consistency problem into a stability problem. make Each UAV uses a state feedback controller The observation error Substitute the state space model from step 1 to obtain the switching system model of the UAV cooperative system: Among them, L Γ(t) For step 2.2 Γ(t) (t1, t2) determines the Laplace matrix, when E Γ(t) When (t1, t2) takes different values, it switches to different subsystems, K is the control matrix, and L is the Laplace matrix of the topology graph; Assume that the tracking error is described as: Among them, I N is the N-order identity matrix, is the average value of the instantaneous status of each drone at time t, that is, n is the dimension of the state vector; Bringing the tracking error into the switching system model of the UAV cooperative system, we obtain the following tracking error model: Step 5.2: Based on Lyapunov stability theory, obtain the decay rate of each subsystem of the UAV cooperative system under the event trigger mechanism and asynchronous DoS attack, and obtain the observation matrix of the state observer; Construct the following Lyapunov function: Where V1(t) = δ T (t)Pδ(t),P∈R n×n is a positive definite matrix; For the Lyapunov function Taking the derivatives respectively, we get: Using Young's inequality, Scaling to obtain: According to the event triggering conditions, f i (t)≤0, so we get: From the above, we can get the derivative of the Lyapunov function V(t): Among them, p * =min(ρ1ρ2...ρ N ),r * =max(ρ1ρ2...ρ N ),θ * =min(θ1θ2...θ N ),ξ * =min(ξ1ξ2...ξ N ); Based on the quadratic form theory, we know that when the following linear matrix inequality is satisfied: And let the observation matrix of the state estimator H = P -1 When Φ, we have Established; * in the matrix indicates The transpose of Φ=diag(Φ i ) is Φ i is the diagonal matrix, β Γ(t) The switching vector is E Γ(t) The decay rate of the subsystem at (t1, t2); By solving the above linear matrix inequality, we can obtain the optimal solution P, Φ, and the attenuation rate β of each subsystem. Γ(t) and the observation matrix H of the state estimator; Step 5.3: Based on the decay rate β of the subsystem in step 5.2 Γ(t) The equivalent attenuation rate method is proposed to obtain the attenuation rate of each UAV and obtain the sufficient conditions for the stability of the UAV cooperative system. For step 5.2 Integrate within each subsystem switching moment, and use recursion to convert the integral from the subsystem switching moment to the entire time interval: in, γ k Indicates the time of system switching, k indicates the number of triggering; set up represents the equivalent attenuation rate of the i-th UAV under the j-th UAV, m={1,2}, represents the equivalent attenuation rate of the i-th UAV when the transmission channel between the i-th UAV and the j-th UAV is in a safe state; represents the equivalent attenuation rate of the i-th UAV when the transmission channel between the i-th UAV and the j-th UAV is under attack; From the definition of equivalent attenuation rate, we can know that the relationship between it and the subsystem attenuation rate is: Then, when When it is established, the value range of p(0,t) is: Considering the asynchronous DoS attack model described in step 2, we get: Based on, V(t)≤e p(0,t) V(0), Therefore When , according to the Lyapunov stability theorem, the observation error of the entire UAV system tends to be stable; In summary, if the equivalent attenuation rate of each drone in a safe environment and a DoS attack environment satisfies and And the maximum attack intensity of the denial of service attack meets When , the observation error of the entire UAV system tends to be stable, that is, the designed state observer meets the performance requirements.

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