An Unmanned Aerial Vehicle Formation Cooperative Control System and Method under Denial-of-Service Attacks

Abstract

The present invention discloses a UAV formation cooperative control system and method under a denial-of-service attack, including a control system body, which comprises a model establishment platform, a trigger mechanism platform and a stability verification platform; the model establishment platform establishes a UAV formation model and a corresponding formation cooperative control model; the trigger mechanism platform determines the dynamic event trigger rule; the stability verification platform proves the stability of the cooperative control method and the absence of Zeno behavior. First, a denial-of-service attack model is established. On this basis, a new dynamic event trigger mechanism is designed, which reduces the system's dependence on communication resources. At the same time, an adaptive coupling weight is introduced, so the given controller is completely distributed. Finally, limitations on the attack frequency and duration are given. By using the second Lyapunov method, the stability of UAV cooperative control is proved, and the absence of Zeno behavior is also proved. This method realizes the cooperative control of UAVs under a denial-of-service attack.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle (UAV) control, and particularly to a UAV formation cooperative control system and method under a denial-of-service (DoS) attack. Background Art

[0002] With the development of unmanned systems, UAV systems have flourished in various fields such as military defense, reconnaissance and monitoring, and communication relay. Compared with a single UAV, multi-UAV cooperation can make autonomous decisions, expand the coverage area, have good robustness and scalability. However, due to the openness and interconnectivity of communication channels, the communication channels between UAVs are vulnerable to various network attacks. The most representative attack mode in communication network attacks is the DoS attack. When the UAV system is under a DoS attack, the information communication between UAVs will be cut off, thus affecting the cooperative control of UAVs. Therefore, it is very necessary to study the distributed security control problem of UAV systems.

[0003] Dynamic event triggering is a novel control strategy. Compared with the traditional static event triggering mechanism, the dynamic event triggering mechanism makes the minimum sampling interval under the dynamic event triggering mechanism not less than the minimum sampling interval under the static event triggering mechanism by introducing internal variables. Therefore, this strategy significantly reduces the demand for communication resources and at the same time improves the flexibility of UAV cooperative control.

[0004] Adaptive coupling weights play a crucial role in multi-agent systems. It can enhance the robustness of the system, achieve fully distributed control and improve the system performance. By introducing adaptive coupling weights, UAV cooperative control can better adapt to different environments, make its control law fully distributed, and have good scalability. Summary of the Invention

[0005] The purpose of the present invention is to provide a UAV formation cooperative control method under a DoS attack, which effectively reduces the dependence on communication resources by introducing a dynamic event triggering mechanism, and gives the limitations on the DoS attack when realizing cooperative control.

[0006] To achieve the above purpose, the present invention provides the following technical solution: A UAV formation cooperative control system under a DoS attack, including a control system body, and the control system body includes a model establishment platform, a triggering mechanism platform and a stability verification platform;

[0007] 1) The model establishment platform establishes a UAV formation model and a corresponding formation cooperative UAV flight model;

[0008] 2) The triggering mechanism platform determines the dynamic event triggering rule, and the minimum sampling interval under the dynamic event triggering mechanism is not less than the minimum sampling interval under the static event triggering mechanism;

[0009] 3) The stability verification platform proves that the cooperative control method generates consistency and no Zeno behavior.

[0010] As a preferred technical solution of the present invention, the model establishment platform includes a quadcopter drone model module, a denial-of-service attack model module, and a formation flight model module. The quadcopter drone model module establishes a kinematic model of a quadcopter drone. (p x ,p y ,p z ) represents the spatial position in the ground coordinate system, (φ, θ, ψ): the attitude angle of the drone, and the kinematic equation of the drone is obtained: where L A represents the distance from the center of gravity of the drone to the propeller, I x ,I y ,I z represent the moments of inertia about the X, Y, and Z axes respectively, (k1, k2, k3, k4, k5, k6) represent the drag coefficients, (T1, T2, T3, T4) represent the propeller lift forces, and T Z represents the force acting on the drone along the Z axis. After linearization, the state equation of the drone system is: where: Note:

[0011] As a preferred technical solution of the present invention, the denial-of-service attack model module assumes that {t h} is the start time of the attack, and τ h is the duration of the attack. Therefore, I h = [t h ,t h + τ h ) is the time interval of the h-th attack. The time set in which the attack exists is defined as: The time set in which the attack does not exist is defined as: Θ = [t0, t]\Ξ. The denial-of-service attack model module includes an attack frequency unit and an attack duration unit. The attack frequency unit defines the number of attacks N(t0, t) in (t, t0). Therefore, the attack frequency N F is defined as: In (t, t0), the duration of the attack should satisfy: |Ξ| ≤ ∈ + τ0(t - t0), where ∈ > 0, τ0(t0, t) = (t - t0)\τ a ,τ a > 0. At the same time, it should be considered that due to the influence of the trigger time, the state cannot be updated in a timely manner when the attack ends. Therefore, is defined as the interval time from the end of the attack to the next trigger time, and Therefore The actual impact time of the h-th attack, updated progress: The set of times when the actual attack exists is defined as: The set of times when the actual attack does not exist is defined as:

[0012] As a preferred technical solution of the present invention, the formation flight model module considers the dynamic model of the UAV system as: Where x i (t) is the n-dimensional state, u i is the m-dimensional input. At the same time, the definition of achieving consistency is given: Under a denial-of-service attack, if the states of each agent satisfy the following conditions, it means that multi-agent system achieves consistency, and further it can be shown that the UAVs achieve formation flight:

[0013] As a preferred technical solution of the present invention, the trigger mechanism platform designs a dynamic event trigger mechanism to increase the event trigger interval. Design of the dynamic event trigger mechanism: Where is the estimated value of the state. Design of the gain matrix K: K is the feedback gain matrix, where K = B T P, P > 0, P satisfies: The adaptive coupling coefficient ω ij (t) satisfies: Where: Q = PBB T P, ρ1 > 0. The consistency error and the measurement error are defined respectively as: For the convenience of subsequent derivation, define x ij : Dynamic event trigger rule: Where is the trigger time, and at the same time: Here β i > 0, θ i > 0, 0 < α i < 1, γ i (t0) > 0.

[0014] As a preferred technical solution of the present invention, the stability verification platform includes a first theorem module and a second theorem module. The first theorem module assumes that the system topology structure is an undirected graph, and requires the dynamic time trigger parameter η i > ([1 - α i / β i ). The UAV formation stability can be achieved if the denial-of-service attack information satisfies the following conditions: Where, ρ1 = min{(α / [2λ max (P)]),(κ i / 2)}, ρ2 = (β / [2λ min (P)]), κ i = η i -([1 - α i / β i ). Proof: For stability analysis, select the Lyapunov function: Where: Taking the derivative gives: Where: The following proof is divided into two cases: when the system is not under a denial-of-service attack and when it is under a denial-of-service attack, and a brief proof is given; The first case: When the system is not suffering from a denial-of-service attack

[0015] Where Since Multiply both sides by Define simultaneously After further mathematical transformation, we have: Here L is the Laplacian matrix of the topological structure, q0 is related to the triggering mechanism parameter, Select To make Simplify to get: Furthermore: Take According to the relationship between W and V1, we get: The second case: When the system is under a denial-of-service attack, at this time: x ij = 0, and it is known at this time Simplify to get: At According to the relationship between W, V, and V1, further simplify to get: Based on the above two cases, without loss of generality, when t ∈ [t h + τ h + Δ, t h+1 ) : When t ∈ [t h , t h + τ h + Δ) : Considering We get According to Theorem 1's limitation on the denial-of-service attack: (τ0 + ΔN F )(ρ1 + ρ2) - ρ1 < 0, we get: As time approaches infinity, V1(t) approaches zero, which means the multi-agent system reaches consensus, and thus the UAV formation achieves stable control.

[0016] As a preferred technical solution of the present invention, under the proposed dynamic event-triggered mechanism, the system will not exhibit Zeno behavior. According to the definition of measurement error, we have: Taking the derivative of the i norm of e

[0017] we get: where is the maximum value. According to the dynamic time-triggered rule and solving the corresponding differential equation, we have: where Let then ξ satisfies the following inequality: Finally, we obtain: It can be seen that only when time approaches infinity does the lower bound of ξ tend to zero. Therefore, within a finite time, ξ is greater than zero, and thus Zeno behavior will not occur.

[0018] Compared with the prior art, the beneficial effects of the present invention are:

[0019] 1. When the UAVs achieve formation control under a denial-of-service attack, compared with the traditional time-triggered mechanism, the sampling interval of the introduced dynamic event-triggered mechanism is longer. Therefore, it can better save communication resources.

[0020] 2. An adaptive coupling coefficient is introduced. Therefore, the designed control protocol is fully distributed and has good scalability.

[0021] 3. A suitable Lyapunov function is selected, and the stability of the UAV cooperative control is strictly proven. At the same time, the limiting conditions for the denial-of-service attack are accurately given. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is a schematic diagram of the architecture of the control system body of the present invention;

[0023] Figure 2 is a schematic diagram of the architecture of the model establishment platform of the present invention;

[0024] Figure 3 is a schematic diagram of the architecture of the trigger mechanism platform of the present invention;

[0025] Figure 4 is a schematic diagram of the architecture of the stability verification platform of the present invention;

[0026] Figure 5 is a flowchart of the present invention;

[0027] Figure 6 is a system communication topology diagram of the present invention;

[0028] Figure 7Information diagram of denial-of-service attack for the present invention;

[0029] Figure 8 Dynamic event trigger diagram for the present invention;

[0030] Figure 9 Static event trigger diagram for the present invention;

[0031] Figure 10 UAV position information diagram for the present invention;

[0032] Figure 11 UAV angle information diagram for the present invention;

[0033] Figure 12 Real-time flowchart for the present invention. Detailed implementation manners

[0034] Next, in combination with the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0035] Please refer to Figure 1 , the present invention provides a UAV formation cooperative control system under denial-of-service attack, including a control system body, and the control system body includes a model establishment platform, a trigger mechanism platform, and a stability verification platform;

[0036] The model establishment platform establishes a UAV formation model and a corresponding formation cooperative control model;

[0037] The trigger mechanism platform determines the dynamic event trigger rule. By introducing internal variables, the sampling interval under this dynamic event trigger mechanism is greater than that of the static event trigger mechanism;

[0038] The stability verification platform proves the stability of the cooperative control method and the absence of Zeno behavior.

[0039] The model establishment platform includes a UAV model module, a denial-of-service attack model module, and a formation flight model module. The UAV model module establishes a quadrotor UAV motion model, (p x , p y , p z ) represents the spatial position in the ground coordinate system, (φ, θ, ψ): UAV attitude angle, and the UAV kinematic equation is obtained:

[0040] Where: L Arepresents the distance from the center of gravity of the drone to the propeller, I x , I y , I z represent the moments of inertia about the X, Y, and Z axes respectively, (k1, k2, k3, k4, k5, k6) represent the drag coefficients, (T1, T2, T3, T4) represent the propeller lift forces, and T Z represents the force acting on the drone along the Z-axis. After linearization, the state equation of the drone system is: where: Note: Ω i = [gθ i , -gφ i , 0] T ,

[0041] As a preferred technical solution of the present invention, the denial-of-service attack model module assumes that {t h} is the initiation time of the attack, and τ h is the duration of the attack. Therefore, I h = [t h , t h + τ h ) is the time interval of the h-th attack. The time set in which the attack exists is defined as: The time set in which the attack does not exist is defined as: Θ = [t0, t]\Ξ. The denial-of-service attack model module includes an attack frequency unit and an attack duration unit. The attack frequency unit defines the number of attacks of N(t0, t) on (t, t0). Therefore, the attack frequency N F is defined as: On (t, t0), the duration of the attack should satisfy: |Ξ| ≤ ∈ + τ0(t - t00, where ∈ > 0, τ0(t0, t) = (t - t0)\τ a , τ a > 0. At the same time, it should be considered that due to the influence of the trigger time, the state cannot be updated in time when the attack ends. Therefore, is defined as the interval time from the end of the attack to the next trigger time, and is defined. Therefore, the actual influence time of the h-th attack is further updated: The time set in which the actual attack exists is defined as: The time set in which the actual attack does not exist is defined as:

[0042] As a preferred technical solution of the present invention, the formation flight model module considers the dynamic model of the drone system as: where x i (t) is the n-dimensional state, ui is an m-dimensional input, and at the same time, the definition of achieving consistency is given: Under a denial-of-service attack, if the states of each agent satisfy the following conditions, it means that the multi-agent system has achieved consistency, and further indicates that the drones have achieved formation flight:

[0043] As a preferred technical solution of the present invention, the trigger mechanism platform designs a dynamic event trigger mechanism to increase the event trigger interval. Design of the dynamic event trigger mechanism: where is the estimated value of the state. Design of the gain matrix K: K is the feedback gain matrix, where K = B T P, P > 0, and P satisfies: Adaptive coupling coefficient ω ij (t) satisfies: where: Q = PBB T P, Define the consistency error and the measurement error respectively as: For the convenience of subsequent derivation, define x ij : Dynamic event trigger rule: where is the trigger time, and at the same time: Here β i > 0, θ i > 0, 0 < α i < 1, Υ i (t0) > 0.

[0044] As a preferred technical solution of the present invention, the stability verification platform includes a first theorem module and a second theorem module. The first theorem module assumes that the system topology structure is an undirected graph, and requires that the dynamic time trigger parameter η i > ([1 - α i / β i ). The drones can achieve formation stability when the denial-of-service attack information satisfies the following conditions: where, ρ1 = min{(α / [2λ max (P)]),(κ i / 2)}, 2 = (β / [2λ min (P)]), κ i = η i - ([1 - α i / β i ). Proof: For stability analysis, select the Lyapunov function: where: Taking the derivative, we get: where: The following proof is divided into two cases: when the system is not under a denial-of-service attack and when it is under a denial-of-service attack, and a brief proof is given. The first case: when the system does not suffer from a denial-of-service attack

[0045] where Since Multiply both sides by Define simultaneously After further mathematical transformation, we have: Here, L is the Laplacian matrix of the topological structure, q0 is related to the triggering mechanism parameter Select Make Simplify to get: Furthermore, we have: Take According to the relationship between W and V1, we get: The second case, when the system is under a denial-of-service attack, at this time: x ij = 0, and at this time it is known that Simplify to get: At According to the relationship between W, V, and V1, further simplify to get: Based on the above two cases, without loss of generality, at t ∈ [t h + τ h + Δ, t h+1 ) we have: At t ∈ [t h , t h + τ h + Δ) we have: Considering We get According to the limitation of the denial-of-service attack by Theorem 1: (τ0 + ΔN F )(ρ1 + ρ2) - ρ1 < 0, we get: as time approaches infinity, V1(t) approaches zero, which means that the multi-agent system reaches consensus, and thus the UAV formation achieves stable control.

[0046] As a preferred technical solution of the present invention, under the proposed dynamic event-triggering mechanism, the system will not exhibit Zeno behavior. According to the definition of measurement error, we have: Take the derivative of the norm of e i (t) to get:

[0047] where is the maximum value. According to the dynamic time-triggering rule and solving the corresponding differential equation, we have: where Let Then ξ satisfies the following inequality:

[0048] Finally, we obtain:

[0049] It can be seen that only when time tends to infinity does the lower bound of ξ tend to zero. Therefore, within a finite time, ξ is greater than zero, and thus Zeno behavior does not occur.

[0050] A method for cooperative control of UAV formations according to the present invention includes the following steps:

[0051] Step 1, establish a UAV model: The model establishment platform gives the control input u i , and solve the gain matrix K;

[0052] Step 2, simulate UAV formation events: The triggering mechanism platform determines the dynamic event triggering rules;

[0053] Step 3, verify the control method: The stability verification platform proves consistency and the absence of Zeno behavior.

[0054] In the present invention, UAV formation flight means that the velocity vectors of all UAVs reach the same value, and a certain predetermined distance is maintained between the UAVs. Redefine as the difference from the ideal state. At this time, the state equation is: Combined with the attached Figure 6 , 7 , 8, 10, and 11, under the condition that the UAV system network is subject to corresponding denial-of-service attacks, the control method using the dynamic event triggering mechanism proposed in this paper realizes UAV formation flight. Combined with the attached Figure 8 and 9 , it can be seen that the triggering interval of the adopted dynamic event triggering rule is greater than that of the static event triggering rule, thereby saving network resources well.

[0055] Although the present invention has been described in detail with reference to the foregoing embodiments, for those skilled in the art, they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the protection scope of the present invention.

Claims

1. A UAV formation cooperative control system under a denial-of-service attack, including a control system body, characterized in that: The control system body includes a model establishment platform, a trigger mechanism platform, and a stability verification platform; The model establishment platform establishes a UAV formation model and a corresponding formation cooperation control model; The trigger mechanism platform introduces a dynamic event trigger rule. By introducing internal variables, the event trigger interval is increased, and the requirement for communication resources is reduced; The stability verification platform proves the stability of cooperative control and the absence of Zeno behavior; The model establishment platform includes a drone model module, a denial-of-service attack model module, and a formation flight model module. A quadrotor drone motion model is established based on the drone model module: (p x , p y , p z ) represents the spatial position in the ground coordinate system, and (φ, θ, ψ) represents the drone attitude angles, obtaining the drone kinematic equation: Among them, L A represents the distance from the center of gravity of the drone to the propeller, I x , I y , I z represent the moments of inertia about the X, Y, and Z axes respectively, (k1, k2, k3, k4, k5, k6) represent the drag coefficients, (T1, T2, T3, T4) represent the propeller lift forces, and T Z represents the force acting on the drone along the Z axis. After linearization, the state equation of the drone system is: Where: Where: Ω i = [gθ i , -gφ i , 0] T , The denial-of-service attack model module assumes that {t h} is the start time of the attack, and τ h is the duration of the attack. Therefore, I h = [t h , t h + τ h ) is the time interval of the h-th attack. The time set during which the attack exists is defined as: The time set during which the attack does not exist is defined as: Θ = [t0, t]\Ξ; The denial-of-service attack model module includes an attack frequency unit and an attack duration unit. The attack frequency unit defines the number of attacks of N(t0, t) on (t, t0). Therefore, the attack frequency N F is defined as: For the attack duration unit, on (t, t0), the duration of the attack should satisfy: |Ξ| ≤ ∈ + τ0(t - t0), where ∈ > 0, τ0(t0, t) = (t - t0)\τ a , τ a > 0. At the same time, it should be considered that due to the influence of the trigger time, the state at the end of the attack cannot be updated in a timely manner. Therefore, is defined as the interval time from the end of the attack to the next trigger time, and is defined. Therefore, is the actual impact time of the h-th attack; Further update: The time set during which the actual attack exists is defined as: The time set during which the actual attack does not exist is defined as: Design a dynamic event triggering mechanism to increase the event triggering interval. Design of the dynamic event triggering mechanism: where is the estimated value of the state. Design of the gain matrix K: K is the feedback gain matrix, where K = B T P, P > 0, P satisfies: Adaptive coupling coefficient ω ij (t) satisfies: where: Q = PBB T P, Define the consistency error and the measurement error as: Define x ij : Dynamic event triggering rule: where is the triggering moment. At the same time: Here β i > 0, θ i > 0, 0 < α i < 1, Υ i (t0) > 0.

2. The collaborative control system for UAV formation under a denial-of-service attack according to claim 1, wherein: The formation flight model module considers the dynamic model of the UAV system as follows: where x i (t) is the n-dimensional state, u i is the m-dimensional input. At the same time, the definition of achieving multi-agent consensus is given: Under a denial-of-service attack, if the states of each agent satisfy the following conditions, it means that multi-agent system consensus is achieved, and further it can be shown that the UAVs achieve formation flight:

3. A drone formation cooperative control system under a denial-of-service attack according to claim 1, characterized in that: The stable verification platform includes a first theorem module and a second theorem module; the first theorem module assumes that the system topology is an undirected graph and requires the dynamic time-triggered parameter η i >([1 - α i / β i ), and the drone formation stable control is achieved when the denial-of-service attack information satisfies the following conditions: where ρ1 = min{(α / [2λ max (P)]),(κ i / 2)}, ρ2 = (β / [2λ min (P)]), κ i = η i - ([1 - α i / β i ), and it is proved that: for stability analysis, the Lyapunov function is selected: where: Taking the derivative, we have: where: The following proof will be divided into two cases: when the system is not under a denial-of-service attack and when it is under a denial-of-service attack, and a brief proof is given; the first case: when the system does not suffer from a denial-of-service attack: Among them Since Multiply both sides by Define simultaneously After further mathematical transformation, we have: Here, L is the Laplacian matrix of the topological structure, and q0 is related to the triggering mechanism parameter. Select Make After simplification, we have: Furthermore, we have: Take According to the relationship between W and V1, we obtain: In the second case, when the system is under a denial-of-service attack, at this time: x ij = 0, it is easy to know that: For After simplification, we have: At After further simplification according to the relationship between W, V, and V1, we have: Based on the above two cases, without loss of generality, when t ∈ [t h + τ h + Δ, t h+1 ): When t ∈ [t h , t h + τ h + Δ): Considering We obtain According to the limitation of the denial-of-service attack by Theorem 1: (τ0 + ΔN F )(ρ1 + ρ2) - ρ1 < 0, we obtain: as time approaches infinity, V1(t) approaches zero, and the multi-agent system reaches consensus, thus achieving stable control of the UAV formation.

4. A drone formation cooperative control system under a denial-of-service attack according to claim 3, characterized in that: Under the proposed dynamic event trigger mechanism of the second theorem module, Zeno behavior will not occur in the system; According to the definition of measurement error, we have: For e i Taking the derivative of the (t)-norm gives: wherein is the maximum value, according to the dynamic time trigger rule and solving the corresponding differential equation, we have: wherein let then ξ satisfies the following inequality: finally, we obtain: When the time tends to infinity, the lower bound of ξ tends to zero. Therefore, within a finite time, ξ is greater than zero, and thus Zeno behavior will not occur.

5. A control method for a UAV formation cooperative control system under a denial-of-service attack, according to any one of claims 1-4, characterized in that It includes the following steps: Step 1. Establish a drone model: The model establishment platform gives the control input u i , and solve the gain matrix K; Step 2: UAV formation event simulation: The trigger mechanism platform determines the dynamic event trigger rule; Step 3: Control method verification: The stability verification platform proves the stability of cooperative control and the absence of Zeno behavior.

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