A multi-agent system mean square consensus control method under hybrid attack

Abstract

The application provides a multi-agent system mean square consensus control method under hybrid attack, relates to the technical field of intelligent control, and comprises the following steps: establishing a multi-agent system model, designing a controller, on the basis, constructing an error system between a follower agent and a leader, and establishing a mean square consensus condition of the multi-agent system under a deception attack and a DOS attack, so that the multi-agent system is controlled to realize leader-following mean square consensus. The application improves the control strategy by comprehensively considering the possible deception attack and DOS attack during the working period of the multi-agent system, so that the leader-follower mean square bounded consensus is realized, and the control efficiency and control precision are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of intelligent control, and in particular to a method for mean square consensus control of a multi-agent system under hybrid attack. BACKGROUND

[0002] In the past two decades, the cooperative control of multi-agent systems has attracted extensive attention. A multi-agent system is composed of a large number of intelligent agents with communication connections, and these intelligent agents achieve common goals through information exchange between each other. In practical applications, such as sensor networks, social networks, distributed control, etc., the consensus between intelligent agents is the basis for achieving cooperative work. However, due to device differences, communication interference, noise and other factors, the information between intelligent agents may deviate during transmission. Mean square consensus refers to the state or information of all intelligent agents in a multi-agent system tending to be consistent in a certain statistical sense. Commonly, the mean square error (MSE) between them can be calculated to measure the degree of consensus. The mean square error is the average of the square of the difference between the state or information of each intelligent agent and the average state or information, reflecting the degree of consensus between intelligent agents.

[0003] However, the communication process between intelligent agents may encounter deception attacks and DOS attacks. Deception attacks occur between followers and neighbor followers, which means that attackers use false information or disguised behavior to mislead, manipulate or destroy the cooperation and decision-making between multiple intelligent agents, thereby achieving the purpose of malicious attack. In such a system, each intelligent agent completes complex tasks through communication and cooperation, so deception attacks will seriously affect the performance and security of the system. DOS attacks occur between leaders and followers, and attackers usually send a large number of invalid requests to the target system or consume a large amount of resources to overload the target system, causing the target system to be unable to provide normal services. How to reduce the adverse effects of attacks encountered during the communication process between intelligent agents has become a technical problem to be solved. SUMMARY

[0004] The present application aims to solve the problem of adverse effects of attacks encountered during the communication process between intelligent agents in current multi-agent systems, and provides a method for mean square consensus control of a multi-agent system under hybrid attack.

[0005] The technical scheme of the present application is implemented as follows:

[0006] The first aspect of the present application provides a method for mean square consensus control of a multi-agent system under hybrid attack, comprising:

[0007] S110, establishing a multi-agent system model;

[0008] Consider a multi-agent system consisting of N followers and 1 leader, whose dynamics equations are as follows:

[0009]

[0010] Wherein, s i (t)∈R n ,u i (t) respectively represent the state and control input of the i-th follower. s0(t)∈R n is the state of the leader, g(·):R n →R is a continuous nonlinear function, and A and B are preset parameter matrices.

[0011] S120, design a controller;

[0012] s0 represents the state value of the leader, and s i represents the state value of other agents in the multi-agent system. The leader is not affected by the control protocol, and each follower obeys the control protocol; the control protocol of the controller is as follows:

[0013]

[0014] Wherein, r ij is a random function satisfying Bernoulli distribution to determine whether to send fraudulent data, p i represents the fraudulent data information from the neighbor follower, satisfies ||P(t)||≤p, p is a normal number, f i is the pulse intensity, c i represents the communication intensity with the leader, m i (t) represents a random function of whether DOS attack occurs between the i-th agent and the leader, δ(·) is Dirac function, a ij is closely related to the topology graph of the multi-agent system. 0<t0<t1<…<t k <t k+1 <…, θ1≤t k -t k-1 ≤θ2, wherein θ1 and θ2 are normal numbers, and the system is left continuous;

[0015] S130, construct an error system between the follower agent and the leader;

[0016] The multi-agent system model can be converted into the following form:

[0017]

[0018] The error η i (t) between the follower agent and the leader is si (t) - s0(t), the error system is:

[0019]

[0020] The vector form of the error system is:

[0021]

[0022] where F = diag[f i ], C = diag[c i ], M(t k ) = diag[m i (t k )], R(t k ) = [r ij (t k )] N×N , G(t, η(t)) = [[g(s1(t)) - g(s0(t))] T , [g(s2(t)) - g(s0(t))] T ,..., [g(s N (t)) - g(s0(t))] T ] T , Ψ is a square matrix with all diagonal elements being 0, and Φ is a diagonal matrix;

[0023] S140, establishing a condition for mean-square consensus of multi-agent systems under deception attack and DOS attack;

[0024] Given that the error converges to When the following inequality is satisfied:

[0025]

[0026] Controlling the multi-agent system to achieve leader-following mean-square consensus.

[0027] Optionally, the deception attack is described as follows, define the injected false data as p i (t), the random function r ij (t) satisfies the Bernoulli distribution, which is defined as follows:

[0028]

[0029] When 0 < α ij <1, the probabilities of the random function r ij (t) are Prob{r ij (t) = 1} = α ij , Prob{r ij(t) = 0} = 1 - a ij .

[0030] Optionally, the DOS attack is described as follows, defining a random function m i (t) satisfies the Bernoulli distribution:

[0031]

[0032] When 0 < β i <1, the random function m i (t) has the probabilities Prob{m i (t) = 1} = β i , Prob{m i (t) = 0} = 1 - β i .

[0033] Optionally, after establishing the mean square consensus condition of the multi-agent system under the deception attack and the DOS attack, the method further comprises:

[0034] Determining the range of the mean square safe consensus based on the pulse control theory, the convex hull theory and the Lyapunov stability theory.

[0035] The second aspect of the embodiments of the application provides a multi-agent system mean square consensus control device under a hybrid attack, comprising: a model establishing module, a control design module, an error system constructing module and a consensus control module, wherein,

[0036] The model establishing module is configured to establish a multi-agent system model;

[0037] Consider a multi-agent system composed of N followers and 1 leader, and the dynamics equation is as follows:

[0038]

[0039] Wherein, s i (t) ∈ R n , u i (t) respectively represent the state and control input of the i-th follower. s0(t) ∈ R n is the state of the leader, g(·): R n → R is a continuous nonlinear function, and A and B are preset parameter matrices;

[0040] The control design module is configured to design a controller;

[0041] s0 represents the state value of the leader, and s i represents the state value of other agents in the multi-agent system. The leader is not affected by the control protocol, and each follower obeys the control protocol; the control protocol of the controller is as follows:

[0042]

[0043] where r ij is a random function satisfying Bernoulli distribution to determine whether to send deceptive data, p i represents deceptive data information from the neighbor follower, satisfies ||P(t)||≤p, p is a normal number, f i is the pulse intensity, c i represents the communication intensity with the leader, m i (t) represents a random function of whether DOS attack occurs between the i-th agent and the leader, δ(·) is the Dirac function, a ij is closely related to the topological graph of the multi-agent system. 0<t0<t1<…<t k <t k+1 <…, θ1≤t k -t k-1 ≤θ2, where θ1 and θ2 are normal numbers, and the system is left continuous;

[0044] The error system construction module is configured to construct an error system between the follower agent and the leader.

[0045] The multi-agent system model can be converted to the following form:

[0046]

[0047] The error η i (t) between the follower agent and the leader is s i (t)-s0(t), and the error system is:

[0048]

[0049] The vector form of the error system is:

[0050]

[0051] where F=diag[f i ], C=diag[c i ], M(t k )=diag[m i (t k )], R(t k )= [r ij (t k )] N×N , G(t, η(t))=[[g(s1(t))-g(s0(t)) T, [g(s2(t))-g(s0(t))] T ,..., [g(s N (t))]-g(s0(t))] T ] T , Ψ is a square matrix with all diagonal elements being 0, and Φ is a diagonal matrix;

[0052] The consistency control module is configured to establish a mean square consistency condition of the multi-agent system under the deception attack and the DOS attack.

[0053] Given the error converges to When the following inequality is satisfied:

[0054]

[0055] The multi-agent system is controlled to achieve leader-following mean square consistency.

[0056] The third aspect of the embodiment of the application provides an electronic device, including a processor and a memory; the memory has a computer program stored therein, wherein the computer program, when executed by the processor, implements the multi-agent system mean square consistency control method under the hybrid attack of the first aspect.

[0057] The fourth aspect of the embodiment of the application provides a computer readable storage medium, which has a computer program stored thereon, and the program, when executed by a processor, implements the steps of the method of the first aspect.

[0058] Compared with the prior art, the technical scheme provided by the application has the beneficial effects that:

[0059] The application provides a multi-agent system mean square consistency control method and device under a hybrid attack, which establishes a multi-agent system model, designs a corresponding controller, and on this basis, constructs an error system between a follower agent and a leader, and establishes a mean square consistency condition of the multi-agent system under a deception attack and a DOS attack, thereby controlling the multi-agent system to achieve leader-following mean square consistency. The application improves the control strategy by comprehensively considering the deception attack and the DOS attack that may exist during the operation of the multi-agent system, thereby achieving leader-following mean square bounded consistency, reducing the adverse effects caused by attacks in the communication process between agents, and improving control efficiency and control accuracy. BRIEF DESCRIPTION OF DRAWINGS

[0060] Figure 1 The flowchart of the multi-agent system mean square consistency control method under a hybrid attack provided by the embodiment of the application is shown in the figure.

[0061] Figure 2A structure diagram of a multi-agent system mean square consensus control device under a hybrid attack provided by an embodiment of the present application is provided.

[0062] Figure 3 A structure diagram of an electronic device provided by an embodiment of the present application is provided. DETAILED DESCRIPTION

[0063] In the following detailed description, numerous specific details are set forth in order to provide a thorough understanding of the embodiments of the present application. However, it will be apparent to one skilled in the art that one or more embodiments of the present application can be practiced without these specific details. In other instances, well-known structures and functions have not been described in detail in order to avoid obscuring the concepts of the present application.

[0064] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the present application. As used herein, the term "includes" and tautological expressions thereof, means the inclusion of the stated features, steps, operations, and / or components but not to the exclusion of one or more other features, steps, operations, or components.

[0065] All terms used herein (including technical and scientific terms) have the meanings commonly understood by one of ordinary skill in the art, unless otherwise defined. It should be noted that the terms used herein are to be interpreted as having a meaning that is consistent with the understanding of a person of ordinary skill in the art, and should not be interpreted in an idealized or overly formal manner.

[0066] Some of the blocks and / or flowcharts in the drawings represent computer program instructions, or programs. These programs can be supplied to a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, when executed by the machine, create a means for implementing the functions / operations specified in the flowcharts and / or block diagrams.

[0067] In some embodiments, please refer to Figure 1 , Figure 1 A flowchart of a multi-agent system mean square consensus control method under a hybrid attack provided by an embodiment of the present application is provided. The multi-agent system mean square consensus control method under a hybrid attack provided by an embodiment of the present application comprises the following steps.

[0068] S110, a multi-agent system model is established.

[0069] Consider a multi-agent system composed of N followers and 1 leader, whose dynamics equation is as follows:

[0070]

[0071] wherein s i (t)∈R n ,u i (t) respectively represent the state and control input of the i-th follower. s0(t)∈R n is the leader state, g(·):R n →R is a continuous nonlinear function, and A and B are preset parameter matrices;

[0072] Step S120, designing a controller;

[0073] s0 represents the state value of the leader, and s i represents the state value of other agents in the multi-agent system. The leader is not affected by the control protocol, and each follower complies with the control protocol; the control protocol of the controller is as follows:

[0074]

[0075] wherein r ij is a random function satisfying Bernoulli distribution to determine whether to send fraudulent data, p i represents fraudulent data information from neighboring followers, satisfies ||P(t)||≤p, p is a normal number, f i is the pulse intensity, c i represents the communication intensity with the leader, and m i (t) represents a random function of whether DOS attack occurs between the i-th agent and the leader, δ(·) is the Dirac function, a ij is closely related to the topology graph of the multi-agent system. 0<t0<t1<…<t k <t k+1 <…, θ1≤t k -t k-1 ≤θ2, wherein θ1 and θ2 are normal numbers, and the system is left continuous;

[0076] S130, constructing an error system between the follower agent and the leader;

[0077] The multi-agent system model can be converted into the following form:

[0078]

[0079] The error η i (t) between the follower agent and the leader is s i (t)-s0(t), and the error system is:

[0080]

[0081] The vector form of the error system is:

[0082]

[0083] Where F = diag[f i ],C=diag[c i ],M(t k )=diag[m i (t k )],R(t k )=[r ij (t k )] N×N , G(t, η(t))=[[g(s1(t))-g(s0(t))] T , [g(s2(t))-g(s0(t))] T ,...,[g(s N (t))]-g(s0(t))] T ] T , Ψ is a square matrix with all diagonal elements 0, and Φ is a diagonal matrix;

[0084] S140, establish the mean square consistency condition of the multi-agent system under deception attack and DOS attack;

[0085] The given error converges to When the following inequality is satisfied:

[0086]

[0087] Controlling multi-agent systems to achieve leader-follower mean square consensus.

[0088] In some embodiments, the deception attack is described as follows, defining the injected fake data as p i (t), random function r ij (t) satisfies the Bernoulli distribution, which is defined as follows:

[0089]

[0090] When 0<α ij <1, random function r ij The probabilities of (t) are Prob(r ij (t) = 1} = α ij 、Prob(r ij (t) = 0 = 1 - α ij .

[0091] In some embodiments, the DOS attack is described as follows, defining a random function m i (t) satisfies the Bernoulli distribution:

[0092]

[0093] When 0<β i <1, random function m i The probabilities of (t) are Prob(m i (t) = 1} = β i 、Prob(m i (t) = 0 = 1 - β i .

[0094] In some embodiments, after establishing the mean square consistency condition of the multi-agent system under deception attack and DOS attack, the method further includes:

[0095] The range of mean square security consistency is determined based on impulse control theory, convex hull theory and Lyapunov stability theory.

[0096] In an alternative embodiment, the Lyapunov function is constructed When t∈(t k-1 , t k ], its derivative is:

[0097]

[0098] From this, we can get Then we can get:

[0099]

[0100] When t = t k hour:

[0101]

[0102] in, V1(t k )=η T (t k )Q(t k )Q(t k )η(t k ), V2(t k )=η T (t k )Q(t k )Y(t k )+Y T (t k )Q(t k )η(t k ), V3(tk ) = Y T (t k ) Y(t k ), and and are discussed as follows:

[0103]

[0104] where μ1= μ min (ZL), μ2= μ min (ZCΦ), μ3= μ max (ZCΦ), and μ4= μ max (ZL). Similarly, we have

[0105]

[0106] where μ5= μ max (ZΨ), and similarly we have

[0107]

[0108] Thus, we have

[0109]

[0110] Further, we have

[0111]

[0112] When t∈[t0, t1], we have and

[0113]

[0114] When t∈(t1, t2], we have

[0115]

[0116] and

[0117]

[0118] By derivation, we have when t∈(t k , t k+1 ], we have

[0119]

[0120] If 0 < ε < 1, and when t∈(t k , t k+1 ], we have

[0121]

[0122] Based on Therefore, when t→+∞, In addition, if ε≥1 and t∈(t k , t k+1 ], similarly, it can be obtained that:

[0123]

[0124] According to When t→+∞, it can be obtained that Therefore, when t→+∞, In summary, the above multi-agent system can realize the mean square bounded consensus, and the error system can converge to the set

[0125] In one example, the multi-agent system includes 1 leader and 4 followers. Wherein each agent can communicate with the leader, and the Laplace matrix is:

[0126]

[0127] Select the initial value g(t, s i (t))=cot(s i (t))+cos(s i (t))sin(s i (t)), Select the parameters f i =0.25, c1=0.84, c2=0.69, c3=0.87, c4=0.62, p=0.8, θ1=0.18<t k -t k-1 =0.2<0.22=θ2, let ε=0.32, The error threshold can be obtained

[0128] The embodiments of the application establish a multi-agent system model, design a corresponding controller, on this basis, construct the error system between the follower agent and the leader, and establish the mean square consensus condition of the multi-agent system under the deception attack and DOS attack, thereby controlling the multi-agent system to realize the leader-following mean square consensus. The present application improves the control strategy by comprehensively considering the possible deception attack and DOS attack during the operation of the multi-agent system, thereby realizing the mean square bounded consensus of the leader and the follower, reducing the adverse effects caused by attacks in the communication process between agents, and improving the control efficiency and control accuracy.

[0129] In some embodiments, refer to Figure 2 , Figure 2 A structural schematic diagram of a multi-agent system mean square consensus control device under hybrid attack provided by an embodiment of the application. The multi-agent system mean square consensus control device 200 under hybrid attack provided by the embodiment of the application comprises a model establishing module 210, a control design module 220, an error system constructing module 230 and a consensus control module 240, wherein,

[0130] The model establishing module 210 is configured to establish a multi-agent system model;

[0131] Consider a multi-agent system composed of N followers and one leader, whose dynamics equation is as follows:

[0132]

[0133] Wherein, s i (t)∈R n , u i (t) respectively represent the state and control input of the i-th follower. s0(t)∈R n is the state of the leader, g(·):R n →R is a continuous nonlinear function, and A and B are preset parameter matrices;

[0134] The control design module 220 is configured to design a controller;

[0135] s0 represents the state value of the leader, and s i represents the state value of other agents in the multi-agent system. The leader is not affected by the control protocol, and each follower obeys the control protocol; the control protocol of the controller is as follows:

[0136]

[0137] Wherein, r ij is a random function satisfying Bernoulli distribution to determine whether to send fraudulent data, p i represents fraudulent data information from neighboring followers, satisfies ||P(t)||≤p, p is a normal number, f i is the intensity of the pulse, c i represents the communication intensity with the leader, m i (t) represents a random function of whether DOS attack occurs between the i-th agent and the leader, δ(·) is Dirac function, a ij is closely related to the topological graph of the multi-agent system. 0<t0<t1<…<t k <t k+1 <…, θ1≤t k -tk-1 ≤ θ2, where θ1 and θ2 are normal numbers, and the system is left continuous;

[0138] An error system construction module 230 is configured to construct an error system between the follower agent and the leader;

[0139] The multi-agent system model can be converted into the following form:

[0140]

[0141] The error η between the follower agent and the leader i (t) = s i (t) - s0(t), the error system is:

[0142]

[0143] The vector form of the error system is:

[0144]

[0145] Where F = diag[f i ], C = diag[c i ], M(t k ) = diag[m i (t k )], R(t k ) = [r ij (t k )] N×N ,

[0146] G(t, η(t)) = [[g(s1(t)) - g(s0(t))] T , [g(s2(t)) - g(s0(t))] T ,..., [g(s N (t)) - g(s0(t))] T ] T , Ψ is a square matrix with all diagonal elements being 0, and Φ is a diagonal matrix;

[0147] A consensus control module 240 is configured to establish a mean square consensus condition of the multi-agent system under the deception attack and the DOS attack;

[0148] Given that the error converges to When the following inequality is satisfied:

[0149]

[0150] The multi-agent system is controlled to realize leader-following mean square consensus.

[0151] In some embodiments, the deception attack is described as follows, defining the injected false data as p i (t), the random function r ij (t) satisfies the Bernoulli distribution, which is defined as follows:

[0152]

[0153] When 0 < α ij <1, the probability of the random function r ii (t) is Prob{r ij (t) = 1} = α ij , Prob{r ij (t) = 0} = 1 - α ij .

[0154] In some embodiments, the DOS attack is described as follows, defining the random function m i (t) satisfies the Bernoulli distribution:

[0155]

[0156] When 0 < β i <1, the probability of the random function m i (t) is Prob{m i (t) = 1} = β i , Prob{m i (t) = 0} = β i .

[0157] In some embodiments, the multi-agent system mean square consensus control device 200 under mixed attack further comprises a range determination module, which is specifically configured to:

[0158] Determine the range of mean square safe consensus based on the pulse control theory, the convex hull theory and the Lyapunov stability theory.

[0159] The multi-agent system mean square consensus control device under mixed attack provided by the embodiments of the present application can realize each process in the corresponding embodiments of the mixed attack multi-agent system mean square consensus control method described above, and to avoid repetition, it will not be repeated here.

[0160] It should be noted that the multi-agent system mean square consensus control device under mixed attack provided by the embodiments of the present application is based on the same application concept as the multi-agent system mean square consensus control method under mixed attack provided by the embodiments of the present application, so the specific implementation of this embodiment can be referred to the foregoing implementation of the mixed attack multi-agent system mean square consensus control method, and the repeated parts will not be repeated.

[0161] In some embodiments, referring to Figure 3 , Figure 3 A structural schematic diagram of an electronic device is provided in embodiments of the present application. An electronic device 300 is provided in embodiments of the present application, comprising a processor 310 and a memory 320; the memory 320 has a computer program stored therein, wherein the computer program, when executed by the processor, implements the mixed attack multi-agent system mean square consensus control method described above.

[0162] Specifically, the processor 310 may, for example, include a general purpose microprocessor, an instruction set processor, and / or a related chipset and / or a specialized microprocessor (such as an application specific integrated circuit (ASIC)), etc. The processor 310 can also include on-board memory for cache use. The processor 310 can be a single processing unit or a plurality of processing units for performing different actions of the method process according to embodiments of the present application.

[0163] The memory 320 may, for example, be any medium capable of containing, storing, communicating, propagating or transmitting instructions. For example, the memory 320 may, for example, include but is not limited to electrical, magnetic, optical, electromagnetic, infrared or semiconductor system, device, apparatus or propagation medium. Specific examples of the memory 320 include magnetic storage devices such as magnetic tape or hard disk (HDD); optical storage devices such as compact discs (CD-ROM); also random access memory (RAM) or flash memory; and / or wired / wireless communication links.

[0164] The present application also provides a computer readable medium having a computer program stored thereon, which, when executed by a processor, implements the mixed attack multi-agent system mean square consensus control method described above. The computer readable medium can be included in the device / apparatus / system described in the above embodiments; or it can exist separately and not be assembled into the device / apparatus / system. The above computer readable medium carries one or more programs, which, when executed, implement the method according to embodiments of the present application.

[0165] According to the embodiments of the present application, the computer readable medium can be a computer readable signal medium or a computer readable storage medium or any combination thereof. The computer readable storage medium can be, for example but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus or device, or any suitable combination thereof. More specific examples of the computer readable storage medium can include, but are not limited to, an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In this application, the computer readable storage medium can be any tangible medium that can contain or store a program for use by or in connection with an instruction execution system, apparatus or device. In this application, the computer readable signal medium can include a computer readable program code transmitted in baseband or as part of a carrier wave in which the computer readable program code is digitally modulated and transmits over a carrier wave. Such a transmitted program code can take any number of forms including, but not limited to, electromagnetic signals, optical signals, or any suitable combination thereof. The computer readable signal medium can also be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate or transport a program for use by or in connection with an instruction execution system, apparatus or device. The program code contained on the computer readable medium can be transmitted using any suitable medium, including but not limited to wireless, wired, optical fiber cable, RF, and the like, or any suitable combination thereof.

[0166] Those skilled in the art will appreciate that features recited in the various embodiments and / or claims of this application can be combined and / or interchanged, even if this is not explicitly stated in the application. In particular, the features of the various embodiments and / or claims of this application can be combined and / or interchanged, without departing from the spirit and teachings of this application. All such combinations and / or interchanges are intended to fall within the scope of this application. Accordingly, the scope of the application should not be limited to the above-described embodiments, but should be determined by the appended claims and their equivalents.

Claims

1. A method for controlling mean square consistency of a multi-agent system under hybrid attacks, characterized by: include: S110, establish a multi-agent system model; Consider a multi-agent system consisting of N followers and 1 leader, whose dynamic equation is as follows: ； in, , Respectively represent The states and control inputs of the followers, For the leader state, is a continuous nonlinear function, A and B are preset parameter matrices; S120, design controller; Indicates the status value of the leader, Represents the state values ​​of other agents in a multi-agent system. The leader is not affected by the control protocol, and each follower complies with the control protocol. The control protocol of the controller is as follows: ； in, Is a random function that satisfies the Bernoulli distribution to decide whether to send fraudulent data. Represents the deceptive data information from neighbor followers, satisfy is a positive constant, is the pulse intensity, represents the communication strength with the leader, A random function indicating whether a DOS attack occurs between the i-th agent and the leader, is the Dirac function, Closely related to the topology of the multi-agent system, , ,in, and is a positive constant, and the system is left continuous; S130, constructing an error system between the follower agent and the leader; The multi-agent system model is converted into the following form: ； The error between the follower agent and the leader , the error system is: ； The vector form of the error system is: ； in, , , , , , , , , , , , is a square matrix whose diagonal elements are all 0, is a diagonal matrix; S140, establish the mean square consistency condition of the multi-agent system under deception attack and DOS attack; The given error converges to , when the following inequality is satisfied: ； The multi-agent system is controlled to achieve leader-follower mean square consensus.

2. The method for controlling mean square consistency of a multi-agent system under hybrid attack according to claim 1 is characterized in that: The deception attack is described as follows, defining the injected false data as , random function It satisfies the Bernoulli distribution, which is defined as follows: ； when , random function The probabilities of 、 .

3. The method for controlling mean square consistency of a multi-agent system under hybrid attack according to claim 1, characterized in that: The DOS attack is described as follows: define the random function Satisfies Bernoulli distribution: ； when , random function The probabilities of 、 .

4. The method for controlling mean square consistency of a multi-agent system under hybrid attack according to claim 1, characterized in that: After establishing the mean square consistency condition of the multi-agent system under deception attack and DOS attack, the method further includes: The range of mean square security consistency is determined based on impulse control theory, convex hull theory and Lyapunov stability theory.

5. A device for controlling mean square consistency of a multi-agent system under hybrid attack, characterized in that: include: Model building module, control design module, error system construction module and consistency control module, among which, The model building module is configured to build a multi-agent system model; Consider a multi-agent system consisting of N followers and 1 leader, whose dynamic equation is as follows: ； in, , Respectively represent The states and control inputs of the followers, For the leader state, is a continuous nonlinear function, A and B are preset parameter matrices; The control design module is configured to design a controller; Indicates the status value of the leader, Represents the state values ​​of other agents in a multi-agent system. The leader is not affected by the control protocol, and each follower complies with the control protocol. The control protocol of the controller is as follows: ； in, Is a random function that satisfies the Bernoulli distribution to decide whether to send fraudulent data. Represents the deceptive data information from neighbor followers, satisfy is a positive constant, is the pulse intensity, represents the communication strength with the leader, A random function indicating whether a DOS attack occurs between the i-th agent and the leader, is the Dirac function, Closely related to the topology of the multi-agent system, , ,in, and is a positive constant, and the system is left continuous; The error system building module is configured to build an error system between the follower agent and the leader; The multi-agent system model is converted into the following form: ； The error between the follower agent and the leader , the error system is: ； The vector form of the error system is: ； in, , , , , , , , , , , , is a square matrix whose diagonal elements are all 0, is a diagonal matrix; The consistency control module is configured to establish a mean square consistency condition for the multi-agent system under deception attacks and DOS attacks; The given error converges to , when the following inequality is satisfied: ； The multi-agent system is controlled to achieve leader-follower mean square consensus.

6. An electronic device comprising a processor and a memory; the memory stores a computer program, wherein: When the computer program is executed by the processor, the computer program implements the mean square consistency control method of a multi-agent system under a hybrid attack according to any one of claims 1 to 4.

7. A computer-readable storage medium having a computer program stored thereon, wherein when the program is executed by a processor, the steps of the method according to any one of claims 1 to 4 are implemented.

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