Method for designing global consensus safety control protocol of multi-agent system with input saturation characteristics

Abstract

The application provides a global consensus safety control protocol design method for a multi-agent system with input saturation characteristics, comprising the following steps: step 1, constructing a corresponding differential equation model for the multi-agent system with input saturation characteristics under a DoS attack in a directed communication topology; step 2, constructing a non-periodic DoS attack model according to the random attack frequency and attack duration of the DoS attack; step 3, using the differential equation model constructed in step 1, giving a constraint condition required to be satisfied by a feedback gain, and thus solving the feedback gain; and step 4, constructing an observer based on a shear of the DoS attack, and designing a global consensus safety control protocol for the multi-agent system with input saturation characteristics based on the feedback gain obtained in step 3. The method can ensure that the multi-agent system with input saturation characteristics can still achieve consensus even if the control input reaches a threshold.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of safety control, and particularly relates to a global consensus safety control protocol design method for a multi-agent system with input saturation characteristics. BACKGROUND

[0002] Multi-agent systems have been widely applied in industrial automation, intelligent transportation, distributed control and other fields. In particular, in scenarios such as unmanned aerial vehicle formation, robot collaboration, and smart grid, achieving the collaborative and consistent control among agents has become a key. However, multi-agent systems in actual environments are often subject to disturbances such as network delay, packet loss, and malicious attacks, which seriously threaten the stability and consistency of the system. In multi-agent systems, denial-of-service (DoS) attack is one of the common types of network attacks. DoS attack blocks or delays information transmission, causing communication interruption between agents, thereby affecting the coordination performance and consistency of the system. In addition, actual multi-agent systems are often subject to physical component limitations, and when the control input signal reaches a certain threshold, the input of the controller reaches saturation, which further increases the difficulty of control design. At present, the consensus control protocol implementation of the multi-agent system with input saturation characteristics under the DoS attack environment is semi-global consensus, which requires the initial state of the multi-agent system to satisfy certain specific conditions. Therefore, it is challenging and of practical value to design a global consensus control protocol for a multi-agent system with input saturation characteristics under a DoS attack environment. The existing literature on the consensus problem of multi-agent systems under DoS attack often assumes a directed communication graph, and there are few studies on the consensus problem of systems under a directed communication graph. SUMMARY

[0003] The technical problem to be solved by the application is to provide a global consensus safety control protocol design method for a multi-agent system with input saturation characteristics under the influence of DoS attack, which realizes the global consensus of the multi-agent system with input saturation characteristics under a directed communication graph by using the state information of adjacent agents and designing feedback gain K, so that the multi-agent system can achieve global consensus at any initial state.

[0004] The method of the application comprises the following steps:

[0005] Step 1, for a multi-agent system with input saturation characteristics under a directed communication topology and DoS attack (denial-of-service attack), a corresponding differential equation model is constructed;

[0006] Step 2, according to the random attack frequency and attack duration of DoS attack, a non-periodic DoS attack model is constructed;

[0007] Step 3, using the differential equation model constructed in step 1, the constraint condition required to be satisfied by the feedback gain is given, so as to solve the feedback gain;

[0008] Step 4, an observer based on the shear of DoS attack is constructed, and based on the feedback gain obtained in step 3, a global consensus safety control protocol of the multi-agent system with input saturation characteristics is designed.

[0009] In step 1, N+1 is defined to represent the number of agents in the multi-agent system with input saturation characteristics, wherein 1~N agents represent followers in the multi-agent system, and the N+1 agent represents the leader in the multi-agent system;

[0010] The directed communication graph between the N+1 agents in the multi-agent system with input saturation characteristics is G={V, E}, wherein represents the node set of the N+1 agents, represents the node of the N+1 agent, represents the edge of the multi-agent system with input saturation characteristics, , i, j take values of 1~N+1, and i≠j; the adjacency matrix of the directed communication topology graph G is defined as , represents the element in the i-th row and j-th column of the adjacency matrix C;

[0011] When node v j can deliver information to v i , the element of the adjacency matrix C is , represents that there is an edge from node v j to node v i ;

[0012] The in-degree matrix D=[d ij ] is defined, wherein d ij represents the element in the i-th row and j-th column of the in-degree matrix D, , the Laplace matrix L=D-C is defined; for any different nodes in V, if there is always a directed path from node v j to node v i , the directed communication topology graph G is called a strongly connected graph;

[0013] In the multi-agent system with only one leader, the Laplace matrix L is written in the following form:

[0014] ,

[0015] where matrix is of dimension N*N, matrix is of dimension N*1, denotes a 0 vector of dimension 1*N; under the directed communication topology, matrix is asymmetric.

[0016] In step 1, the differential equation model includes:

[0017] The differential equation model of the i-th follower is:

[0018] ,

[0019] The differential equation model of the leader is:

[0020] ,

[0021] where, denotes the state vector of the i-th agent at time t, and is of dimension n; denotes the derivative of the state vector of the i-th agent at time t with respect to time t; denotes the input vector of the i-th agent at time t, of dimension p; define to denote the input saturation of the multi-agent system, denotes where is a sign function, when , when , when , ; denotes the smallest element in the set; A denotes the system matrix of the multi-agent system with input saturation characteristics, of dimension n*n, B denotes the input matrix of the multi-agent system with input saturation characteristics, of dimension n*p;

[0022] The matrices A, B are set, where (A, B) is controllable, and satisfy: the geometric multiplicity of the eigenvalues of matrix A is p and the algebraic multiplicity of the eigenvalues of matrix A is p+q, q is a constant greater than 0, and the size of the Jordan block of all 0 eigenvalues is at most 2, and the remaining eigenvalues are non-repeated pure imaginary numbers; and matrix B is full rank;

[0023] According to the setting of the matrices A, B, a basic transformation is selected to satisfy the following equation:

[0024] ,

[0025] where for a block matrix, , , where I denotes a unit matrix and T denotes a transpose;

[0026] A matrix Z is defined as:

[0027] ,

[0028] where matrix ;

[0029] It is derived that the following equation is true:

[0030] ,

[0031] A control protocol is designed so that the multi-agent system with input saturation characteristics satisfies:

[0032] ,

[0033] where denotes the limit value as time t tends to infinity.

[0034] Step 2 includes: setting the multi-agent system with input saturation characteristics to be subjected to a DoS attack in a 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 can no longer transmit information with adjacent agents, and the agents can only receive their own state information.

[0035] In step 2, the start time of the kth DoS attack is defined as , and the time sequence of the multi-agent system with input saturation characteristics subjected to the attack is described as The end time of the kth DoS attack is defined as , and the attack duration of the kth attack is defined as The time interval set of the uncertain nonlinear multi-agent system subjected to the DoS attack in each is described as :

[0036] ,

[0037] where denotes the union set of the first attack duration to the kth attack duration, all attack durations, denotes the intersection set, denotes two set time points;

[0038] The set of time intervals during which the uncertain nonlinear multi-agent system is not subject to DoS attack at each time is denoted as :

[0039] ,

[0040] where denotes the difference set of the set

[0041] The definition of the total time during which the system is subject to DoS attack in the time interval (0, t) is denoted as

[0042] ,

[0043] where and are constants and satisfy , .

[0044] Step 3 includes designing the feedback gain K, which needs to satisfy the following constraint condition:

[0045] ,

[0046] where is a constant greater than 0, denotes a unit matrix of size p*p, and p is the dimension of the system input;

[0047] The constraint condition is written in the form of the following matrix:

[0048] ,

[0049] where S is an auxiliary matrix that satisfies , and is obtained; at the same time, the condition needs to satisfy that the matrix K exists if and only if where denotes the null space of a matrix, denotes a subset of the set

[0050] The existence of the feedback gain K is equivalent to proving that the following formula is satisfied: , and the formula holds, where x represents the state vector of the system and u represents the input vector of the system;

[0051] Since (A, B) is controllable, we obtain:

[0052] ,

[0053] where Rank of a matrix, the rank of matrix A is n-p, the rank of matrix B is p, so we have:

[0054] ,

[0055] Where imA represents the range space of matrix A, imB represents the range space of matrix B, and is defined as:

[0056] ,

[0057] From Ax=0, we get Zx=0, and we get ;

[0058] Since And matrix B has p rows, which means that matrix B is injective, so Bu=0 means u=0, and we get Su=0, which means that the feedback gain K is solvable.

[0059] Step 4 includes constructing an observer to observe the multi-agent system with input saturation characteristics, and the observer is designed as:

[0060] ,

[0061] Where represents the observation state of the i-th agent state at time t, represents the derivative of the observation 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; according to the feedback gain K designed in step 3, the global consensus safety control protocol of the multi-agent system with input saturation characteristics under DoS attack is designed, which is specifically written as:

[0062] ,

[0063] Where represents the set of time intervals from 0 to t that are not subject to DoS attack, represents the set of time intervals from 0 to t that are subject to DoS attack;

[0064] Define the tracking consensus error at time t as , and calculate the derivative of the tracking consensus error :

[0065] ,

[0066] The following definitions are made:

[0067] ,

[0068] ,

[0069] ,

[0070] ,

[0071] where denotes the compact representation of the state of the N agents at time t, denotes the transpose of the state of the Nth agent at time t, denotes the compact representation of the tracking consensus error of the N agents at time t, denotes the transpose of the tracking consensus error of the Nth agent at time t, denotes the compact representation of the input of the N agents at time t, denotes the transpose of the input of the Nth agent at time t, denotes the compact representation of the observation state of the N agents at time t, denotes the transpose of the observation state of the Nth agent at time t;

[0072] When , i.e. when not subjected to DoS attacks, the closed loop system writes:

[0073] ,

[0074] where denotes the derivative of the compact representation of the observation state of the N agents at time t; denotes the identity matrix of size N, denotes the identity matrix of size n, denotes the derivative of the compact representation of the tracking consensus error of the N agents at time t, denotes the Kronecker product.

[0075] Step 4 further comprises defining an auxiliary variable , which gives:

[0076] ,

[0077] defining the matrix , is written:

[0078] ,

[0079] where is a Hurwitz matrix, there exists a positive definite matrix and a positive constant such that:

[0080] ,

[0081] where is an auxiliary variable, denotes the identity matrix of dimension (N*n)*(N*n);

[0082] When , i.e. when under DoS attack, the closed-loop system writes

[0083] ,

[0084] we obtain ,

[0085] For multi-agent systems with input saturation under DoS attack, we construct a Lyapunov function at time t :

[0086] ,

[0087] where denotes the element in the j-th row of the vector at time t , and there exists a positive constant such that the following linear matrix inequality has a solution :

[0088] ,

[0089] Taking the derivative of the Lyapunov function with respect to time t when under DoS attack and when not under DoS attack, respectively, we obtain the function :

[0090] ,

[0091] where the intermediate parameter , the intermediate parameter , denotes the largest element in the set, denotes the smallest eigenvalue of the matrix, denotes the largest eigenvalue of the matrix;

[0092] Define two auxiliary variables and :

[0093] ,

[0094] ,

[0095] Select the parameter , we obtain

[0096] ,

[0097] wherein e represents a natural constant, represents a function value of the Lyapunov function at time 0.

[0098] The application further provides an electronic device comprising a processor and a memory, wherein the memory stores program codes, and the program codes, when executed by the processor, cause the processor to perform the steps of the method.

[0099] The application further provides a storage medium storing computer programs or instructions, and the computer programs or instructions, when executed on a computer, perform the steps of the method.

[0100] The application further provides a UAV system distributed control model comprising physical components such as sensors, controllers, actuators and the like, and the control method causes the controller to perform the steps of the method when executed by the controller.

[0101] The application has the following beneficial effects: the control protocol design method can ensure that the multi-agent system with input saturation characteristics can still achieve consistency even if the control input reaches the threshold value, and the multi-agent system with input saturation characteristics can achieve global consistency, that is, regardless of the initial state of the system, consistency can be achieved eventually, and the stability and robustness of the multi-agent system with input saturation characteristics are improved. BRIEF DESCRIPTION OF DRAWINGS

[0102] Figure 1 is the communication topology graph of the multi-agent UAV system with input saturation characteristics.

[0103] Figure 2 is a graph showing the change of the x-direction position component of the i-th UAV of the multi-agent UAV system with input saturation characteristics over time.

[0104] Figure 3 is a graph showing the change of the y-direction position component of the i-th UAV of the multi-agent UAV system with input saturation characteristics over time.

[0105] Figure 4 is a graph showing the change of the z-direction position component of the i-th UAV of the multi-agent UAV system with input saturation characteristics over time.

[0106] Figure 5 is a graph showing the change of the x-direction velocity component of the i-th UAV of the multi-agent UAV system with input saturation characteristics over time.

[0107] Figure 6 is a graph simulating the time-varying y-direction velocity component of the i-th unmanned aerial vehicle of the multi-agent unmanned aerial vehicle system with input saturation characteristics according to the present application.

[0108] Figure 7 is a graph simulating the time-varying z-direction velocity component of the i-th unmanned aerial vehicle of the multi-agent unmanned aerial vehicle system with input saturation characteristics according to the present application.

[0109] Figure 8 is a graph simulating the time-varying x-direction acceleration component of the i-th unmanned aerial vehicle of the multi-agent unmanned aerial vehicle system with input saturation characteristics according to the present application.

[0110] Figure 9 is a graph simulating the time-varying y-direction acceleration component of the i-th unmanned aerial vehicle of the multi-agent unmanned aerial vehicle system with input saturation characteristics according to the present application.

[0111] Figure 10 is a graph simulating the time-varying z-direction acceleration component of the i-th unmanned aerial vehicle of the multi-agent unmanned aerial vehicle system with input saturation characteristics according to the present application. DETAILED DESCRIPTION

[0112] The above and / or other aspects of the present application will become apparent and more readily appreciated from the following description, taken in conjunction with the accompanying drawings, in which:

[0113] The embodiment of the present application provides a design method of a global consensus safe control protocol of a multi-agent system with input saturation characteristics under the influence of a DoS attack, and comprises the following steps:

[0114] Step 1, constructing a differential equation model of the multi-agent system with input saturation characteristics.

[0115] The differential equation model of the i-th follower is:

[0116] ,

[0117] The differential equation model of the leader is:

[0118] ,

[0119] wherein, represents the state vector of the i-th agent at time t, and has a dimension of 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, and has a dimension of p; define to represent the input saturation of the multi-agent system, denotes the minimum element in the set; A denotes the system matrix of the multi-agent system with input saturation property, with dimension n*n, B denotes the input matrix of the multi-agent system with input saturation property, with dimension n*p; ; denotes the minimum element in the set; A denotes the system matrix of the multi-agent system with input saturation property, with dimension n*n, B denotes the input matrix of the multi-agent system with input saturation property, with dimension n*p;

[0120] The global consensus control objective of the multi-agent system with input saturation property is to design a control protocol such that the multi-agent system with input saturation property satisfies

[0121] ,

[0122] The control protocol designed based on the observer is

[0123] ,

[0124] wherein denotes the observed state of the state of the i-th agent at time t, denotes the derivative of the observed state of the i-th agent at time t. denotes the element in the i-th row and j-th column of the adjacency matrix C. denotes the set of time intervals during which the i-th agent is not attacked by DoS attack from time 0 to time t, denotes the set of time intervals during which the i-th agent is attacked by DoS attack from time 0 to time t. denotes the control input of the i-th agent at time t.

[0125] Substituting into the multi-agent system with input saturation property, the following closed-loop system can be obtained.

[0126] When , i.e. when not attacked by DoS attack, the closed-loop system is written as

[0127] ,

[0128] When , i.e. when attacked by DoS attack, the closed-loop system is written as

[0129] ;

[0130] ​​​​​​​​Step 2, select the appropriate Lyapunov function:

[0131] ,

[0132] First, calculate when not under DoS attack The derivative with respect to time t, at this time Is expressed as:

[0133] ,

[0134] Let represent The derivative with respect to time t, calculated as:

[0135] ,

[0136] According to the design condition of the feedback matrix K, we get:

[0137] ,

[0138] Where is a constant greater than 0, the equation continues to write as:

[0139] ,

[0140] Select the variable satisfy the following equation:

[0141] ,

[0142] At the same time because , so define the auxiliary variable , :

[0143] ,

[0144] ,

[0145] Substitute the above equation, we get:

[0146] ,

[0147] Where .

[0148] Calculate when under DoS attack The derivative with respect to time t, at this time Is expressed as:

[0149] ,

[0150] Let represent With respect to the derivative of time t, it is calculated that:

[0151] ,

[0152] Since the matrix Z is a positive definite matrix, it is obtained that:

[0153] ,

[0154] Where Combining the cases of being subjected to DoS attack and not being subjected to DoS attack, the following conclusions are obtained:

[0155] ,

[0156] Next, two cases are discussed for whether the time t is in the DoS attack interval, the first case is that when the time t is not in the DoS attack interval, it is obtained that:

[0157] ,

[0158] The second case is that when the time t is in the DoS attack interval, it is obtained that:

[0159] ,

[0160] Since And , it is derived that:

[0161] ,

[0162] The parameter is selected, and it is obtained that:

[0163] ,

[0164] Through the above proof, it is obtained that the multi-agent system with input saturation characteristics under DoS attack can realize global consistency, and next the reliability of the method of the present application will be verified through simulation experiment.

[0165] The simulation experiment is a numerical simulation experiment for realizing state consistency tracking of six unmanned aerial vehicles (five followers and one leader). The positions of the unmanned aerial vehicles in three directions in the three-dimensional coordinate system are set as: , the velocities are represented as , and the accelerations are represented as . The model of the unmanned aerial vehicle system is written as:

[0166] ,

[0167] The state of the unmanned aerial vehicle is defined as a 6-dimensional vector, Control input of the UAV is a 3-dimensional vector, According to the model of the UAV system, the system matrix of the multi-agent UAV system with input saturation characteristics is set Input matrix Selecting parameters Solving the feedback gain K, the following can be obtained .

[0168] In the simulation experiment, the communication topology between the UAVs is set as a directed graph, that is, the UAVs can only one-way transmit state information. The communication topology graph of the multi-agent UAV system with input saturation characteristics constructed is shown in Figure 1 The numbers 1, 2, 3, 4, and 5 in the figure represent the numbers of the follower UAVs, and 6 represents the number of the leader UAV. The Laplacian matrix L of the communication graph is:

[0169] ,

[0170] Simulation result analysis: Figure 2 、 Figure 3 、 Figure 4 、 Figure 5 、 Figure 6 、 Figure 7 is a UAV state change graph, wherein represents the x-direction position state of the i-th UAV, represents the y-direction position state of the i-th UAV, represents the z-direction position state of the i-th UAV, represents the x-direction velocity state of the i-th UAV, represents the y-direction velocity state of the i-th UAV, represents the z-direction velocity state of the i-th UAV. Figure 8 、 Figure 9 、 Figure 10 is a UAV control input change graph, wherein represents the x-direction acceleration state of the i-th UAV, represents the y-direction acceleration state of the i-th UAV, represents the z-direction acceleration state of the i-th UAV. From the simulation graph, it can be seen that when subjected to a DoS attack, the multi-agent UAV system with input saturation characteristics can still achieve global consistency even when the control input reaches the threshold.

[0171] The application provides a design method of a global consensus safety control protocol of a multi-agent system with input saturation characteristics under the influence of a DoS attack. The above is only the preferred embodiment of the application, and it should be pointed out that, for those skilled in the art, several improvements and refinements can be made without departing from the principle of the application, and these improvements and refinements should also be regarded as the protection scope of the application. The components not explicitly described in the embodiment can be implemented by using the prior art.

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 safety control protocol for the multi-agent system with input saturation characteristics; 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: ， 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 that the limit value is obtained when time t tends to infinity; 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; 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 , .

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: ， 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 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.

4. The method according to claim 3, 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.

5. The method according to claim 4, 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.

6. 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 5.

7. 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 5 are executed.

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