CN116820100B - Unmanned vehicle formation control method under spoofing attack - Google Patents

Abstract

The invention discloses an unmanned vehicle formation control method under spoofing attack, which comprises the following steps: (1) Taking an unmanned vehicle as a communication node, and establishing a communication topological relation according to the communication node; (2) Constructing a system dynamic model of the unmanned vehicle, wherein the system dynamic model comprises a pilot and follower system dynamic models; (3) Establishing a deception attack dynamic model by considering network security problems; (4) The time-varying formation control protocol based on the pulse attack signal compensator is provided, and a corresponding dynamic error system model is established; (5) Based on the Liapunov theory, a sufficient condition for stabilizing an error system is given, and a formation tracking error boundary is obtained. The control method provided by the invention can realize time-varying output formation under the condition of ensuring certain precision, can reduce the traffic of an actual system, and can effectively resist deception attack.

Description

A method of unmanned vehicle formation control under deception attack

Technical field

The invention belongs to the field of unmanned vehicle collaborative formation control, and in particular relates to an unmanned vehicle formation control method under deception attack.

Background technique

An unmanned vehicle is an intelligent system that can complete tasks autonomously. In an unmanned vehicle, multiple unmanned vehicles can collaborate to complete more complex tasks and leverage their respective advantages in the system. Unmanned vehicles do not require direct operation by personnel and can work in complex or dangerous environments. They have many advantages, such as efficiency, safety, and convenience. Therefore, unmanned vehicles are widely used in military, civilian, industrial, scientific research and other fields. In the military field, unmanned vehicles can be used for reconnaissance, surveillance, strike and other tasks, which can improve combat efficiency and ensure combat safety. In the civilian field, unmanned vehicles can be used in logistics, transportation, environmental protection and other fields, which can improve work efficiency and reduce the waste of human resources. Among them, time-varying output formation is one of the important research directions in unmanned vehicles. Its goal is to enable a group of unmanned vehicles to complete specific tasks in a dynamic environment in a certain form and pattern, such as air-ground coordinated reconnaissance, coordinated guidance, etc. . The time-varying output formation of unmanned vehicles is of vital significance in many fields such as manufacturing and military. Improving the operating efficiency and performance of unmanned vehicles and the robustness of time-varying output formations has become a key issue in current research.

However, as the application scale of unmanned vehicles continues to expand, unmanned vehicle formation technology is also facing network security challenges. Malicious attackers may use deception attacks to interfere with the normal operation of unmanned vehicle formations, resulting in unmanned vehicle formations. s failure. Therefore, resisting the impact of spoofing attacks and ensuring the reliability and security of autonomous vehicle perception and decision-making systems have become one of the important directions for autonomous vehicle research.

Among the control methods for the time-varying output formation of unmanned vehicles, many existing continuous control methods will inevitably increase the network communication burden in some cases, which is caused by the large-scale distributed communication of unmanned vehicles. . However, the pulse control protocol is adopted so that each unmanned vehicle independently receives neighbor status information only at the sampling instant. Information transmission can be greatly reduced, thereby reducing network communication burden and the risk of communication loss.

It should be pointed out that in the face of limited network security and resources, exploring time-varying output formation control methods for unmanned vehicles that resist attacks and reduce communication burdens is an urgent problem that needs to be solved.

Contents of the invention

Purpose of the invention: The purpose of the present invention is to provide a method for controlling the formation of unmanned vehicles under deception attacks, which can enable the unmanned vehicles to achieve the desired time-varying formation configuration while maintaining a certain accuracy, and can reduce the communication volume of the actual system. At the same time, it effectively resists spoofing attacks.

Technical solution: An unmanned vehicle formation control method under deception attack of the present invention includes the following steps:

Step 1: Use an unmanned vehicle as a communication node, establish a communication topology relationship based on several communication nodes, and define the coupling weight of the leader and follower in the unmanned vehicle formation;

Step 2: Construct a leader system dynamic model and a follower system dynamic model in the unmanned vehicle formation based on communication topology relationships and coupling weights;

Step 3: Based on the leader system dynamic model and follower system dynamic model, establish a deception attack dynamic model based on network security on the unmanned vehicle node communication channel;

Step 4: Based on the spoofing attack dynamic model, a time-varying formation control protocol based on the pulse attack signal compensator is proposed, and a dynamic error system model corresponding to the time-varying formation control protocol is established;

Step 5: Based on Lyapunov theory, sufficient conditions for the stability of the error system are given in the dynamic error system model to prove the effectiveness of the time-varying formation control protocol based on the pulse attack signal compensator, and obtain the formation error of the unmanned vehicle Tracking error bound, so that the unmanned vehicle can achieve the desired triangular formation while ensuring accuracy.

Further, in step 1, an unmanned vehicle is used as a communication node, and a communication topology relationship is established based on several communication nodes:

Where l _ij represents the (i, j) element of matrix L, a _ij =1 indicates that node i can receive information from node j, and the information flow direction is one-way, a _ij =0 indicates that there is no communication channel between nodes i and j;

The coupling weight of the leader and the follower is defined as B=diag{b ₁ , b ₂ ,..., b _n }, b _i =1 indicates that node i can receive the leader information, otherwise _bi =0.

Further, step 2 is specifically: the system dynamic models of the leader 0 and the i-th follower in the autonomous vehicle are respectively:

where R ₀ , S ₀ , A, B and C are constant system matrices with appropriate dimensions, x ₀ (t) and y ₀ (t) are the states and outputs of the leader, x _i (t), y _i ( t) and u _i (t) represent the status, output and control input of the follower respectively.

Further, in step 3, based on the network security on the unmanned vehicle node communication channel, a deception attack dynamic model is established, specifically including:

Considering that the spoofing attack occurs on the communication channel of the unmanned vehicle node, the spoofing attack model is established as w _ij (t _k )q _ij (t _k ), where q _ij (t _k ) represents the communication from node i to node j at time t _k For the attack signal in the channel, the matrix Q(t _k )=[q _ij (t _k )] _n×n is defined, and satisfies ||Q(t _k )|| ² ≤ q, q represents the total energy of the attack signal, w _ij (t _k ) obeys Bernoulli distribution, and its probability density function is:

Among them, w _ij (t _k )=1 indicates that a spoofing attack has occurred, otherwise w _ij (t _k )=0, λ _ij ∈[0,1) is used to describe the communication channel from node i to node j at time t _k The probability of a spoofing attack occurring, let W(t _k )=[w _ij (t _k )] _n×n , then we have

Further, in step 4, based on the spoofing attack dynamic model, a time-varying formation control protocol based on the pulse attack signal compensator is proposed, specifically:

in

η _i (t) is the compensation value of the attack signal compensator of unmanned vehicle i, δ (.) is the Dirac function, c>0 is the coupling gain of the compensator, h _i is piecewise continuously differentiable, indicating no The output formation shape information of people and vehicles satisfies the following formula:

Among them, R _hi and S _hi are matrices with appropriate dimensions to be selected; K _1i , K _2i , K _3i are the controller gains to be designed;

First according to the following linear matrix equation

Obtain the solutions of (X _i ,U _i ) and (X _hi ,U _hi );

Then, select the appropriate K _1i according to the algorithm design steps, and K _2i and K _3i can be obtained from the following equations

K _2i =U _i -K _1i X _i

K _3i =U _hi -K _1i X _hi .

Further, in step 4, the dynamic error system model is specifically:

Define e _i =y _i (t)-y _hi (t)-y ₀ (t) as the system error, and the goal of unmanned vehicle formation control is formulated as:

in is a positive constant, and E(||.|| ² ) represents the expectation of the Euclidean vector norm or its derived matrix 2-norm.

Further, in step 5, based on Lyapunov theory, sufficient conditions for the stability of the error system are given:

If the distributed elastic formation controller gain K _1i satisfies R+SK _1i is Hurwitz's, and K _2i =U _i -K _1i X _i ,K _3i =U _hi -K _1i X _hi , if there are positive scalars α ₁ ,α ₂ , the positive definite matrix Ψ and the positive definite matrix P=diag(P ₁ ,...,P _n ) satisfy the following matrix inequality:

R ₀ ^T Ψ+ΨR ₀ -α ₂ Ψ＜0

Γ>κI

in,

Among them, a, b, d, and g are positive scalars to be selected; from this, it can be obtained that the tracking error system is stable under the designed formation controller, and the unmanned vehicle can achieve the desired time-varying formation within a certain error bound.

Further, in step 5, the tracking error bound of the unmanned vehicle formation error is:

Right now:

Among them, φ=||[C _i C ₀ ]||.

Beneficial effects: Compared with the existing technology, the present invention has the following significant advantages: The present invention discloses an unmanned vehicle formation control method under deception attack. Based on the pulse attack signal compensator, it can not only effectively compensate for the defects caused by spoofing attacks, but also reduce the burden on large-scale communication networks and enable unmanned vehicles to receive neighbor status information at the sampling time. At the same time, the compensator feeds back the compensation value to the formation controller, and then based on the control input determined by each unmanned vehicle of the formation controller, the desired formation can be completed. The method disclosed in the present invention can enable unmanned vehicles to achieve the desired time-varying formation configuration while maintaining a certain accuracy, and can reduce the communication volume of the actual system while effectively resisting spoofing attacks. The invention can also reduce communication burden and save resources; receive neighbor status information and send own status information in real time to complete the desired formation.

Description of drawings

Figure 1 is a control structure block diagram of an unmanned vehicle formation control method under deception attack provided by the present invention;

Figure 2 is a schematic diagram of the communication topology between four unmanned vehicles according to the embodiment of the present invention;

Figure 3 is the time-varying output formation trajectory of three followers at different moments according to the embodiment of the present invention;

Figure 4 is an elastic time-varying output formation error curve of three unmanned vehicles according to the embodiment of the present invention;

Figure 5 is the error norm bound ||e(t)|| ² of three unmanned vehicles according to the embodiment of the present invention.

Detailed ways

The technical solution of the present invention will be further described below with reference to the accompanying drawings.

The present invention will be further described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, those of ordinary skill in the art can make various changes or modifications to the present invention, and these equivalent forms are also within the scope defined by the appended claims of this application.

As shown in Figures 1 to 5, this embodiment provides a method for controlling an unmanned vehicle formation under a deception attack. This example uses a formation of four unmanned vehicles as an example to further illustrate and explain the present invention.

Now expect them to form a triangular formation. To achieve this formation, the following steps need to be taken:

Step 1: Consider an unmanned vehicle as a communication node, and establish a communication topology relationship based on the communication node:

Among them, l _ij represents the (i, j) element of matrix L, a _ij =1 indicates that node i can receive information from node j, and the information flow is one-way, and a _ij =0 indicates that there is no communication channel between nodes i and j. In addition, the coupling weight of the leader and the follower is defined as B=diag{b ₁ , b ₂ ,..., b _n }, b _i =1 indicates that node i can receive the leader information, otherwise _bi =0.

Step 2: The system dynamic models of the leader 0 and the i-th follower in the unmanned vehicle are respectively:

where R ₀ , S ₀ , A, B and C are constant system matrices with appropriate dimensions, x ₀ (t) and y ₀ (t) are the states and outputs of the leader, x _i (t), y _i ( t) and u _i (t) represent the follower’s status, output and control input respectively.

Step 3: Consider network security issues and establish a dynamic model of deception attacks, including:

Considering that the deception attack occurs on the communication channel of the unmanned vehicle node, the deception attack model is established as w _ij (t _k )q _ij (t _k ). Where q _ij (t _k ) represents the attack signal in the communication channel from node i to node j at time t _k . Define the matrix Q(t _k )=[q _ij (t _k )] _n×n , and satisfy ||Q(t _k )|| ² ≤ q, q represents the total energy of the attack signal.

w _ij (t _k ) obeys Bernoulli distribution, and its probability density function is

Among them, w _ij (t _k )=1 indicates that a spoofing attack has occurred, otherwise w _ij (t _k )=0. λ _ij ∈[0,1) is used to describe the probability of a spoofing attack occurring in the communication channel from node i to node j at time t _k . Let W(t _k )=[w _ij (t _k )] _n×n , then we have

Step 4: A time-varying formation control protocol based on pulse attack signal compensator is proposed. The specific design is as follows:

in

K _1i , K _2i , K _3i are matrices of appropriate dimensions, according to the following linear matrix equations

Obtain solutions to (X _i ,U _i ) and (X _hi ,U _hi ).

Select the appropriate K _1i according to the design steps. K _2i and K _3i can be obtained from the following equations

K _2i =U _i -K _1i X _i

K _3i = U _hi -K _1i X _hi

Determine the desired time-varying formation function of unmanned vehicles. The specific steps are as follows;

Define the output formation shape information of unmanned vehicles as h(t)=[h ₁ ^T (t),h ₂ ^T (t),...h _n ^T (t)] ^T , which satisfies:

Among them, h _i (t)∈R ⁿ is piecewise continuously differentiable, R _h and S _h are system matrices of appropriate dimensions, and y _hi is the output formation status information of the i-th unmanned vehicle.

Consider establishing a corresponding dynamic error system model, as follows:

Define e _i =y _i (t)-y _hi (t)-y ₀ (t) as the system error. The goal of unmanned vehicle formation control in step 5 is formulated as:

in is a positive constant, and E(||.|| ² ) represents the expectation of the Euclidean vector norm or its derived matrix 2-norm.

Step 5: Based on Lyapunov theory, sufficient conditions for the stability of the error system are given:

There are positive scalars α ₁ , α ₂ , a positive definite matrix Ψ and a positive definite matrix P=diag(P ₁ ,...,P _n ), which satisfy the following matrix inequality:

A ₀ ^T Ψ+ΨA ₀ -α ₂ Ψ＜0

Γ>κI

in:

T _max ＝max{t _k+1 -t _k },T _min ＝min{t _k+1 -t _k },k＝1,2...

According to theoretical derivation, the formation tracking error bound of unmanned vehicles is

Right now:

Among them, φ=||[C _i C ₀ ]||.

In this embodiment, four unmanned vehicles are selected as an example. Their communication topology is shown in Figure 2, where number 0 is the leader and numbers 1-3 are followers. The system dynamic model parameters of the four unmanned vehicles are:

Follow the design steps and select

c=0.45, a=0.05, b=0.5, d=0.5, g=0.01, q=0.1

λ _max (P) = 1.3134, κ = 0.2138, T _max = T _min = 0.2

Here, the expected time-varying formation function of the unmanned vehicle formation is:

Bringing in the above values, we can get the tracking error bound as

The simulation results are shown in Figure 3-5. The left picture of Figure 3 depicts the initial positions of the three followers, and the right picture shows the formation shape of the followers at t=50s. Figure 4 shows the elastic time-varying output formation error curves of three unmanned vehicles. It can be seen that the unmanned vehicles have achieved time-varying output formation while ensuring a certain accuracy. Figure 5 shows the norm bound of the time-varying output formation error ||e(t)|| ^2. The obtained norm of the formation tracking error is convergent, which proves the correctness of the theoretical derivation. It can be seen from the above simulation results that the unmanned vehicle formation control method under deception attacks disclosed by the present invention ensures the stability of the formation error dynamic system, can reduce the communication volume of the actual system, and effectively resists deception attacks, showing that this method The effectiveness of the invented technical solution.

The above-described specific embodiments further describe the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above-mentioned are only specific embodiments of the present invention and are not intended to limit the scope of the present invention. . At the same time, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims (4)

1. An unmanned vehicle formation control method under deception attack, which is characterized by including the following steps: Step 1: Use an unmanned vehicle as a communication node and establish a communication topology relationship based on several communication nodes; Step 2: Construct the leader system dynamic model and follower system dynamic model in the unmanned vehicle formation; Step 3: Based on the network security on the unmanned vehicle node communication channel, establish a deception attack dynamic model; Step 4: Based on the spoofing attack dynamic model, a time-varying formation control protocol based on the pulse attack signal compensator is proposed, and a dynamic error system model corresponding to the time-varying formation control protocol is established; Step 5: Based on Lyapunov theory, sufficient conditions for the stability of the error system are given in the dynamic error system model to prove the effectiveness of the time-varying formation control protocol based on the pulse attack signal compensator, and obtain the formation error of the unmanned vehicle Tracking error bound, so that the unmanned vehicle can achieve the desired triangular formation while ensuring accuracy; In step 3, based on the network security on the unmanned vehicle node communication channel, a deception attack dynamic model is established, including: Considering that the spoofing attack occurs on the communication channel of the unmanned vehicle node, the spoofing attack model is established as w _ij (t _k )q _ij (t _k ), where q _ij (t _k ) represents the communication from node i to node j at time t _k For the attack signal in the channel, the matrix Q(t _k )=[q _ij (t _k )] _n×n is defined, and satisfies ||Q(t _k )|| ² ≤ q, q represents the total energy of the attack signal, w _ij (t _k ) obeys Bernoulli distribution, and its probability density function is: Among them, w _ij (t _k )=1 indicates that a spoofing attack has occurred, otherwise w _ij (t _k )=0, λ _ij ∈[0,1) is used to describe the communication channel from node i to node j at time t _k The probability of a spoofing attack occurring, let W(t _k )=[w _ij (t _k )] _n×n , then we have In step 4, based on the spoofing attack dynamic model, a time-varying formation control protocol based on the pulse attack signal compensator is proposed as follows: in η _i (t) is the compensation value of the attack signal compensator of unmanned vehicle i, δ (.) is the Dirac function, c>0 is the coupling gain of the compensator, h _i is piecewise continuously differentiable, indicating no The output formation shape information of people and vehicles satisfies the following formula: Among them, R _hi and S _hi are matrices with appropriate dimensions to be selected; K _1i , K _2i , K _3i are the controller gains to be designed; First according to the following linear matrix equation Obtain the solutions of (X _i ,U _i ) and (X _hi ,U _hi ); Then, select the appropriate K _1i according to the algorithm design steps, and K _2i and K _3i can be obtained from the following equations K _2i =U _i -K _1i X _i K _3i =U _hi -K _1i X _hi ; In step 4, the dynamic error system model is specifically: Define e _i =y _i (t)-y _hi (t)-y ₀ (t) as the system error, and the goal of unmanned vehicle formation control is formulated as: in is a positive constant, E(||.|| ² ) represents the expectation of the Euclidean vector norm or its derived matrix 2-norm; In step 5, the tracking error bound of the unmanned vehicle formation error is: Right now: Among them, φ=||[CS ₀ ]||. 2. An unmanned vehicle formation control method under deception attack according to claim 1, characterized in that, in step 1, one unmanned vehicle is used as a communication node, and a communication topology relationship is established based on several communication nodes: Where l _ij represents the (i, j) element of matrix L, a _ij =1 indicates that node i can receive information from node j, and the information flow direction is one-way, a _ij =0 indicates that there is no communication channel between nodes i and j; The coupling weight of the leader and the follower is defined as B=diag{b ₁ , b ₂ ,..., b _m }, b _i =1 indicates that node i can receive the leader information, otherwise b _i =0. 3. An unmanned vehicle formation control method under deception attack according to claim 1, characterized in that step 2 is specifically: the system dynamic models of the leader 0 and the i-th follower in the unmanned vehicle are respectively : where R ₀ , S ₀ , R, S and C are constant system matrices with appropriate dimensions, x ₀ (t) and y ₀ (t) are the leader’s states and outputs, x _i (t), y _i ( t) and u _i (t) represent the status, output and control input of the follower respectively. 4. An unmanned vehicle formation control method under deception attack according to claim 1, characterized in that, in step 5, based on Lyapunov theory, sufficient conditions for the stability of the error system are given: If the distributed elastic formation controller gain K _1i satisfies R+SK _1i is Hurwitz's, and K _2i =U _i -K _1i X _i ,K _3i =U _hi -K _1i X _hi , if there are positive scalars α ₁ ,α ₂ , the positive definite matrix Ψ and the positive definite matrix P=diag(P ₁ ,...,P _n ) satisfy the following matrix inequality: R ₀ ^T Ψ+ΨR ₀ -α ₂ Ψ＜0 Γ>κI in, T _max ＝max{t _k+1 -t _k },T _min ＝min{t _k+1 -t _k },k＝1,2... Among them, a, b, d, and g are positive scalars to be selected; from this, it can be obtained that the tracking error system is stable under the designed formation controller, and the unmanned vehicle can achieve the desired time-varying formation within a certain error bound.