Self-adaptive elastic formation control method for quad-rotor unmanned aerial vehicles under DoS attack

Abstract

The invention provides a self-adaptive elastic formation control method for a quad-rotor unmanned aerial vehicle under DoS attack, and relates to the technical field of unmanned aerial vehicle safety control, and the method is based on a multi-aerial vehicle formation system in a leader-follower mode under an undirected network topological graph. Establishing a mathematical model for the DoS attack blocking the communication channel, and establishing a changed multi-machine system network topology according to the DoS attack; constructing a distributed elastic observer to obtain unknown leader information under DoS attack, constructing a tracking formation error containing a time-varying offset signal according to the output of the observer, and taking a neighborhood in which the formation error can be converged to zero as a control target; and designing a self-adaptive elastic formation controller by using a backstepping method to realize self-adaptive elastic formation control of the four-rotor unmanned aerial vehicle. According to the control method provided by the invention, the condition that at least one communication channel is subjected to DoS attack is considered, and the constructed adaptive elastic formation controller can ensure that the tracking formation error of the multi-machine formation system is converged to a neighborhood of zero under the DoS attack, so that an expected formation is achieved.

Description

Technical Field

[0001] The present invention relates to the field of unmanned aerial vehicle (UAV) safety control, and in particular to a method for adaptive elastic formation control of a quad-rotor UAV under DoS attack. Background Art

[0002] Quadcopter drones are small in size, light in weight, simple in structure, and low in cost. They are widely used in civil fields such as agricultural and forestry plant protection, disaster relief, and power inspection. With the development of control technology, multi-drone formation control technology can solve the limitations of load and endurance, while improving the efficiency of complex task execution, enabling them to efficiently perform military tasks such as battlefield reconnaissance and military operations. 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 interaction to synchronize the dynamics of multiple drone formations in the system. Since multi-drone formations are extremely dependent on network topology and network communication channels during flight, once attacked by malicious networks, attackers can easily steal or tamper with drone information, or even seize control of drones. Therefore, drone security control technology cannot be ignored. The present invention mainly studies DoS attacks in network attacks, which are characterized in that attackers maliciously occupy the communication resources of the target system by sending a large number of requests, causing system network congestion, thereby blocking the system network communication channel so that followers cannot obtain information about leaders and adjacent individuals. Summary of the invention

[0004] In view of the above-mentioned security problems existing in the prior art, the purpose of the present invention is to provide a method for adaptive elastic formation control of quadrotor drones under DoS attacks. The technical problem to be solved by the present invention is to ensure that the quadrotor drone formation system can achieve the desired formation under DoS attacks.

[0005] To achieve the above purpose, the technical solution provided by the present invention is: a method for controlling a quad-rotor drone's adaptive elastic formation under DoS attack, the specific method comprising:

[0006] A method for controlling an adaptive elastic formation of a quad-rotor UAV under a DoS attack is characterized in that when a DoS attack occurs, at least one communication channel in a multi-rotor formation system is blocked, and individual UAVs cannot obtain information about a leader and adjacent individuals; a distributed elastic observer is constructed so that the multi-rotor formation system can still obtain unknown leader information under a DoS attack; a fuzzy logic system is used to estimate unknown nonlinear equations of the system, and an adaptive elastic formation controller and a parameter adaptive update law are designed in combination with a backstepping method to realize adaptive elastic formation control of the quad-rotor UAV, comprising the following steps:

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

[0008] Step 2, construct the dynamic model of the leader and follower in the quadrotor UAV formation system;

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

[0010] Step 4: Build a distributed elastic observer to enable followers to estimate unknown leader information when they are attacked by DoS.

[0011] Step 5, construct the state error, and use the backstepping method and fuzzy logic system to design an adaptive elastic formation controller, so that the system can realize the adaptive elastic formation control of the quadrotor drone 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 derive a visual curve graph of the drone status in the system.

[0013] Compared with the existing multi-machine formation control method for DoS attacks, the advantages of the present invention are:

[0014] 1. A distributed elastic observer is designed, which enables followers to use the observer to estimate unknown leader information and its high-order derivatives when they are attacked by DoS, thereby ensuring the performance of the formation while reducing the computing resources consumed.

[0015] 2. A tracking formation error containing a time-varying offset signal is constructed, combined with a distributed elastic observer and a fuzzy logic system, and the controller is designed using the backstepping method, which makes the design process of the control method systematic and reduces the complexity of the control method. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The present invention is a flow chart of the design of a method for controlling a quad-rotor unmanned aerial vehicle's adaptive elastic formation under DoS attack.

[0017] Figure 2 The present invention discloses a network topology diagram of a method for adaptive elastic formation control of a quad-rotor unmanned aerial vehicle under DoS attack.

[0018] Figure 3 The present invention discloses an adaptive elastic formation control method for a quad-rotor UAV under DoS attack and a follower UAV angle tracking diagram in MATLAB simulation.

[0019] Figure 4The present invention is a method for controlling a four-rotor unmanned aerial vehicle (UAV) adaptive elastic formation under DoS attack and a follower unmanned aerial vehicle angular velocity tracking diagram in MATLAB simulation.

[0020] Figure 5 The present invention discloses a method for controlling a four-rotor unmanned aerial vehicle's adaptive elastic formation under DoS attack, and tracks a formation error tracking diagram in a MATLAB simulation.

[0021] Figure 6 It is a distributed elastic observer error tracking diagram of a four-rotor unmanned aerial vehicle adaptive elastic formation control method under DoS attack in MATLAB simulation. DETAILED DESCRIPTION

[0022] The following is a further detailed description of a method for controlling a quad-rotor drone's adaptive elastic formation under DoS attack proposed by the present invention in conjunction with the accompanying drawings and specific embodiments. The advantages and features of the present invention will become clearer based on the following description.

[0023] The specific implementation example is as follows: Step 1: Introduce graph theory, use network topology graph to describe the information interaction relationship between individual drones in a multi-drone formation system, and construct a network topology model based on the leader-follower mode under undirected graph theory:

[0024] use It represents a multi-drone formation system consisting of a virtual leader and N followers. Each drone in the system is called a node. Represents a collection of nodes. Represents a collection of node communication paths; Represents the set of neighbor nodes that can communicate normally with the i-th node, and uses the adjacency matrix Indicates the communication status between neighbor nodes. Indicates that the i-th node and the j-th node can communicate normally, otherwise In-degree matrix Indicates the number of neighbor nodes that each node can communicate with, where Represents the in-degree of the i-th node; defines the leader adjacency matrix When the i-th node can receive the leader information Use with 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 the leader information can be transmitted to the drone individual through at least one continuous channel.

[0025] Step 2: Construct the dynamic model of the leader and follower in the quadrotor UAV formation 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:

[0027]

[0028] where x i ,y i ,z i represents the location information of the i-th UAV; φ i ,θ i ,ψ i Indicates the roll angle, pitch angle and yaw angle of the drone; T i Represents the total thrust of the drone; m i and g represent the mass and gravitational acceleration of the UAV respectively; J i,x ,J i,y ,J i,z Represents the three-axis moment of inertia of the drone; I i,x ,I i,y ,I i,z ,I i,φ ,I i,θ ,I i,ψ Indicates the air resistance coefficient; U i,φ ,U i,θ ,U i,ψ Represents the attitude control torque of the drone. Since the dynamic model of the quadcopter drone is strictly feedback, 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 quadrotor drone can be rewritten as:

[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 represents the control input of the i-th UAV; y i,k represents the system output of the i-th UAV.

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

[0033]

[0034] where Λ 0,k Represents the state of the leader drone, y 0,k represents the system output of the leader drone, A∈R m×m , C∈R m are the known system matrices and vectors respectively; in order to achieve the expected multi-machine formation control, the time-varying formation offset vector is defined Each of these They are all continuously divisible.

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

[0036] For any definition represents the duration of the mth DoS attack that cuts off the communication channel between the i-th UAV and the j-th UAV, where and Respectively represent the start time and end time of the mth DoS attack, represents the duration of the mth DoS attack; the time set when the i-th and j-th drones are affected by the DoS attack is defined as Create a DoS attack time series collection:

[0037]

[0038] where Σ D (t0,t) represents the time series set in which at least one communication channel in the multi-aircraft formation system is blocked by DoS attack, Σ N (t0, t) represents the time series set of normal communication of multi-machine formation system. Since DoS attack requires energy support, in order to conform to the actual situation, it is assumed that there is a constant Make

[0039] When a DoS attack occurs, the system network topology changes accordingly. The specific changes are as follows:

[0040]

[0041] Defining control objectives: Establishing tracking formation errors The controller is designed so that the tracking formation error of the multi-aircraft formation system can converge to the neighborhood of zero under DoS attack.

[0042] Step 4: Build a distributed elastic observer. The specific method is as follows:

[0043] When a multi-machine formation system is attacked by DoS, at least one communication channel in the system will be blocked, and the follower drone may not be able to receive the leader information. The present invention constructs a distributed elastic observer so that the follower drone affected by the DoS attack can estimate the leader information. The distributed elastic observer of the i-th follower drone is designed as:

[0044]

[0045]

[0046] where ρ i,k and γ i,k All represent normal numbers to be designed; Indicates that the communication channel between the i-th UAV and the leader is blocked by DoS attack, otherwise Λ i,k represents the estimated value of the leader information, state ξ i,k,1 ,ξ i,k,2 ,...,ξ i,k,n-1 To calculate Λ i,k The higher order derivatives of .

[0047] Step 5: Combined with the above distributed elastic observer, the state error is constructed and the adaptive elastic formation controller is designed using the backstepping method. The specific method is as follows:

[0048] When the multi-aircraft formation system is attacked by DoS, the adjacency matrix coefficients between the affected UAVs become zero, resulting in regular formation errors. The first term is discontinuous, so the backstepping method cannot be used to design the controller. To solve this problem, the present invention uses the dynamic model (1) of the follower drone and the Λ calculated by the distributed elastic observer (4) i,k , define the tracking state error:

[0049]

[0050] where α i,k Represents a virtual controller;

[0051] Step 1: According to formulas (1), (4) and (5), we can get z i,k,1 The derivative of is:

[0052]

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

[0054]

[0055] Designing a virtual controller α i,k :

[0056]

[0057] Among them, k i,k,1 is a constant to be designed that is greater than zero;

[0058] Step 2: According to formula (1) and (5), we can get z i,k,2 The derivative of is:

[0059]

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

[0061]

[0062] Among them, r i,k is a constant to be designed that is greater than zero, represents the estimation error, represents the adaptive parameter, Represents the pair Θ i,k The estimated value of ω i,k The weight vector representing the fuzzy logic system;

[0063] Derivative of formula (10):

[0064]

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

[0066]

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

[0068]

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

[0070]

[0071] Substituting formula (14) into formula (13), we can 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] From formula (18), we can see that 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 the adaptive law (16), the formation error can be tracked. It can converge to the neighborhood of zero, that is, the multi-aircraft formation system can reach the desired formation and achieve the control goal under DoS attack.

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

[0079] A multi-rotor formation system is composed of a leader quadrotor UAV and three follower quadrotor UAVs. 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 UAV in the formation process, and a visualized state curve diagram of each UAV in the multi-machine formation system under DoS attack is obtained.

[0080] The advantage is that, by designing a distributed elastic observer, the follower can use the observer to estimate the unknown leader information and its high-order derivatives when it is attacked by DoS, thereby ensuring the formation performance while reducing the computing resources consumed; by constructing a tracking formation error containing a time-varying offset signal, combining a distributed elastic observer and a fuzzy logic system, and using the backstepping method to design the controller, the design process of the control method is systematized and the complexity of the control method is reduced; under the action of the proposed adaptive elastic formation control method for quadrotor UAVs, the multi-machine formation system can achieve the desired formation under DoS attacks and achieve the control goal.

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

Claims

1. A method for adaptive elastic formation control of a quadrotor drone under DoS attack, characterized in that: When the followers are attacked by DoS, the unknown leader information is estimated by using the distributed elastic observer, and the adaptive elastic formation controller and parameter adaptive update law are designed by using the backstepping method and fuzzy logic system to realize the adaptive elastic formation control of the quadrotor UAV, so that the tracking formation error converges to the neighborhood of zero and achieves the desired formation, including the following steps: Step 1: Introduce graph theory and build a network topology model of leader-follower mode based on undirected graph to describe the communication relationship between multiple drones; Step 2, construct the dynamic model of the leader and follower in the quadrotor UAV formation system; Step 3: Establish a mathematical model of DoS attack and the network topology after DoS attack, establish the tracking formation error, and define the control target; Step 4: Build a distributed elastic observer to enable followers to estimate unknown leader information when they are attacked by DoS. Step 5, construct the state error, and use the backstepping method and fuzzy logic system to design an adaptive elastic formation controller, so that the system can realize the adaptive elastic formation control of the quadrotor drone under DoS attack, and make the tracking formation error converge to the neighborhood of zero; Step 6: Use MATLAB to simulate and verify the adaptive elastic formation control method of a quadrotor drone under DoS attack, and derive a visual curve graph of the drone status in the system.

2. The method for controlling a quad-rotor drone's adaptive elastic formation under DoS attack according to claim 1, characterized in that: Step 1: Introduce graph theory, use network topology to describe the information interaction relationship between individual drones in a multi-drone formation system, and construct a network topology model based on the leader-follower mode under undirected graph theory: use It represents a multi-drone formation system consisting of a virtual leader and N followers. Each drone in the system is called a node. Represents a collection of nodes. Represents a collection of node communication paths; Represents the set of neighbor nodes that can communicate normally with the i-th node, and uses the adjacency matrix Indicates the communication status between neighbor nodes. Indicates that the i-th node and the j-th node can communicate normally, otherwise In-degree matrix Indicates the number of neighbor nodes that each node can communicate with, where Represents the in-degree of the i-th node; defines the leader adjacency matrix When the i-th node can receive the leader information Use with 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 the leader information can be transmitted to the drone individual through at least one continuous channel.

3. The method for controlling a quad-rotor drone's adaptive elastic formation under DoS attack according to claim 1, characterized in that: Step 2: Construct the dynamic model of the leader and follower in the quadrotor UAV formation system. The specific method is as follows: (1) The dynamic model of the i-th follower UAV in the multi-aircraft formation system is described as: where x i ,y i ,z i represents the location information of the i-th UAV; φ i ,θ i ,ψ i Indicates the roll angle, pitch angle and yaw angle of the drone; T i Represents the total thrust of the drone; m i and g represent the mass and gravitational acceleration of the UAV respectively; J i,x ,J i,y ,J i,z Represents the three-axis moment of inertia of the drone; I i,x ,I i,y ,I i,z ,I i,φ ,I i,θ ,I i,ψ Indicates the air resistance coefficient; U i,φ ,U i,θ ,U i,ψ Represents the attitude control torque of the drone. Since the dynamic model of the quadcopter drone is strictly feedback, the following variables are defined: (x i,1,1 ,x i,2,1 ,…,x i,6,1 )=(x i ,y i ,z i ,f i ,i i ,ψ i ), The dynamic model of the quadrotor drone can be rewritten as: 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 represents the control input of the i-th UAV; y i,k represents the system output of the i-th UAV; (2) The leader system is described as: where Λ 0,k represents the state of the leader drone, y 0,k represents the system output of the leader drone, A∈R m×m , C∈R m are the known system matrices and vectors respectively; in order to achieve the expected multi-machine formation control, the time-varying formation offset vector is defined Each of these They are all continuously divisible.

4. The method for controlling a quad-rotor drone's adaptive elastic formation under DoS attack according to claim 1, characterized in that: Step 3: Establish a mathematical model of DoS attack and the network topology after DoS attack, establish the tracking formation error, and define the control target. The specific method is as follows: For any definition represents the duration of the mth DoS attack that cuts off the communication channel between the i-th UAV and the j-th UAV, where and Respectively represent the start time and end time of the mth DoS attack, represents the duration of the mth DoS attack; the time set when the i-th and j-th drones are affected by the DoS attack is defined as Create a DoS attack time series collection: where Σ D (t0,t) represents the time series set in which at least one communication channel in the multi-aircraft formation system is blocked by DoS attack, Σ N (t0, t) represents the time series set of normal communication of multi-machine formation system; since DoS attack requires energy support, in order to conform to the actual situation, it is assumed that there is a constant Make When a DoS attack occurs, the system network topology changes accordingly. The specific changes are as follows: Defining control objectives: Establishing tracking formation errors The controller is used to make the tracking formation error of the multi-aircraft formation system converge to the neighborhood of zero under DoS attack.

5. The method for controlling a quad-rotor drone's adaptive elastic formation under DoS attack according to claim 1, characterized in that: Step 4: Build a distributed elastic observer. The specific method is as follows: When a multi-machine formation system is attacked by DoS, at least one communication channel in the system will be blocked, and the follower drone may not be able to receive the leader information. The present invention constructs a distributed elastic observer so that the follower drone affected by the DoS attack can estimate the leader information. The distributed elastic observer of the i-th follower drone is designed as: where ρ i,k and γ i,k All represent normal numbers to be designed; Indicates that the communication channel between the i-th UAV and the leader is blocked by DoS attack, otherwise Λ i,k represents the estimated value of the leader information, state ξ i,k,1 ,ξ i,k,2 ,...,ξ i,k,n-1 To calculate Λ i,k The higher order derivatives of .

6. The method for controlling a quad-rotor drone's adaptive elastic formation under DoS attack according to claim 1, characterized in that: Step 5: Combined with the above distributed elastic observer, the state error is constructed and the adaptive elastic formation controller is designed using the backstepping method. The specific method is as follows: When the multi-aircraft formation system is attacked by DoS, the adjacency matrix coefficients between the affected drones become zero, resulting in conventional distributed formation errors. The first term is discontinuous, so the backstepping method cannot be used to design the controller. To solve this problem, the present invention uses the dynamic model (1) of the follower drone and the Λ calculated by the distributed elastic observer (4) i,k , define the tracking state error: where α i,k Represents a virtual controller; Step 1: According to formulas (1), (4) and (5), we can get z i,k,1 The derivative of is: Design of Lyapunov function V i,k,1 : Designing a virtual controller α i,k : Among them, k i,k,1 is a constant to be designed that is greater than zero; Step 2: According to formula (1) and (5), we can get z i,k,2 The derivative of is: Design of Lyapunov function V i,k : Among them, r i,k is a constant to be designed that is greater than zero, represents the estimation error, represents the adaptive parameter, Represents the pair Θ i,k The estimated value of ω i,k The weight vector representing the fuzzy logic system; Derivative of formula (10): Introducing fuzzy logic system to estimate the nonlinear term F of the system i,k : in and is a constant to be designed that is greater than zero; then formula (11) can be rewritten as: According to Young's inequality, we have: Substituting formula (14) into formula (13), we can design the controller u i,k and Adaptive Law According to formulas (15), (16) and Young's inequality, we have: choose and have: From formula (18), we can see that 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 the adaptive law (16), the formation error can be tracked. It can converge to the neighborhood of zero, that is, the multi-aircraft formation system can reach the desired formation under DoS attack and achieve the control goal.

7. The method for controlling a quad-rotor drone's adaptive elastic formation under DoS attack according to claim 1, characterized in that: Step 6: To verify the reliability of the above control method, a simulation experiment is performed using MATLAB. The specific method is as follows: A multi-rotor formation system is composed of a leader quadrotor UAV and three follower quadrotor UAVs. 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 UAV in the formation process, and a visualized state curve of each UAV in the multi-rotor formation system under DoS attack is obtained.

Images