Global consistency security control protocol design method for multi-agent system with input saturation characteristic

Abstract

The invention provides a global consistency security control protocol design method for a multi-agent system with input saturation characteristics, which comprises the following steps of: 1, constructing a corresponding differential equation model for the multi-agent system with the input saturation characteristics under DoS attack under directed communication topology; 2, constructing a non-periodic DoS attack model according to the random attack frequency and attack duration of the DoS attack; 3, giving a constraint condition which needs to be met by feedback gain by utilizing the differential equation model constructed in the step 1, so as to solve the feedback gain; and 4, constructing an observer based on DoS attack shear, and designing a global consistency security control protocol of the multi-agent system with input saturation characteristics based on the feedback gain obtained in the step 3. The method can ensure that the multi-agent system with the input saturation characteristic can still realize consistency even if the control input reaches the threshold value.

Description

Technical Field

[0001] The present invention belongs to the field of safety control technology, and in particular relates to a method for designing a global consistency safety control protocol for a multi-agent system with input saturation characteristics. Background Art

[0002] Multi-agent systems have been widely used in industrial automation, intelligent transportation, distributed control, and other fields. In particular, achieving coordination and consistent control among agents has become crucial in scenarios such as drone formations, collaborative robots, and smart grids. However, in real-world environments, multi-agent systems are often subject to disruptions such as network latency, packet loss, and malicious attacks, which can seriously threaten system stability and consistency. Denial-of-Service (DoS) attacks are a common type of network attack in multi-agent systems. DoS attacks disrupt communication between agents by blocking or delaying information transmission, thereby impacting the coordination performance and consistency of the system. Furthermore, real-world multi-agent systems are often limited by physical components. When the control input signal reaches a certain threshold, the controller input reaches saturation, further complicating control design. Existing consensus control protocols for multi-agent systems with input saturation under DoS attacks typically achieve semi-global consistency, requiring the initial state of the multi-agent system to meet certain specific conditions. Therefore, designing global consensus control protocols for multi-agent systems with input saturation under DoS attacks presents both challenges and practical value. Existing literature studies on the consistency problem of multi-agents under DoS attacks often assume that they are in an undirected communication graph, and there are relatively few studies on the system consistency problem under a directed communication graph. Summary of the Invention

[0003] Purpose of the invention: The technical problem to be solved by the present invention is to address the deficiencies of the existing technology and to provide a method for designing a global consistency security control protocol for a multi-agent system with input saturation characteristics under the influence of DoS attacks. The method enables the multi-agent system with input saturation characteristics to achieve global consistency in any initial state by utilizing the state information of adjacent agents in a directed communication graph and designing the feedback gain K.

[0004] The method of the present invention comprises the steps of: Step 1: For a multi-agent system with input saturation characteristics under DoS attack (denial of service attack) in a directed communication topology, construct the corresponding differential equation model; Step 2: Construct a non-periodic DoS attack model based on the random attack frequency and attack duration of the DoS attack; Step 3: Using the differential equation model constructed in step 1, the constraints that the feedback gain needs to satisfy are given, thereby solving the feedback gain; Step 4: Build an observer based on DoS attack shear, and based on the feedback gain obtained in step 3, design a global consistency security control protocol for the multi-agent system with input saturation characteristics.

[0005] In step 1, define N+1 to represent the number of agents in a multi-agent system with input saturation characteristics, where agents 1 to N are represented as followers in the multi-agent system, and the N+1th agent is represented as the leader in the multi-agent system; The directed communication graph between N+1 agents in a multi-agent system with input saturation is G={V, E}, where represents a set of nodes of N+1 agents, represents the node of the N+1th agent, represents an edge of a multi-agent system with input saturation properties, , i and j are 1~N+1, and i≠j; define the adjacency matrix of the directed communication topology graph G , Represents the element in row i and column j of the adjacency matrix C; When node v j Able to v i Pass information, elements of the adjacency matrix C , Represents the slave node v j To node v i There is an edge; Define the in-degree matrix D = [d ij ], where d ij represents the element in row i and column j of the in-degree matrix D, , define the Laplace matrix L=DC; for any different node in V, if there is always a line from node v j To node v i If there is a directed path, the directed communication topology graph G is called a strongly connected graph; In a multi-agent system with only one leader, the Laplace matrix L is written as follows: , where the matrix The dimension is N*N, the matrix The dimension is N*1, Represents a 0 vector of dimension 1*N; in a directed communication topology, the matrix It is asymmetric.

[0006] In step 1, the differential equation model includes: The differential equation model of the i-th follower is: , The differential equation model of the leader is: , in, represents the state vector of the i-th agent at time t, and has dimension n; represents the derivative of the state vector of the i-th agent at time t with respect to time t; represents the input vector of the i-th agent at time t, with dimension p; definition to represent the input saturation of the multi-agent system, Expressed as ,in is a symbolic function, when hour, ,when hour, ,when hour, ; Represents the smallest element in the set; A represents the system matrix of the multi-agent system with input saturation characteristics, with a dimension of n*n, and B represents the input matrix of the multi-agent system with input saturation characteristics, with a dimension of n*p; Set matrices A and B, where (A, B) is controllable and satisfies: the geometric multiplicity of the eigenvalues ​​of matrix A is p and the algebraic multiplicity of the eigenvalues ​​of matrix A is p+q, where q is a constant greater than 0, and the size of the equivalent block of all zero eigenvalues ​​is at most 2, and the remaining eigenvalues ​​are non-repeating pure imaginary numbers; and matrix B is full rank; According to the settings of matrices A and B, select a basic transformation The following formula is satisfied: , in is a block matrix, , , , where I represents the identity matrix and T represents the transpose; Define a matrix Z: , where the matrix ; The following formula is established: , Design a control protocol so that a multi-agent system with input saturation characteristics satisfies: , in It means to find the limit value when time t tends to infinity.

[0007] Step 2 includes: assuming that a multi-agent system with input saturation characteristics is subjected to a DoS attack in the system communication network, and the attack frequency and attack duration of the DoS attack are unknown; when the multi-agent system with input saturation characteristics is subjected to a DoS attack, the agents will no longer be able to transmit information to adjacent agents, and the agents can only receive their own status information.

[0008] In step 2, according to the random attack frequency and attack duration of the DoS attack, the start time of the kth DoS attack is defined as , the time series of attacks on a multi-agent system with input saturation characteristics is described as , the end time of the kth DoS attack is defined as , define the duration of the kth attack , the uncertain nonlinear multi-agent system will be The set of time intervals under DoS attack is described as : , in represents the union of the duration of all attacks from the first attack to the kth attack. represents the intersection, Indicates two set time points; Uncertain nonlinear multi-agent system in each The set of time intervals during which there is no DoS attack is described as : , Where \ represents the difference of sets; definition is the total time of DoS attack in the time interval (0, t), which is described as: , in and is a constant and satisfies , .

[0009] Step 3 includes: designing the feedback gain K, which needs to satisfy the following constraints: , in, is a constant greater than 0, Represents the identity matrix of size p*p, where p is the dimension of the system input; The constraints are written in the form of the following matrix: , Where S is an auxiliary matrix that satisfies ,get ; Simultaneous conditions The matrix K exists if and only if ,in represents the null space of a matrix, Represents a subset of a set; The existence of the feedback gain K is equivalent to proving that when the following formula is satisfied: ,formula holds true, x represents the state vector of the system, and u represents the input vector of the system; Since (A, B) is controllable, we get: , in Represents the rank of the matrix. The rank of matrix A is np and the rank of matrix B is p, so: , Where imA represents the value range space of matrix A, and imB represents the value range space of matrix B, which are defined as: , From Ax=0, we can deduce Zx=0 and get ; because And the matrix B has p rows, which means that the matrix B is injective, so Bu=0 means u=0, and we get Su=0, which means that the feedback gain K has a solution.

[0010] Step 4 involves constructing an observer to observe the multi-agent system with input saturation characteristics. The observer is designed to: , in represents the observed state of the i-th agent at time t, represents the derivative of the observed state of the i-th agent at time t; represents the element in the i-th row and j-th column of the adjacency matrix C. Based on the feedback gain K designed in step 3, a global consistency security control protocol for the multi-agent system with input saturation characteristics under DoS attacks is designed, which is specifically written as: , in represents the set of time intervals between 0 and t during which there is no DoS attack. Represents the set of time intervals between 0 and t that are subject to DoS attacks; The tracking consistency error at time t is defined as , calculate the derivative of the tracking consistency error : , Make the following definitions: , , , , in A simple expression of the states of N agents at time t, represents the transpose of the state of the Nth agent at time t, A simple expression of the tracking consistency error of N agents at time t, represents the transpose of the tracking consistency error of the Nth agent at time t, A simple expression of the input of N agents at time t, represents the transpose of the Nth agent input at time t, A simple expression of the observed states of N agents at time t, represents the transpose of the observed state of the Nth agent at time t; when , that is, when there is no DoS attack, the closed-loop system is written as: , in The derivative of a simple expression representing the observed states of N agents at time t; represents the identity matrix of size N, represents the identity matrix of size n, The derivative of the simplified expression of the tracking consistency error of N agents at time t, represents the Kronecker product.

[0011] Step 4 also includes: defining an auxiliary variable ,get: , Define the matrix , is written as: , in is a Hurwitz matrix, there exists a positive definite matrix and a constant greater than 0 ,satisfy: , in is an auxiliary variable, Represents the identity matrix of dimension (N*n)*(N*n); when , that is, when subjected to a DoS attack, the closed-loop system is written as: , get: , Construct a Lyapunov function at time t for a multi-agent system with input saturation under DoS attack : , in Indicates time t The elements in the jth row of the vector, and there exists a positive constant So that the following linear matrix inequality has a solution : , The Lyapunov function is derived with respect to time t when it is attacked by DoS and when it is not attacked by DoS, and the function is obtained. : , The intermediate parameters , intermediate parameters , Represents the largest element in a set. represents the smallest eigenvalue of the matrix, represents the largest eigenvalue of the matrix; Define two auxiliary variables and : , , Select Parameters ,get: , Among them, e represents a natural constant, Represents the function value of the Lyapunov function at time 0.

[0012] The present invention also provides an electronic device, comprising a processor and a memory, wherein the memory stores program code, and when the program code is executed by the processor, the processor executes the steps of the method.

[0013] The present invention also provides a storage medium storing a computer program or instruction, which executes the steps of the method when the computer program or instruction is run on a computer.

[0014] The present invention also provides a distributed control model for an unmanned aerial vehicle system, comprising physical components such as sensors, controllers, and actuators. When the above-mentioned control method is executed by the controller, the controller performs the steps of the method described.

[0015] The present invention has the following beneficial effects: The control protocol design method proposed in the present invention can ensure that, in a directed communication topology, even if a DoS attack occurs, resulting in a loss of communication between agents in a multi-agent system with input saturation characteristics, the system can still achieve consistency even when the control input reaches a threshold. Furthermore, the control protocol design method enables the multi-agent system with input saturation characteristics to achieve global consistency, that is, regardless of the system's initial state, ultimately achieves consistency, thereby improving the stability and robustness of the multi-agent system with input saturation characteristics. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a communication topology diagram of the multi-agent UAV system with input saturation characteristics of the present invention.

[0017] Figure 2 This is a graph showing the change in the x-direction position component of the ith UAV in a multi-agent UAV system with input saturation characteristics simulated by the present invention over time.

[0018] Figure 3 This is a graph showing the change in the y-direction position component of the i-th UAV in a multi-agent UAV system with input saturation characteristics simulated by the present invention over time.

[0019] Figure 4 This is a graph showing the change in the z-direction position component of the ith UAV in a multi-agent UAV system with input saturation characteristics simulated by the present invention over time.

[0020] Figure 5 This is a graph showing how the x-direction velocity component of the ith UAV in the multi-agent UAV system with input saturation characteristics simulated by the present invention changes with time.

[0021] Figure 6This is a graph showing the change in the y-direction velocity component of the i-th UAV in a multi-agent UAV system with input saturation characteristics simulated by the present invention over time.

[0022] Figure 7 This is a graph showing the change in the z-direction velocity component of the ith UAV in a multi-agent UAV system with input saturation characteristics simulated by the present invention over time.

[0023] Figure 8 This is a graph showing how the x-direction acceleration component of the ith UAV in the multi-agent UAV system with input saturation characteristics simulated by the present invention changes with time.

[0024] Figure 9 This is a graph showing how the acceleration component in the y direction of the i-th UAV in the multi-agent UAV system with input saturation characteristics simulated by the present invention changes with time.

[0025] Figure 10 This is a graph showing how the acceleration component in the z direction of the ith UAV in the multi-agent UAV system with input saturation characteristics simulated by the present invention changes with time. DETAILED DESCRIPTION

[0026] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more apparent.

[0027] An embodiment of the present invention provides a method for designing a global consistency security control protocol for a multi-agent system with input saturation characteristics under the influence of a DoS attack, comprising the following steps: Step 1: Construct a differential equation model of a multi-agent system with input saturation characteristics.

[0028] The differential equation model of the i-th follower is: , The differential equation model of the leader is: , in, represents the state vector of the i-th agent at time t, and has dimension n; represents the derivative of the state vector of the i-th agent at time t with respect to time t; represents the input vector of the i-th agent at time t, with dimension p; definition to represent the input saturation of the multi-agent system, Expressed as ,in is a symbolic function, when hour, ,when hour, ,when hour, ; Represents the smallest element in the set; A represents the system matrix of the multi-agent system with input saturation characteristics, with a dimension of n*n, and B represents the input matrix of the multi-agent system with input saturation characteristics, with a dimension of n*p; The goal of global consensus control for multi-agent systems with input saturation is to design a control protocol , so that in any initial state, the multi-agent system with input saturation characteristics satisfies: , Control Protocol Based on Observer Design Designed to: , in represents the observed state of the state of the i-th agent at time t, represents the derivative of the observed state of the i-th agent at time t. Represents the element in the i-th row and j-th column of the adjacency matrix C. represents the set of time intervals between 0 and t during which there is no DoS attack. Represents the set of time intervals between time 0 and time t during which a DoS attack occurs. is represented as the control input of the i-th agent at time t.

[0029] Will Substituting it into a multi-agent system with input saturation characteristics, we can obtain the following closed-loop system.

[0030] when , that is, when there is no DoS attack, the closed-loop system is written as: , when , that is, when subjected to a DoS attack, the closed-loop system is written as: ; Step 2, choose a suitable Lyapunov function: , First calculate the time when there is no DoS attack The derivative with respect to time t, at this time Expressed as: , use express The derivative with respect to time t is calculated as: , According to the design conditions of the feedback matrix K, we get: , in is a constant greater than 0, and the formula can be written as follows: , Select variables Satisfy the following formula: , At the same time because , so define auxiliary variables , : , , After substituting the above formula, we get: , in .

[0031] When the computer is under DoS attack The derivative with respect to time t, at this time Expressed as: , use express The derivative with respect to time t is calculated as: , Since the matrix Z is a positive definite matrix, we can conclude that: , in Combining the two situations of being attacked by DoS and not being attacked by DoS, we can draw the following conclusions: , Next, we discuss whether time t is within the DoS attack interval in two cases. In the first case, when time t is not within the DoS attack interval, we can conclude that: , In the second case, when time t is within the DoS attack interval, we can get: , because and , so we can deduce: , Select Parameters ,get: , Through the above proof, it is concluded that the multi-agent system with input saturation characteristics can achieve global consistency under DoS attack. Next, the reliability of the method of the present invention will be verified through simulation experiments.

[0032] The simulation experiment is a numerical simulation experiment of the state of 6 UAVs (5 followers and 1 leader) to achieve consistent tracking. The positions of the UAVs in three directions in the three-dimensional coordinate system are set as: , the speed is expressed as , the acceleration is expressed as The model of the UAV system is written as: , Defining drone status is a 6-dimensional vector, , the control input of the UAV is a 3-dimensional vector, , according to the model of the UAV system, set the system matrix of the multi-agent UAV system with input saturation characteristics , input matrix , select parameters , solving the feedback gain K, we can get .

[0033] In the simulation experiment, the communication topology between drones is set as a directed graph, that is, drones can only transmit state information unilaterally. The communication topology of the constructed multi-agent drone system with input saturation characteristics is shown in the figure below. Figure 1 As shown in the figure, the numbers 1, 2, 3, 4, and 5 represent the numbers of the follower drones, and 6 represents the number of the leader drone. The Laplace matrix L of this communication graph is: , Simulation results analysis: Figure 2 、 Figure 3 、 Figure 4 、 Figure 5 、 Figure 6 、 Figure 7 is the state change diagram of the UAV, where Indicates the x-direction position state of the i-th UAV, Indicates the position status of the i-th UAV in the y direction, Indicates the position state of the i-th UAV in the z direction, Indicates the speed state of the i-th UAV in the x direction, Indicates the velocity state of the i-th UAV in the y direction, Indicates the velocity state of the i-th drone in the z direction. Figure 8 、 Figure 9 、 Figure 10 is the change graph of the UAV control input, where Indicates the acceleration state of the i-th drone in the x direction, Indicates the acceleration state of the i-th drone in the y direction, It can be seen from the simulation diagram that when subjected to DoS attacks, the multi-agent UAV system with input saturation characteristics can still achieve global consistency even when the control input reaches the threshold.

[0034] This invention provides a method for designing a globally consistent security control protocol for a multi-agent system with input saturation under DoS attacks. While there are numerous methods and approaches for implementing this technical solution, the above-described preferred embodiments of the invention are merely exemplary. It should be noted that those skilled in the art may make improvements and modifications without departing from the principles of the invention, and such improvements and modifications are also within the scope of protection of the invention. Any components not specified in this embodiment may be implemented using existing technologies.

Claims

1. A design method for a global consistency safety control protocol for a multi-agent system with input saturation characteristics, characterized by: The following steps are involved: Step 1: For a multi-agent system with input saturation characteristics under DoS attack in a directed communication topology, a corresponding differential equation model is constructed; Step 2: Construct a non-periodic DoS attack model based on the random attack frequency and attack duration of the DoS attack; Step 3: Using the differential equation model constructed in step 1, the constraints that the feedback gain needs to satisfy are given, thereby solving the feedback gain; Step 4: Build an observer based on DoS attack shear, and based on the feedback gain obtained in step 3, design a global consistency security control protocol for the multi-agent system with input saturation characteristics.

2. The method according to claim 1, characterized in that In step 1, define N+1 to represent the number of agents in a multi-agent system with input saturation characteristics, where agents 1 to N are represented as followers in the multi-agent system, and the N+1th agent is represented as the leader in the multi-agent system; The directed communication graph between N+1 agents in a multi-agent system with input saturation is G={V, E}, where represents a set of nodes of N+1 agents, represents the node of the N+1th agent, represents an edge of a multi-agent system with input saturation properties, , i and j are 1~N+1, and i≠j; define the adjacency matrix of the directed communication topology graph G , Represents the element in row i and column j of the adjacency matrix C; When node v j Able to v i Pass information, elements of the adjacency matrix C , Represents the slave node v j To node v i There is an edge; Define the in-degree matrix D = [d ij ], where d ij represents the element in row i and column j of the in-degree matrix D, , define the Laplace matrix L=DC; for any different node in V, if there is always a line from node v j To node v i If there is a directed path, the directed communication topology graph G is called a strongly connected graph; In a multi-agent system with only one leader, the Laplace matrix L is written as follows: ， where the matrix The dimension is N*N, the matrix The dimension is N*1, Represents a 0 vector of dimension 1*N; in a directed communication topology, the matrix It is asymmetric.

3. The method according to claim 2, characterized in that In step 1, the differential equation model includes: The differential equation model of the i-th follower is: ， The differential equation model of the leader is: ， in, represents the state vector of the i-th agent at time t, and has dimension n; represents the derivative of the state vector of the i-th agent at time t with respect to time t; represents the input vector of the i-th agent at time t, with dimension p; definition to represent the input saturation of the multi-agent system, Expressed as ,in is a symbolic function, when hour, ,when hour, ,when hour, ; Represents the smallest element in the set; A represents the system matrix of the multi-agent system with input saturation characteristics, with a dimension of n*n, and B represents the input matrix of the multi-agent system with input saturation characteristics, with a dimension of n*p; Set matrices A and B, where (A, B) is controllable and satisfies: the geometric multiplicity of the eigenvalues ​​of matrix A is p and the algebraic multiplicity of the eigenvalues ​​of matrix A is p+q, where q is a constant greater than 0, and the size of the equivalent block of all zero eigenvalues ​​is at most 2, and the remaining eigenvalues ​​are non-repeating pure imaginary numbers; and matrix B is full rank; According to the settings of matrices A and B, select a basic transformation The following formula is satisfied: ， in is a block matrix, , , , where I represents the identity matrix and T represents the transpose; Define a matrix Z: ， where the matrix ; The following formula is established: ， Design a control protocol so that a multi-agent system with input saturation characteristics satisfies: ， in It means to find the limit value when time t tends to infinity.

4. The method according to claim 3, characterized in that Step 2 includes: assuming that a multi-agent system with input saturation characteristics is subjected to a DoS attack in the system communication network, and the attack frequency and attack duration of the DoS attack are unknown; when the multi-agent system with input saturation characteristics is subjected to a DoS attack, the agents will no longer be able to transmit information to adjacent agents, and the agents can only receive their own status information.

5. The method according to claim 4, characterized in that In step 2, according to the random attack frequency and attack duration of the DoS attack, the start time of the kth DoS attack is defined as , the time series of attacks on a multi-agent system with input saturation characteristics is described as , the end time of the kth DoS attack is defined as , define the duration of the kth attack , the uncertain nonlinear multi-agent system will be The set of time intervals under DoS attack is described as : ， in represents the union of the duration of all attacks from the first attack to the kth attack. represents the intersection, Indicates two set time points; Uncertain nonlinear multi-agent system in each The set of time intervals during which there is no DoS attack is described as : ， Where \ represents the difference of sets; definition is the total time of DoS attack in the time interval (0, t), which is described as: ， in and is a constant and satisfies , .

6. The method according to claim 5, characterized in that Step 3 includes: designing the feedback gain K, which needs to satisfy the following constraints: ， in, is a constant greater than 0, Represents the identity matrix of size p*p, where p is the dimension of the system input; The constraints are written in the form of the following matrix: ， Where S is an auxiliary matrix that satisfies ,get ; Simultaneous conditions The matrix K exists if and only if ,in represents the null space of a matrix, Represents a subset of a set; The existence of the feedback gain K is equivalent to proving that when the following formula is satisfied: ,formula holds true, x represents the state vector of the system, and u represents the input vector of the system; Since (A, B) is controllable, we get: ， in Represents the rank of the matrix. The rank of matrix A is np and the rank of matrix B is p, so: ， Where imA represents the value range space of matrix A, and imB represents the value range space of matrix B, which are defined as: ， From Ax=0, we can deduce Zx=0 and get ; because And the matrix B has p rows, which means that the matrix B is injective, so Bu=0 means u=0, and we get Su=0, which means that the feedback gain K has a solution.

7. The method according to claim 6, characterized in that Step 4 involves constructing an observer to observe the multi-agent system with input saturation characteristics. The observer is designed to: ， in represents the observed state of the i-th agent at time t, represents the derivative of the observed state of the i-th agent at time t; represents the element in the i-th row and j-th column of the adjacency matrix C. Based on the feedback gain K designed in step 3, a global consistency security control protocol for the multi-agent system with input saturation characteristics under DoS attacks is designed, which is specifically written as: ， in represents the set of time intervals between 0 and t during which there is no DoS attack. Represents the set of time intervals between 0 and t that are subject to DoS attacks; The tracking consistency error at time t is defined as , calculate the derivative of the tracking consistency error : ， Make the following definitions: ， ， ， ， in A simple expression of the states of N agents at time t, represents the transpose of the state of the Nth agent at time t, A simple expression of the tracking consistency error of N agents at time t, represents the transpose of the tracking consistency error of the Nth agent at time t, A simple expression of the input of N agents at time t, represents the transpose of the Nth agent input at time t, A simple expression of the observed states of N agents at time t, represents the transpose of the observed state of the Nth agent at time t; when , that is, when there is no DoS attack, the closed-loop system is written as: ， in The derivative of a simple expression representing the observed states of N agents at time t; represents the identity matrix of size N, represents the identity matrix of size n, The derivative of the simplified expression of the tracking consistency error of N agents at time t, represents the Kronecker product.

8. The method according to claim 7, characterized in that Step 4 also includes: defining an auxiliary variable ,get: ， Define the matrix , is written as: ， in is a Hurwitz matrix, there exists a positive definite matrix and a constant greater than 0 ,satisfy: ， in is an auxiliary variable, Represents the identity matrix of dimension (N*n)*(N*n); when , that is, when subjected to a DoS attack, the closed-loop system is written as: ， get: , Construct a Lyapunov function at time t for a multi-agent system with input saturation under DoS attack : ， in Indicates time t The elements in the jth row of the vector, and there exists a positive constant So that the following linear matrix inequality has a solution : ， The Lyapunov function is derived with respect to time t when it is attacked by DoS and when it is not attacked by DoS, and the function is obtained. : ， The intermediate parameters , intermediate parameters , Represents the largest element in a set. represents the smallest eigenvalue of the matrix, represents the largest eigenvalue of the matrix; Define two auxiliary variables and : ， ， Select Parameters ,get: ， Among them, e represents a natural constant, Represents the function value of the Lyapunov function at time 0.

9. An electronic device, characterized in that: The method comprises a processor and a memory, wherein the memory stores program codes, and when the program codes are executed by the processor, the processor is caused to perform the steps of the method according to any one of claims 1 to 8.

10. A storage medium, characterized in that: A computer program or instruction is stored, and when the computer program or instruction is run on a computer, the steps of the method according to any one of claims 1 to 8 are executed.

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