A method for adaptive flexible formation control of quadrotor unmanned aerial vehicles under DoS attack

Abstract

The application provides a kind of DoS attack under quad-rotor unmanned aerial vehicle adaptive flexible formation control method, it is related to unmanned aerial vehicle safety control technical field, this method is based on the multi-machine formation system of leader-follower mode under undirected network topology diagram, for the DoS attack of blocking communication channel establishes mathematical model and according to DoS attack establishes the network topology of changed multi-machine system;Distributed flexible observer is constructed to obtain unknown leader information under DoS attack, and the tracking formation error containing time-varying offset signal is constructed according to the output of the observer, and the neighborhood where the formation error can converge to zero is taken as the control target;Adaptive flexible formation controller is designed by using backstepping method, and adaptive flexible formation control of quad-rotor unmanned aerial vehicle is realized.The control method proposed in the application considers the case that at least one communication channel is attacked by DoS, and the adaptive flexible formation controller constructed can ensure that the tracking formation error of multi-machine formation system converges to the neighborhood of zero under DoS attack, and the desired formation is achieved.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) security control, specifically to an adaptive elastic formation control method for quadrotor UAVs under DoS attacks. Background Technology

[0002] Quadcopter drones are characterized by their small size, light weight, simple structure, and low cost, and are widely used in civilian fields such as agricultural and forestry plant protection, disaster relief, and power line inspection. With the development of control technology, multi-drone formation control technology can overcome limitations in payload and endurance, while improving the efficiency of complex missions, enabling them to efficiently perform military tasks such as battlefield reconnaissance and combat. Multi-drone formation control has become an important research direction in the field of drones.

[0003] The core idea of ​​multi-drone formation control is to update the status of each drone through individual information exchange, thereby achieving dynamic synchronization of multiple drones within the system. Since multi-drone formations are highly dependent on network topology and communication channels during flight, attackers can easily steal or tamper with drone information, or even seize control of the drones, once subjected to malicious network attacks. Therefore, drone security control technology cannot be ignored. This invention primarily studies DoS attacks in network attacks, characterized by attackers maliciously occupying the target system's communication resources by sending a large number of requests, causing network congestion and thus blocking the system's network communication channels, preventing followers from obtaining information from the leader and neighboring drones. Summary of the Invention

[0004] To address the aforementioned security issues in existing technologies, the present invention aims to provide an adaptive elastic formation control method for quadcopter drones under DoS attacks. The technical problem to be solved by the present invention is to ensure that the quadcopter drone formation system can achieve the desired formation under DoS attacks.

[0005] To achieve the above objectives, the technical solution provided by this invention is: an adaptive elastic formation control method for quadcopter drones under DoS attacks, the specific method including:

[0006] An adaptive elastic formation control method for quadrotor UAVs under DoS attacks is characterized by the following steps: When a DoS attack occurs, at least one communication channel within the multi-UAV formation system is blocked, preventing individual UAVs from acquiring information about the leader and neighboring UAVs; a distributed elastic observer is constructed to enable the multi-UAV formation system to still acquire unknown leader information under DoS attacks; a fuzzy logic system is used to estimate the unknown nonlinear equations of the system, and an adaptive elastic formation controller and parameter adaptive update law are designed using the backstepping method to achieve adaptive elastic formation control of the quadrotor UAVs.

[0007] Step 1: Introduce graph theory and construct a leader-follower network topology model based on undirected graphs to describe the communication relationships between multiple drones;

[0008] Step 2: Construct dynamic models of the leader and followers in a quadcopter drone swarm system;

[0009] Step 3: Establish a mathematical model of the DoS attack and the network topology after the DoS attack, establish tracking formation error, and define control objectives;

[0010] Step 4: Build a distributed resilient observer to estimate unknown leader information when followers are subjected to DoS attacks.

[0011] Step 5: Construct state error, and design an adaptive elastic formation controller using backstepping method and fuzzy logic system, so that the system can achieve adaptive elastic formation control of quadcopter UAV under DoS attack, and make the tracking formation error converge to the neighborhood of zero.

[0012] Step 6: Use MATLAB to simulate and verify the proposed control algorithm, and export a visual curve of the UAV state within the system.

[0013] Compared to existing multi-machine swarm control methods for DoS attacks, the advantages of this invention are:

[0014] 1. A distributed elastic observer is designed, which enables followers to estimate unknown leader information and its higher-order derivatives when subjected to DoS attacks, thus ensuring formation performance while reducing computational resources.

[0015] 2. A tracking formation error incorporating time-varying offset signals is constructed. Combined with a distributed elastic observer and a fuzzy logic system, the controller is designed using the backstepping method, which systematizes the design process of the control method and reduces its complexity. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the design of an adaptive elastic formation control method for quadrotor drones under DoS attacks, as per the present invention.

[0017] Figure 2 This is a network topology diagram of an adaptive elastic formation control method for quadrotor drones under DoS attacks, as described in this invention.

[0018] Figure 3 This invention relates to an adaptive elastic formation control method for quadrotor UAVs under DoS attacks, and the following UAV angle tracking diagram is shown in a MATLAB simulation.

[0019] Figure 4This invention relates to an adaptive elastic formation control method for quadrotor UAVs under DoS attacks, and the angular velocity tracking diagram of a follower UAV in a MATLAB simulation.

[0020] Figure 5 This invention relates to an adaptive elastic formation control method for quadrotor UAVs under DoS attacks, which tracks formation error in a MATLAB simulation.

[0021] Figure 6 This is an error tracking diagram of a distributed elastic observer in MATLAB simulation of an adaptive elastic formation control method for quadrotor UAVs under DoS attack according to the present invention. Detailed Implementation

[0022] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, provides a further detailed explanation of the adaptive elastic formation control method for quadrotor UAVs under DoS attacks proposed in this invention. The advantages and features of this invention will become clearer from the following description.

[0023] The specific implementation is as follows: Step 1, introduce graph theory, use network topology graphs to describe the information interaction relationships between individual UAVs in a multi-UAV formation system, and construct a network topology model based on the leader-follower pattern under undirected graph theory:

[0024] use This represents a multi-drone formation system consisting of a virtual leader and N followers. Each individual drone in the system is called a node. Represents a set of nodes. Represents the set of node communication paths; using Represents the set of neighboring nodes that can communicate normally with the i-th node, and uses an adjacency matrix. Indicates the communication status between neighboring nodes, when This indicates that the i-th node and the j-th node can communicate normally; otherwise... Use the in-degree matrix This represents the number of neighboring nodes that each node can communicate with, where Let the in-degree of the i-th node be represented; define the leader adjacency matrix. When the i-th node can receive the leader information and use This represents the in-degree, adjacency, and leader adjacency of each node in the system. To ensure the connectivity of the network topology, it is assumed that leader information can be transmitted to individual drones through at least one continuous channel.

[0025] Step 2: Construct dynamic models of the leader and followers in the quadcopter drone swarm system. The specific method is as follows:

[0026] (1) The dynamic model of the i-th follower UAV in the multi-aircraft formation system is described as follows:

[0027]

[0028] Where x i ,y i ,z i φ represents the location information of the i-th drone; i ,θ i ,ψ i This indicates the roll, pitch, and yaw angles of the drone; T i Indicates the total thrust of the drone; m i and g represent the mass and gravitational acceleration of the drone, respectively; J i,x J i,y J i,z Indicates the three-axis rotational inertia of the drone; I i,x ,I i,y ,I i,z ,I i,φ ,I i,θ ,I i,ψ U represents the air drag coefficient; i,φ U i,θ U i,ψ This represents the attitude control torque of the drone. Since the dynamic model of a quadcopter drone is strictly feedback-based, the following variables are defined:

[0029] (x i,1,1 ,x i,2,1 ,,x i,6,1 )=(x i ,y i ,z i ,φ i ,θ i ,ψ i ), The dynamic model of the quadcopter drone can be rewritten as follows:

[0030]

[0031] Where i = 1, 2, ..., N represents the index number of the i-th UAV; k = 1, 2, ..., 6 represents the x, y, z, φ, θ, ψ position and attitude subsystems, respectively; u i,k y represents the control input for the i-th UAV; i,k This represents the system output of the i-th drone.

[0032] (2) The leader system is described as follows:

[0033]

[0034] Among them Λ 0,k Indicates the status of the leader's drone, y 0,k The system output of the leader drone, A∈R m×m C∈R m These are the known system matrix and vector; to achieve the desired multi-machine formation control, a time-varying formation offset vector is defined. Each of them All are continuously differentiable.

[0035] Step 3: Establish a mathematical model of the DoS attack and the network topology after the DoS attack, establish tracking formation error, and define the control target. The specific method is as follows:

[0036] For any definition This represents the duration of the m-th DoS attack that cuts off the communication channels between the i-th and j-th drones, where... and These represent the start and end times of the m-th DoS attack, respectively. Let m represent the duration of the m-th DoS attack; define the set of times when the i-th and j-th drones are affected by the DoS attack as . Establish a DoS attack time series set:

[0037]

[0038] Where Σ D (t0,t) represents the time series set in which at least one communication channel in a multi-machine formation system is blocked by a DoS attack, Σ N (t0,t) represents the time series set of normal communication in a multi-machine swarm system. Since DoS attacks require energy support, to conform to reality, we assume the existence of a constant. Make

[0039] When a DoS attack occurs, the system network topology changes accordingly, specifically as follows:

[0040]

[0041] Define the control objective: Establish tracking formation error The controller is designed so that the tracking formation error of the multi-machine formation system can converge to the neighborhood of zero under a DoS attack.

[0042] Step 4, construct a distributed resilience observer, the specific method is as follows:

[0043] When a multi-drone formation system is subjected to a DoS attack, at least one communication channel within the system will be blocked, and follower drones may be unable to receive leader information. This invention constructs a distributed elastic observer to enable follower drones affected by a DoS attack to estimate leader information. The distributed elastic observer for the i-th follower drone is designed as follows:

[0044]

[0045]

[0046] Where ρ i,k and γ i,k Both represent positive constants to be designed; This indicates that the communication channel between the i-th drone and the leader has been blocked by a DoS attack; otherwise... Λ i,k This represents an estimated value of the leader's information, state ξ. i,k,1 ,ξ i,k,2 ,...,ξ i,k,n-1 Used to calculate Λ i,k The higher-order derivatives of .

[0047] Step 5: Combining the distributed resilient observer described above, an adaptive resilient formation controller is designed using the backstepping method by constructing state errors. The specific method is as follows:

[0048] When a multi-drone formation system is subjected to a DoS attack, the adjacency matrix coefficients between the affected drones become zero, leading to normal formation errors. Its first term is discontinuous, therefore the backstepping method cannot be used to design a controller. To solve this problem, the present invention uses the dynamic model (1) of the follower UAV and Λ calculated by the distributed elastic observer (4) to... i,k Define the tracking state error:

[0049]

[0050] Where α i,k Indicates a virtual controller;

[0051] Step 1: From formulas (1), (4) and (5), we can obtain z i,k,1 The derivative is:

[0052]

[0053] Design the Lyapunov function V i,k,1 :

[0054]

[0055] Design a virtual controller αi,k :

[0056]

[0057] Where, k i,k,1 The design constant is greater than zero;

[0058] Step 2: From formulas (1) and (5), we can obtain z i,k,2 The derivative is:

[0059]

[0060] Design the Lyapunov function V i,k :

[0061]

[0062] Where, r i,k For the design constant that is greater than zero, Indicates the estimation error. Indicates adaptive parameters, Indicates the relationship between Θ i,k The estimated value, ω i,k Represents the weight vector of a fuzzy logic system;

[0063] Differentiate formula (10):

[0064]

[0065] Introducing fuzzy logic system to estimate the system nonlinear term F i,k :

[0066]

[0067] in And since it is a constant greater than zero, formula (11) can be rewritten as:

[0068]

[0069] According to Young's inequality, we have:

[0070]

[0071] Substituting formula (14) into formula (13), we design the controller u. i,k And adaptive law

[0072]

[0073] According to formulas (15), (16) and Young's inequality, we have:

[0074]

[0075] choose and have:

[0076]

[0077] As can be seen from formula (18), by constructing a distributed elastic observer (4), designing the state error (5), and using the backstepping method and fuzzy logic system to design the controller (15) and adaptive law (16), the formation error can be tracked. The neighborhood that can converge to zero means that a multi-machine formation system can achieve the desired formation under a DoS attack and achieve the control objective.

[0078] Step 6: To verify the reliability of the above control method, a simulation experiment is conducted using MATLAB. The specific method is as follows:

[0079] A multi-drone formation system is formed by one leader quadcopter drone and three follower quadcopter drones. The leader is represented by "Leader" and the followers are represented by "1,2,3". The expected distance between the followers is time-varying. MATLAB is used to visualize the state of each drone during the formation process, and the visualized state curve of each drone in the multi-drone formation system under DoS attack is obtained.

[0080] The advantages are as follows: by designing a distributed elastic observer, followers can estimate unknown leader information and its higher-order derivatives when subjected to DoS attacks, ensuring formation performance while reducing computational resources; by constructing a tracking formation error containing time-varying offset signals, combined with a distributed elastic observer and a fuzzy logic system, and using backstepping for controller design, the design process of the control method is systematized, reducing the complexity of the control method; under the proposed adaptive elastic formation control method for quadrotor UAVs, the multi-aircraft formation system can achieve the desired formation under DoS attacks, realizing the control objective.

[0081] The above description is merely a description of preferred embodiments of the present invention and is not intended to limit the scope of the present invention in any way. Any changes or modifications made by those skilled in the art based on the above disclosure shall fall within the protection scope of the claims.

Claims

1. A method for adaptive elastic formation control of quadrotor UAVs under DoS attacks, characterized in that, When the follower is under a DoS attack, the unknown leader information is estimated using a distributed elastic observer (4). An adaptive elastic formation controller and parameter adaptive update law are designed using the backstepping method and fuzzy logic system to realize the adaptive elastic formation control of the quadcopter UAV, so that the tracking formation error converges to the neighborhood of zero and the desired formation is achieved. The steps include: Step 1: Introduce graph theory and construct a leader-follower network topology model based on undirected graphs to describe the communication relationships between multiple drones; Step 2, construct the dynamic model of the leader and follower in the quadcopter UAV formation system (1); Step 3: Establish a mathematical model of the DoS attack and the network topology after the DoS attack, establish tracking formation error, and define control objectives; Step 4: Construct a distributed resilient observer (4) to enable followers to estimate unknown leader information when they are subjected to DoS attacks; Step 5: Construct state error, and design an adaptive elastic formation controller using backstepping method and fuzzy logic system, so that the system can achieve adaptive elastic formation control of quadcopter UAV under DoS attack, and make the tracking formation error converge to the neighborhood of zero. Step 6: Use MATLAB to simulate and verify an adaptive elastic formation control method for quadrotor UAVs under DoS attack, and export a visualization curve of the UAV state within the system. Step 4, construct the distributed elastic observer (4), the specific method is as follows: When a multi-drone formation system is subjected to a DoS attack, at least one communication channel within the system will be blocked, and follower drones may not be able to receive leader information. By constructing a distributed resilient observer (4), the follower drones affected by the DoS attack can estimate the leader information. The distributed elastic observer (4) for each follower drone is: (4) in and Both represent positive constants to be designed; Indicates the first The communication channel between the drone and the leader was blocked by a DoS attack; otherwise ; This represents an estimated value of the leader's information, and their status. Used to calculate The higher-order derivatives; Step 1: Introduce graph theory and use network topology graphs to describe the information interaction relationships between individual UAVs in a multi-UAV formation system, constructing a network topology model based on the leader-follower pattern under undirected graph theory: use It indicates that it is led by a virtual leader and A multi-drone formation system consisting of several followers, where each individual drone is called a node. Represents a set of nodes. Represents the set of node communication paths; using Indicates that it can be used with the first The set of neighboring nodes that a node can communicate with normally, and an adjacency matrix is ​​used to define this set. Indicates the communication status between neighboring nodes, when Indicates the first The node and the first Each node can communicate normally; otherwise... ; using the in-degree matrix This represents the number of neighboring nodes that each node can communicate with, where Indicates the first The in-degree of each node; define the leader adjacency matrix. When the first When a node can receive leader information and use This represents the in-degree, adjacency, and leader adjacency of each node in the system; to ensure the connectivity of the network topology, it is assumed that leader information can be transmitted to individual drones through at least one continuous channel. Step 2, construct the dynamic model of the leader and followers in the quadcopter UAV formation system (1), the specific method is as follows: The dynamic model of the follower (1) in a multi-aircraft formation system The dynamic model of a follower (1) is described as follows: (1) in Indicates the first Location information of each drone; This indicates the roll, pitch, and yaw angles of the drone; This indicates the total thrust of the drone; and These represent the mass and gravitational acceleration of the drone, respectively. This represents the three-axis rotational inertia of the drone; Indicates the air drag coefficient; The torque representing the attitude control of the UAV is defined by the following variables, since the dynamic model of the follower (1) is strictly feedback: ， ， ， The dynamic model of the follower (1) can be rewritten as: (2) in Indicates the first The index number of each drone; They represent Position and attitude subsystem; Indicates the first Control inputs for a drone; Indicates the first The system output of the drone; (2) The leader system is described as follows: (3) in Indicates the status of the leader's drone. This indicates the system output of the leader drone. , These are the known system matrix and vector; to achieve the desired multi-machine formation control, a time-varying formation offset vector is defined. Each of them All are continuously differentiable.

2. The adaptive elastic formation control method for quadrotor UAVs under DoS attacks according to claim 1, characterized in that, Step 3: Establish a mathematical model of the DoS attack and the network topology after the DoS attack, establish tracking formation error, and define the control target. The specific method is as follows: For any ,definition Indicates cutting off the first The drone and the first The first drone communication channel Duration of the DoS attack, among which and They represent the first The start and end times of this DoS attack. Indicates the first The duration of the DoS attack; Definition of the first , The set of times when drones were affected by DoS attacks is Establish a DoS attack time series set: in This represents the set of time series in a multi-machine formation system where at least one communication channel is blocked by a DoS attack. This represents the time series set indicating normal communication in a multi-machine swarm system; since DoS attacks require energy support, to reflect reality, we assume the existence of a constant. , making ; When a DoS attack occurs, the system network topology changes accordingly, specifically as follows: Define the control objective: Establish tracking formation error By utilizing the controller, the tracking formation error of the multi-machine formation system can converge to the neighborhood of zero under DoS attack.

3. The adaptive elastic formation control method for quadrotor UAVs under DoS attacks according to claim 2, characterized in that, Step 5: Combining the distributed elastic observer (4) described above, an adaptive elastic formation controller is designed using the backstepping method by constructing state errors. The specific method is as follows: When a multi-drone formation system is subjected to a DoS attack, the adjacency matrix coefficients between affected drones become zero, leading to normal distributed formation errors. Its first term is discontinuous, therefore the backstepping method cannot be used to design a controller. Therefore, based on the follower's dynamic model (1) and the calculation by the distributed elastic observer (4), Define the tracking state error: (5) in Indicates a virtual controller; Step 1: From formulas (1), (4) and (5), we can obtain The derivative is: (6) Design a Lyapunov function. : (7) Design a virtual controller : (8) in, The design constant is greater than zero; Step 2: From formulas (1) and (5), we can obtain The derivative is: (9) Design a Lyapunov function. : (10) in, For the design constant that is greater than zero, Indicates the estimation error. Indicates adaptive parameters, Indicates to The estimated value, Represents the weight vector of a fuzzy logic system; Differentiate formula (10): (11) Introducing fuzzy logic system to estimate system nonlinear terms : (12) in , And it is a design constant that is greater than zero; then formula (11) can be rewritten as: (13) According to Young's inequality, we have: (14) Substitute formula (14) into formula (13) to design the controller. And adaptive law : (15) (16) According to formulas (15), (16) and Young's inequality, we have: (17) choose and ,have: (18) As can be seen from formula (18), by constructing a distributed elastic observer (4), designing the state error (5), and using the backstepping method and fuzzy logic system to design the controller (15) and adaptive law (16), the formation error can be tracked. The neighborhood that can converge to zero means that a multi-machine formation system can achieve the desired formation under a DoS attack and achieve the control objective.

4. The adaptive elastic formation control method for quadrotor UAVs under DoS attacks according to claim 3, characterized in that, Step 6: To verify the reliability of the above control method, a simulation experiment is conducted using MATLAB. The specific method is as follows: A multi-drone formation system is formed by one leader quadcopter drone and three follower quadcopter drones. The leader is represented by "Leader" and the followers are represented by "1,2,3". The expected distance between the followers is time-varying. MATLAB is used to visualize the state of each drone during the formation process, and the visualized state curve of each drone in the multi-drone formation system under DoS attack is obtained.

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