Consensus control method for multi-agent system under asynchronous denial-of-service attack

Abstract

The application relates to a kind of asynchronous denial-of-service attack under multi-agent system security consistency control method, belong to the technical field of safety cooperative control of multi-agent system under network attack, the control method of the application considers the situation that the two passages of sensor to controller and controller to actuator of CPS are respectively subjected to DoS attack on one hand, the start and duration of attack of two passages can be different, which is closer to the attack mode of attacker to CPS system in actuality. On the other hand, under the condition that the multi-agent system composed of multiple CPSs is subjected to external disturbance, the method of the application ensures that the system still satisfies security consistency under asynchronous DoS attack, and enhances the security and reliability of the system.

Description

Technical Field

[0001] This invention belongs to the field of security collaborative control technology for multi-agent systems under network attacks, specifically relating to a security consistency control method for multi-agent systems under asynchronous denial-of-service attacks. Background Technology

[0002] Cyber-Physical Systems (CPS) are complex, multi-dimensional systems integrating computing, networking, and the physical environment. They achieve integrated design of computing, communication, and physical systems, making the entire system more efficient, reliable, and capable of real-time synchronization. Due to these characteristics, CPS have wide applications, including autonomous vehicle systems, process control systems, robotic systems, and smart grids. However, the data transmission layer of CPS typically connects to a network, which inherently exposes them to network attacks. The long-distance communication channels they possess further increase the risk of malicious network intrusion, making transmitted information an easy target for attacks. Therefore, secure collaborative control under network attacks is extremely important.

[0003] However, traditional security consistency control methods have shortcomings under cyberattacks, mainly in the following aspects:

[0004] (1) When multiple channels of a traditional CPS system are subjected to network attacks, only the scenario where two channels of the CPS are simultaneously subjected to a Denial of Service (DoS) attack is typically considered. However, in real-world systems, the attack methods and locations of malicious network attacks are random and uncertain. Therefore, the probability of the two channels of the CPS—sensor-to-controller and controller-to-actuator—being attacked is independent and equal. In practice, attackers can attack both channels of the CPS separately to increase attack efficiency, thereby increasing the success rate of the attack and further reducing the stability of the system.

[0005] (2) Based on traditional security control strategies, only the case of a single CPS being attacked by the network is usually considered, and it is not possible to protect against the case of a multi-agent system composed of multiple CPS being attacked by the network.

[0006] (3) Network security control strategies designed based on traditional methods do not take into account the situation where multi-agent systems are subjected to network attacks and external interference at the same time, which affects the stability of the system. Summary of the Invention

[0007] This invention aims to provide a robust, secure, and consistent control method for multi-agent systems (CPS) under asynchronous denial-of-service (DoS) attacks, thereby solving or improving the aforementioned technical problems. Specifically, this invention considers, on the one hand, the scenario where the sensor-to-controller and controller-to-actuator channels of a CPS are subjected to separate DoS attacks. The start and duration of the attacks on the two channels may differ, thus more closely resembling the actual attack patterns of attackers on CPS systems. On the other hand, considering the external interference affecting a multi-agent system composed of multiple CPSs, the method of this invention ensures that the system maintains secure consistency under asynchronous DoS attacks, enhancing the system's security and reliability.

[0008] This invention provides a method for secure consistency control of a multi-agent system under asynchronous denial-of-service attacks, the specific steps of which are as follows:

[0009] S1. Design an observer based on a multi-agent system model;

[0010] S2. Design an asynchronous denial-of-service attack model;

[0011] S3. Design the controller of the multi-agent system to obtain controller state values; obtain control data packets based on controller state values; send the control data packets to the buffer and update the buffer data packets sequentially; finally send them to the actuator to obtain the control input protocol;

[0012] S4. Calculate the parameters required in the control scheme, and obtain the state feedback gain matrix based on the parameter values; design the number of data packets; obtain the control input signal based on the number of data packets and the control input protocol in step 3;

[0013] S5: Use the controller from step S4 to obtain the control input signal; input the control input signal into the actuator to perform robust, secure, and consistent control of the multi-agent system under asynchronous DoS attacks.

[0014] Optionally, the specific steps for designing the observer based on the multi-agent system model in S1 are as follows:

[0015] Establish a linear discrete model of the agent, with the following expression:

[0016] x i (k+1)=Ax i (k)+Bu i (k)+B d d i (k)

[0017] y i (k)=Cx i (k)

[0018] in, This represents the state of the i-th agent at sampling step k+1; This represents the state of the i-th agent after k steps of sampling; This represents the output vector of the i-th agent after k sampling steps; It is the input of the i-th agent during k-step sampling. Let A, B, B be an unknown bounded perturbation applied to the i-th agent during k-step sampling. d C and C represent the state matrix, input matrix, disturbance matrix, and output matrix of the CPS system model, respectively.

[0019] Based on a linear discrete model of an agent, an observer is established, expressed as follows:

[0020]

[0021] in, This represents the state estimate of the i-th agent at time k+1; Let G represent the state estimate of the i-th agent at time k; G is the observer gain.

[0022] Optionally, an observer error system is established, with the following expression:

[0023]

[0024] in, This represents the state observation error of the i-th agent during the k+1th sampling step; This represents the state observation error of the i-th agent during k-step sampling.

[0025] Based on the observer error system, solve for the observer gain G that satisfies the linear matrix inequality LMI;

[0026] The expression for the linear matrix inequality (LMI) is:

[0027]

[0028] Where, ψ s =A-GC;I n Represents the identity matrix of dimension n; γ represents the constants and P. s This represents a positive definite symmetric matrix.

[0029] Optionally, the specific steps for designing an asynchronous denial-of-service attack model in S2 are as follows:

[0030] S21. Set the frequency limit for asynchronous denial-of-service attacks;

[0031] S22. Set time limits for asynchronous denial-of-service attacks;

[0032] S23. Based on the frequency and time constraints of asynchronous denial-of-service attacks, obtain the asynchronous denial-of-service attack model.

[0033] Optionally, the expression for setting the asynchronous denial-of-service attack frequency limit in S21 is:

[0034]

[0035] Where, n a (t1,t2) represents the number of effective DoS switching transitions between the sensors and controllers of multiple agents in the multi-agent system between time t1 and time t2; a represents the set of channels between the sensors and controllers of multiple agents, a∈{s,c}; s represents the channel from the sensor to the controller, and c represents the channel from the controller to the actuator; η a T represents the jitter boundary between sensors and controllers of multiple agents in a multi-agent system. Da This represents the average dwell time between the DoS system's on and off transitions.

[0036] Optionally, the expression in S22 that sets the time limit condition for asynchronous denial-of-service attacks is:

[0037]

[0038] Among them, |D a (t1,t2)| represents the time between time t1 and time t2 when the channels between the sensors and controllers of multiple agents in the CPS system are subjected to a DoS attack; κ a T represents the regularization term for the channels between sensors and controllers of multiple agents in a CPS system. a This indicates the duration of the DoS attack limit.

[0039] Optionally, the expression for the asynchronous denial-of-service attack model in S23 is:

[0040]

[0041] Among them, R a Indicates the maximum duration of a single attack; Δ a Indicates the time interval for channel data transmission.

[0042] Optionally, the expression for designing the controller of a multi-agent system in S3 is:

[0043]

[0044] in, This represents the state value of the i-th agent controller at time k; This represents the state value of the i-th agent controller at time k-1.

[0045] Optionally, the expression for the control data packet that obtains the controller status value in S3 is:

[0046]

[0047]

[0048] in, This represents the data packet sent by the controller of the i-th agent to the buffer at time k; m represents the number of data packets; K μ =[K T ,(K(A+BK)) T ,L,(K(A+BK) m-1 ) T ] T K represents the state feedback matrix; N i Represents the set of neighbors of node i; a ij Indicates the communication state between the i-th agent and the j-th agent, a ij =1 indicates that the i-th agent communicates with the j-th agent. In this case, the j-th agent is a neighbor of the i-th agent. ij =0 indicates that the i-th agent and the j-th agent do not communicate;

[0049] u represents the state value of the j-th agent controller at time k; c (k+m|k) represents the set of data packets sent by the agent's controller to the buffer at time k; x c (k) represents the set of state values ​​of the agent controller at time k.

[0050] Optionally, the expression for the data packet in the buffer in S3 is:

[0051]

[0052]

[0053] in, This represents the data packet in the buffer of the i-th agent at time k; This represents the data packet in the buffer of the i-th agent at time k-1.

[0054] Compared with the prior art, the present invention has at least the following beneficial effects:

[0055] 1. Under the proposed robust and secure consistency control framework for multi-agent systems, the control method proposed in this invention ensures the output consistency of multiple agents under the influence of network attacks by inputting data packets containing multiple data in the buffer layer, thereby ultimately achieving robust and secure consistency of the multi-agent system with anti-interference capabilities.

[0056] 2. It takes into account the asynchronous denial-of-service attack scenario under external interference. The scenario is more complex and more in line with the attack schemes of attackers in reality. The attack is more targeted and the security and reliability of the multi-agent system are stronger.

[0057] 3. Robust, safe, and consistent control of the system is achieved by designing a buffer. The designed control scheme is relatively simple and easy to implement in engineering. Attached Figure Description

[0058] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0059] Figure 1 Flowchart of the steps of this invention;

[0060] Figure 2 The present invention provides a multi-agent system framework for denial-of-service attacks.

[0061] Figure 3 The multi-agent system communication network topology diagram of this invention;

[0062] Figure 4 Location trajectory diagram of the multi-agent system of the present invention without DoS attack;

[0063] Figure 5 The velocity trajectory diagram of the multi-agent system of the present invention without DoS attack;

[0064] Figure 6 A schematic diagram of the position error of the observer system in the absence of a DoS attack according to the present invention;

[0065] Figure 7 A schematic diagram of the velocity error of the observer system in the absence of a DoS attack according to the present invention;

[0066] Figure 8 A schematic diagram of a DoS attack on the controller-to-actuator channel of this invention;

[0067] Figure 9 A schematic diagram of a DoS attack on the sensor-to-controller channel of this invention;

[0068] Figure 10 The position trajectory diagram of the second-order multi-agent system of the present invention when subjected to an asynchronous DoS attack;

[0069] Figure 11 The velocity trajectory diagram of the second-order multi-agent system of the present invention when subjected to an asynchronous DoS attack;

[0070] Figure 12 The location trajectory diagram of a multi-agent system subjected to an asynchronous DoS attack after the addition of a control strategy in this invention;

[0071] Figure 13 The velocity trajectory diagram of a multi-agent system subjected to an asynchronous DoS attack after the addition of a control strategy in this invention. Detailed Implementation

[0072] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0073] A specific embodiment of the present invention, such as Figure 1-13 A secure consistency control method for multi-agent systems under asynchronous denial-of-service attacks is disclosed, with the specific steps as follows:

[0074] S1. Design the observer based on the multi-agent system (i.e., CPS system) model;

[0075] The CPS system model consists of multiple agents, and the linear discrete model of each agent is as follows:

[0076] x i (k+1)=Ax i (k)+Bu i (k)+B d d i (k)

[0077] y i (k)=Cx i (k)

[0078] in, This represents the state of the i-th agent at sampling step k+1; This represents the state of the i-th agent after k steps of sampling; This represents the output vector of the i-th agent after k sampling steps; It is the input of the i-th agent during k-step sampling. Let A, B, B be an unknown bounded perturbation applied to the i-th agent during k-step sampling. d C and C represent the state matrix, input matrix, disturbance matrix, and output matrix of the CPS system model, respectively.

[0079] For example, the agent is a car or a motor. In this case, the state of the car is the position, velocity, and acceleration of the car, and the state of the motor is the rotational speed. The output vector of the car is the displacement measurement value of the car. When the agent is a car, the system matrix is ​​a matrix related to the inherent properties of the car, such as mass and friction coefficient.

[0080] The observer's expression is:

[0081]

[0082] in, This represents the state estimate of the i-th agent at time k+1; Let G represent the state estimate of the i-th agent at time k; G is the observer gain.

[0083] Furthermore, the observer error system is established, and its expression is:

[0084]

[0085] Among them, e i s (k+1) represents the state observation error of the i-th agent during the k+1th sampling step; This represents the state observation error of the i-th agent during k-step sampling.

[0086] Furthermore, in order to design the observer, based on the observer error system, a linear matrix inequality (LMI) is constructed, which applies to a given positive constant γ and an arbitrarily chosen positive definite symmetric matrix P. s Solve for the condition that satisfies

[0087] The observer gain; where ψ s =A-GC.

[0088] The observer gain G is obtained by solving the above linear matrix inequality LMI, and the Lyapunov function is designed. Where P s Let I be the selected positive definite symmetric matrix. N Represents an N-dimensional identity matrix. Representing the Kronecker product of matrices, Pe can be obtained according to the properties of the Lyapunov function. i s (k)P<γPd i (k)P, i∈1,L,N, where N represents the total number of agents; the observer system is asymptotically stable, and the observer error system achieves the observer performance Pe. s (k)P<γPd(k)P, the designed observer meets the requirements.

[0089] S2. Design an asynchronous denial-of-service attack model;

[0090] S21. Set asynchronous denial-of-service attack frequency limits:

[0091]

[0092] Where, n a (t1,t2) represents the number of effective DoS switching transitions between the sensors and controllers of multiple agents in the CPS system between time t1 and time t2; a represents the set of channels between the sensors and controllers of multiple agents, a∈{s,c}; s represents the channel from the sensor to the controller, and c represents the channel from the controller to the actuator; η a T represents the jitter boundary between sensors and controllers of multiple agents in a CPS system. Da This represents the average dwell time between enabling and disabling the transition during a DoS attack;

[0093] Furthermore,

[0094] S22. Set time limits for asynchronous denial-of-service attacks:

[0095]

[0096] Among them, |D a (t1,t2)| represents the time between time t1 and time t2 when the channels between the sensors and controllers of multiple agents in the CPS system are subjected to a DoS attack; κ a The regularization term represents the channels between sensors and controllers of multiple agents in a CPS system, used to make the above expression continuous; T a Indicates the duration of the DoS attack limit;

[0097] Furthermore, and

[0098] S23. Based on the frequency and time constraints of asynchronous denial-of-service attacks, the asynchronous denial-of-service attack model is obtained, and its expression is:

[0099]

[0100] Among them, R a Indicates the maximum duration of a single attack; Δ a This represents the time interval for channel data transmission, where a∈{s,c}.

[0101] Furthermore, the CPS system periodically transmits sampling and control data between its two channels, with the data transmission time interval between the sensor and the controller being Δ. s The data transmission time interval from the controller to the actuator is Δ c The set Δ c and Δ s satisfy a∈{s,c}, and guarantee Δ c ≤Δ s Let {s} r} r∈N s0≥t0 represents the system state value estimated by the observer. Successfully transmitted past execution cycles, making {z m} m∈N z0≥t0 represents the operation cycle in which control data was successfully transmitted, where s r This indicates the cycle in which the system state value estimated by the observer was successfully transmitted; s0 indicates the cycle in which the first control data was successfully transmitted; t0 indicates the start time; z m z0 indicates the first cycle in which control data was successfully transmitted.

[0102] Furthermore, {s r} r∈N Satisfying s0≤R s and s r+1 -s r ≤R s +1, {z m} m∈N satisfying z0≤R c and z m+1 -z m ≤R c +1, where R s ,R c These represent the maximum single attack time of the sensor-to-controller channel and the maximum single attack time of the controller-to-actuator channel, respectively; z m+1 This indicates the (m+1)th successful transmission cycle.

[0103] S3. Design the controller of the multi-agent system to obtain the controller state value; obtain the control data packet based on the controller state value; send the control data packet to the buffer and update the buffer data packet in sequence; finally send it to the actuator to obtain the control input protocol.

[0104] S31. Design a controller for a multi-agent system to obtain controller state values, expressed as:

[0105]

[0106] in, This represents the state value of the i-th agent controller at time k; This represents the state value of the i-th agent controller at time k-1.

[0107] It is understandable that if the sensor-to-controller channel of the multi-agent system at time k is not subjected to a network attack, i.e., k∈{s} r} r∈N The controller estimates the state of the i-th agent at time k. Update, s r This indicates that the system state values ​​estimated by the observer have been successfully transmitted to the previous cycle.

[0108] If the sensor-to-controller channel of a multi-agent system at time k is attacked by a network, i.e. The controller then retains the state value from the previous moment.

[0109] S32. Obtain the control data packet for the controller status value. The expression is:

[0110]

[0111]

[0112] in, This represents the data packet sent by the controller of the i-th agent to the buffer at time k; m represents the number of data packets; K μ =[K T ,(K(A+BK)) T ,L,(K(A+BK) m-1 ) T ] T K represents the state feedback matrix; N i Represents the set of neighbors of node i; a ij Indicates the communication state between the i-th agent and the j-th agent, a ij =1 indicates that the i-th agent communicates with the j-th agent. In this case, the j-th agent is the neighbor of the i-th agent. If they cannot communicate, then a ij =0;

[0113] u represents the state value of the j-th agent controller at time k; c (k+m|k) represents the set of data packets sent by the agent's controller to the buffer at time k. L represents the Laplace matrix. x c(k) represents the set of state values ​​of the agent controller at time k.

[0114] Understandable, It contains control data from time k to time k+m.

[0115] S33. Send the control data packet to the buffer for updating, and obtain the data packet from the buffer. The expression is:

[0116]

[0117]

[0118] in, I represents the data packet in the buffer of the i-th agent at time k; n This represents the identity matrix of dimension n; n represents the dimension of the agent's state. This represents the data packet in the buffer of the i-th agent at time k-1.

[0119] It is understandable that if the controller-to-actuator channel of the CPS system at time k is not subjected to a network attack, i.e., k∈{z} m} m∈N The data packets sent by the controller are transmitted to the actuator to update its buffer.

[0120] If the controller-to-actuator channel of the CPS system at time k is attacked by a network attack, i.e. If the data packet sent by the controller fails to be transmitted, the buffer will update the buffer data based on Γ and the data packet of the previous moment because it cannot receive new data.

[0121] S34. Send the buffer data packet to the actuator to obtain the control input protocol, the expression of which is:

[0122]

[0123]

[0124] Where u(k) represents the control input signal at time k, u(k) = col{u1(k), L, u N (k)};I N Represents a matrix of dimension N; u a (k+m|k) represents the data packet set in the buffer at time k; u i (k) represents the control input of the i-th agent at time k; This represents the data packet in the buffer of the i-th agent.

[0125] S4. Calculate the parameters required in the control scheme, and obtain the state feedback gain matrix based on the parameter values; design the number of data packets; obtain the control input signal based on the determined number of data packets and the control input protocol in step 3;

[0126] S41. Calculate the parameters required in the control scheme and obtain the state feedback gain matrix;

[0127] Preferably, the parameter required in the control scheme is a positive definite symmetric matrix P;

[0128] Given a positive definite matrix Q, find the positive definite symmetric matrix P that satisfies the following expression:

[0129] PA+A T P+2λ i PBB T P+Q≤0, i∈2,L,N;

[0130] Where A represents the state matrix; B represents the input matrix; λ i Represents the eigenvalues ​​of the Laplace matrix L;

[0131] The state feedback matrix K is obtained based on the positive definite symmetric matrix P, and its expression is:

[0132] K = -B T P.

[0133] S42. Design the number of data packets;

[0134] The number of data packets can be obtained based on the data packet constraint condition. The expression is:

[0135]

[0136] in, λ (Q) represents the smallest eigenvalue in a given positive definite matrix Q, β2=P2λ2PBB T PP, L represents the largest eigenvalue in the positive definite symmetric matrix P; L represents the Laplace matrix of the system; B represents the input matrix; K represents the state feedback matrix; μ A Let denote the logarithmic matrix norm of matrix A; e denotes the natural base. I represents the largest eigenvalue of the matrix; N Represents an identity matrix of dimension N; 1 NL is an N-dimensional vector with all elements equal to 1, where N represents the number of agents; the eigenvectors corresponding to the Laplacian matrix L are orthogonally transformed to form a matrix. υ represents the exception The matrix formed by orthogonalizing the other eigenvectors;

[0137] Furthermore, the number of data packets m is designed to be the smallest positive integer that satisfies the condition.

[0138] It is understandable that the number of data packets is equal to the number of buffer data packets or control data packets.

[0139] S43. Based on the number of data packets determined in step 42 and the control input protocol in step 3, obtain the control input signal u(k).

[0140] S5: Use the controller from step S4 to obtain the control input signal; input the control input signal into the actuator to perform robust, secure, and consistent control of the multi-agent system under asynchronous DoS attacks.

[0141] To illustrate the effectiveness of the method proposed in this invention, the following detailed description of the above technical solution is provided through a specific embodiment, demonstrating how to construct such a system. Figure 3 The MATLAB simulation system shown consists of 5 intelligent agents.

[0142] The relevant parameters of the multi-agent system model are shown below:

[0143]

[0144] The initial position and velocity of the system are X[0]=[4,-6,12,-12,8]′ and V[0]=[4,-6,12,-12,8]′. The external disturbance present in the system is d(k)=0.5*sin(0.05k). Furthermore, the CPS system H... ∞ The performance parameter γ = 1.5; in this example, the given observer gain G, state feedback matrix K, and Q are respectively:

[0145]

[0146] When not under a DoS attack, with the buffer size set to m=5, the position and velocity trajectories of the multi-agent system are as follows: Figure 4 and Figure 5 As shown;

[0147] For observer systems initial value At this point, the position and velocity errors between the state estimated by the observer and the actual system state are as follows: Figure 6 and Figure 7 As shown.

[0148] The two sets of figures above illustrate that the designed system state feedback gain matrix K and observer gain matrix G enable the multi-agent system to achieve asymptotic consistency in the absence of DoS attacks, and the observer error system satisfies robustness H. ∞ performance.

[0149] When subjected to a DoS attack, the total simulation time is set to 10 seconds, where the DoS attack time from the sensor to the controller is of size |D s (0,10)|=4.64s,n s (0,10)=15, the size from the DoS attack controller to the executor is |D c (0,10)|=4.95s,n c (0,10) = 15, and then we can obtain: η s =0.81,κ s =0.354,T Ds =0.704,T s =2.155,η c =1.23,κ c =0.738,T Dc =0.726,T c =2.02. To ensure Set Δ c =Δ s =0.01. From this, we can obtain the asynchronous DoS attack the system is subjected to, such as... Figure 8 and Figure 9 As shown.

[0150] In fact, the theoretical upper bound of m implies, to some extent, that it analyzes the worst-case scenario where both channels are attacked, i.e., the attack duration and frequency are relatively high, leading to a rather conservative conclusion. Based on this, we can consider using a smaller m to obtain more satisfactory system performance. Therefore, we choose m = 10. Figure 10 In the diagram, x1, x2, x3, x4, and x5 represent status information, and different shaded areas indicate different channels receiving DoS attacks.

[0151] pass Figure 10 It can be seen that DoS attacks on the controller-to-actuator and sensor-to-controller channels are independent. Some attacks target only one channel, while others attack both channels simultaneously. Of course, there are also cases where the system is unaffected by the attacks.

[0152] pass Figure 10 and Figure 11Comparing the data with the system state without a DoS attack, it can be seen that when the system is under a DoS attack, the inability to update the state in a timely manner leads to a longer time to reach consistency. Therefore, by designing a data update control strategy based on a state observer, the system's position and velocity state trajectories under asynchronous DoS attacks can be made as follows: Figure 12 and Figure 13 In summary, through comparison, it can be concluded that the control scheme proposed in this invention can ensure robust, safe, and consistent multi-agent systems under asynchronous DoS attacks on multiple channels.

[0153] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for security consistency control of a multi-agent system under asynchronous denial-of-service attack, a plurality of agents constituting a CPS system model, characterized in that, The specific steps are as follows: S1. Design an observer based on a multi-agent system model; S2. Design an asynchronous denial-of-service attack model, with the following steps: S21. Set the frequency limit for asynchronous denial-of-service attacks; S22. Set time limits for asynchronous denial-of-service attacks; S23. Based on the frequency and time constraints of asynchronous denial-of-service attacks, the asynchronous denial-of-service attack model is obtained, and its expression is: in, , s This indicates the channel from the sensor to the controller. c This indicates the channel from the controller to the actuator; Indicates the maximum duration of a single attack; Indicates the time interval for channel data transmission; Channels representing each agent The shaking boundary; Indicates channel Regular terms; Indicates the duration of the DoS attack limit; This represents the average dwell time between the DoS system's on and off transitions; S3. Design the controller of the multi-agent system to obtain controller state values; obtain control data packets based on controller state values; send the control data packets to the buffer and update the buffer data packets sequentially; finally send them to the actuator to obtain the control input protocol; The expression for the controller of the multi-agent system is as follows: in, express k Time of the first The state values ​​of each intelligent agent controller; express k -1 moment The state values ​​of each intelligent agent controller; express k Time of the first State estimates of each agent; This indicates that the system state values ​​estimated by the observer have been successfully transmitted to the previous cycle. The expression for the control data packet containing the controller status value is: in, Indicates the first The controller of each intelligent agent is in Data packets sent to the buffer at any time; m Indicates the number of data packets; ; Represented as a state feedback matrix; Represents a node The neighbor set; Indicates the first The first agent and the second j The communication status of each agent Indicates the first The first agent and the second The agents communicate with each other; at this time, the first agent... The agent is the first The neighbor of an intelligent agent, Indicates the first The first agent and the second The agents do not communicate; Represents the state matrix of the CPS system model; Represents the input matrix of the CPS system model; express Time of the first The state values ​​of each intelligent agent controller; The controller of the intelligent agent is in The set of data packets sent to the buffer at any given time; ; express k The state value set of the agent controller at any given time; ; Represents the Laplace matrix; ; Indicates dimension as Matrix; The expression for the data packet in the buffer is: in, express Time of the first Data packets in an agent's buffer; express Time of the first Data packets in an agent's buffer; This indicates that the control data was successfully transmitted in the previous cycle. S4. Calculate the parameters required in the control scheme, and obtain the state feedback gain matrix based on the parameter values; design the number of data packets; obtain the control input signal based on the number of data packets and the control input protocol in step 3; S5: Obtain the control input signal using step S4; input the control input signal into the actuator to perform robust, secure, and consistent control of the multi-agent system under asynchronous DoS attacks.

2. The method according to claim 1, characterized in that, The specific steps for designing the observer based on the multi-agent system model in S1 are as follows: Establish a linear discrete model of the agent, with the following expression: in, express k +1 step sampling The state of each agent; express k Step sampling The state of each agent; express k Step sampling The output vector of each agent; yes k Step sampling Input of an agent, express k Applying during step sampling at the first Unknown bounded perturbations on an intelligent agent These represent the perturbation matrix and output matrix of the CPS system model, respectively. Based on a linear discrete model of an agent, an observer is established, expressed as follows: in, express k +1 moment State estimates of each agent; This is the observer gain.

3. The method according to claim 2, characterized in that, Establish the observer error system, expressed as: in, express k +1 step sampling The state observation error of each agent; express k Step sampling The state observation error of each agent ; Based on the observer error system, solve for the observer gain that satisfies the linear matrix inequality LMI. ; The expression for the linear matrix inequality (LMI) is: in, ; Indicates dimension as The identity matrix; Represents positive constants and This represents a positive definite symmetric matrix.

4. The method according to claim 3, characterized in that, The expression for setting the frequency limit for asynchronous denial-of-service attacks in S21 is: in, express t 1 moment and t Channel between 2 time points The number of valid DoS switch transitions that occurred.

5. The method according to claim 4, characterized in that, The expression for setting the time limit condition for asynchronous denial-of-service attacks in S22 is: in, express t 1 moment and t 2 Time Channels The duration of the DoS attack.

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