A method and system for asynchronous dynamic intermittent safety control of coupled networks

Abstract

The embodiment of the present application provides a method and system for asynchronous dynamic intermittent safety control of a coupled network. The method can obtain multiple attack signals including injection attack signals and replacement attack signals after establishing a dynamic model of a follower network, a target network, and a state error variable, and set an intermittent controller according to the dynamic network model and the multiple attack signals, and then set a dynamic mechanism based on an exponential function to convert the state error variable into an interval control function. The interval control function is used to achieve safe mean square synchronization control between the follower network model and the target network model. The method can utilize a node-adaptive double deception attack probability model, based on the average intermittent control rate and the dynamic event trigger threshold coupling method, to construct an asynchronous anti-attack intermittent dynamic collaborative control strategy for complex coupled networks, which can alleviate the difficulties in modeling multiple attacks and the lack of coordination of control strategies.

Description

Technical Field

[0001] The present application relates to the field of network security and control technology, and in particular to a method and system for asynchronous dynamic intermittent security control of a coupled network. Background Art

[0002] Complex dynamic networks can be used to describe the operating mechanisms of critical infrastructure such as aircraft formations, smart grids, and wireless sensor networks, and are widely used in areas such as mobile autonomous systems and the Industrial Internet of Things. Synchronous control theory can be applied to the synchronous control of dynamic networks. Synchronous control theory is used to explain swarm behavior and plays an important role in engineering scenarios such as secure communications and image encryption. Synchronous control theory can be implemented based on idealized assumptions: the communication links between network nodes are secure and reliable, the local data of sensors and actuators has not been tampered with, and the control process is not interfered with by malicious attacks.

[0003] However, as dynamic networks expand in scale and become increasingly open, such as in 5G communications and cloud-edge-end collaborative architectures, collaboration between network nodes relies heavily on information exchange. This makes multiple deception attacks, such as false data injection, signal replay, and identity spoofing, a security threat to dynamic networks. Attackers can exploit the topology or node dynamics of coupled networks to disrupt network synchronization, reduce control efficiency, and even trigger cascading failures by tampering with transmitted data. In coupled dynamic networks, distributed sensors and actuators rely on open channels for information exchange, making control commands and measurement data vulnerable to deception attacks such as eavesdropping and tampering, severely undermining network confidentiality, integrity, and synchronization performance. Deception attacks are highly concealed and can remain latent for long periods of time by forging or manipulating data, inducing cascading failures and posing a far-reaching threat.

[0004] To improve the security of dynamic networks, continuous secure synchronization control can be implemented to counter deception attacks, such as security synchronization control based on an idealized continuous control framework. However, this control approach struggles to address the challenges of limited communication resources, asynchronous node responses, and dynamic heterogeneity of attacks in open networks. Furthermore, defense mechanisms lack tolerance for multiple coordinated attacks, and continuous control strategies can easily lead to resource overconsumption, making it difficult to meet the high-performance and robustness requirements of distributed coupled networks. Summary of the Invention

[0005] In view of this, an embodiment of the present application provides a coupled network asynchronous dynamic intermittent security control method and system to solve the problems of difficulty in modeling multiple attacks and insufficient coordination of control strategies in security control methods.

[0006] According to one aspect of the present application, a method for asynchronous dynamic intermittent safety control of a coupled network is provided, the method comprising:

[0007] Establishing a coupled dynamic network model, the coupled dynamic network model includes a follower network model, a target network model, and a state error variable, wherein the follower network model is a dynamic model of the follower node state relative to time; the target network model is a dynamic model of the leader node state relative to time; and the state error variable is the difference between the follower network model and the target network model;

[0008] Acquire multiple attack signals, wherein the multiple attack signals include an injection attack signal and a replacement attack signal; the injection attack signal is a function representation of the injection attack signal suffered by multiple follower nodes and a dynamic network random variable; the replacement attack signal is a function representation of the replacement attack signal suffered by multiple follower nodes and a dynamic network random variable;

[0009] An intermittent controller is set according to the dynamic network model and the multiple attack signals, wherein the intermittent controller is an asynchronous non-periodic intermittent dynamic event triggered controller; the controller is used to make the state expected value of the state error variable converge to a preset compact set;

[0010] A dynamic mechanism is set based on an exponential function, and the state error variable is converted into an interval control function according to the intermittent controller and the dynamic mechanism. The interval control function is used to achieve safe mean square synchronization control between the follower network model and the target network model.

[0011] In some embodiments, establishing a coupled dynamic network model includes:

[0012] Acquire a follower node state, where the follower node state is a transposed representation of a matrix consisting of node states of a plurality of follower nodes in the follower network;

[0013] Acquiring modeling data, the modeling data including: a preset coefficient matrix, a nonlinear driving function, a coupling weight matrix, multiple attack signals, and an intermittent dynamic event trigger control input; the preset coefficient matrix including a first coefficient matrix and a second coefficient matrix;

[0014] The follower network model is established according to the modeling data and the follower node state.

[0015] In some embodiments, establishing the follower network model according to the modeling data and the follower node state includes:

[0016] Calculating a product of the first coefficient matrix and the follower node state to obtain a first model part;

[0017] Obtaining an inner coupling strength coefficient and an adjacency matrix, and calculating a second model part according to the inner coupling strength coefficient, the adjacency matrix and the follower node state;

[0018] Inputting the follower node state into the nonlinear driving function to obtain a follower driving function value;

[0019] Calculating the product of the follower driving function value and the second coefficient matrix to obtain a third model part;

[0020] A following network model is generated, where the following network model is the sum of the first model part, the second model part, the third model part, the multiple attack signals, and the intermittent dynamic event triggering control input.

[0021] In some embodiments, calculating the second model part according to the inner coupling strength coefficient, the adjacency matrix and the follower node state includes:

[0022] Acquire a node combination state, where the node combination state includes a first follower node state and a second follower node state, where the first follower node state and the second follower node state are respectively used to represent states of any two follower nodes belonging to different follower networks;

[0023] Calculating a state difference between the first follower node state and the second follower node state;

[0024] Calculating inner coupling data according to the state difference, the inner coupling data being the product of the adjacency matrix and the state difference, the inner coupling data being used to characterize the inner coupling strength between the first follower node and the second follower node;

[0025] The second model part is calculated according to the in-coupling data, where the second model part is the sum of the in-coupling data corresponding to the combined states of all nodes in the follower network.

[0026] In some embodiments, establishing a coupled dynamic network model includes:

[0027] Acquire a leader node state, where the leader node state is a transposed representation of a matrix consisting of node states of a plurality of the leader nodes in the target network;

[0028] Acquire a preset coefficient matrix and a nonlinear driving function, wherein the preset coefficient matrix includes a first coefficient matrix and a second coefficient matrix;

[0029] inputting the leader node state into the nonlinear driving function to obtain a leader driving function value;

[0030] The preset coefficient matrix is ​​used as a weighted weight to calculate a weighted sum of the leader node state and the leader driving function value to obtain the target network model.

[0031] In some embodiments, obtaining multiple attack signals includes:

[0032] Obtain the first attack signal and Bernoulli distribution random variable suffered by any follower node;

[0033] An injection attack signal is defined according to the first attack signal and the Bernoulli distribution random variable, wherein the injection attack signal is the sum of the products of the first attack signal and the Bernoulli distribution random variable corresponding to all nodes in the follower network;

[0034] An injection attack probability expectation matrix is ​​calculated based on the injection attack signal.

[0035] In some embodiments, obtaining multiple attack signals includes:

[0036] Obtaining a second attack signal suffered by any follower node, where the second attack signal is a transposed representation of a matrix of follower node states when multiple follower networks suffer a replacement attack;

[0037] A replacement attack signal is defined according to the second attack signal and the Bernoulli distribution random variable, wherein the replacement attack signal is the sum of the products of the second attack signals corresponding to all nodes in the follower network and the Bernoulli distribution random variable;

[0038] A replacement attack probability expectation matrix is ​​calculated based on the replacement attack signal.

[0039] In some embodiments, setting an intermittent controller according to the dynamic network model and the multiple attack signals includes:

[0040] Acquire a preset compact set, where the preset compact set is used to represent that a state expected value of a state error variable is less than or equal to a preset positive number within a preset control time period;

[0041] Dividing the dynamic network model into a control interval and a non-control interval, wherein the control interval is used to represent a state interval that simultaneously satisfies an event trigger interval condition within an activation period of intermittent control;

[0042] defining an event trigger instant, and inputting the event trigger instant into the state error variable to obtain an instantaneous error;

[0043] The control data of the control interval is set based on the preset asynchronous intermittent control adjustable gain parameter, the internal coupling strength coefficient and the instantaneous error in combination with the preset compact set.

[0044] In some embodiments, setting a dynamic mechanism based on an exponential function, and converting the state error variable into an interval control function according to the intermittent controller and the dynamic mechanism, comprises:

[0045] Get the preset exponential function;

[0046] Calculate the transmission interval error between the current data to be transmitted and the last triggered transmission data;

[0047] Calculating a first value according to the transmission interval error and the state error variable, the first value being a difference between a square of a norm of the transmission interval error and a square of a norm of the state error variable;

[0048] Obtaining a conversion coefficient and an asynchronous intermittent control adjustable gain parameter, and calculating a second value, where the second value is a product of the first value, the asynchronous intermittent control adjustable gain parameter, and the conversion coefficient;

[0049] Constructing an event triggering mechanism according to the preset exponential function and the second value, and determining event triggering instantaneous and dynamic adaptive variables according to the event triggering mechanism;

[0050] The state error variable is converted into an interval control function based on the trigger instant and the dynamic adaptive variable.

[0051] According to another aspect of the present application, a coupled network asynchronous dynamic intermittent safety control system is provided, the system comprising:

[0052] A model building module is used to build a coupled dynamic network model, wherein the coupled dynamic network model includes a follower network model, a target network model, and a state error variable. The follower network model is a dynamic model of the follower node state relative to time; the target network model is a dynamic model of the leader node state relative to time; and the state error variable is the difference between the follower network model and the target network model.

[0053] An attack signal module is configured to obtain multiple attack signals, wherein the multiple attack signals include an injection attack signal and a replacement attack signal; the injection attack signal is a function representation of the injection attack signal suffered by multiple follower nodes and a dynamic network random variable; the replacement attack signal is a function representation of the replacement attack signal suffered by multiple follower nodes and a dynamic network random variable;

[0054] A setting module is configured to set an intermittent controller according to the dynamic network model and the multiple attack signals, wherein the intermittent controller is an asynchronous non-periodic intermittent dynamic event triggered controller; the controller is configured to make the state expected value of the state error variable converge to a preset compact set;

[0055] A control module is used to set a dynamic mechanism based on an exponential function, and to convert the state error variable into an interval control function according to the intermittent controller and the dynamic mechanism, wherein the interval control function is used to achieve safe mean square synchronization control between the follower network model and the target network model.

[0056] According to another aspect of the present application, a computer device is provided, comprising a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor, wherein the processor implements the above-mentioned method for asynchronous dynamic intermittent safety control of a coupled network when executing the program.

[0057] According to another aspect of the present application, a storage medium is provided, on which a computer program is stored. When the program is executed by a processor, the above-mentioned asynchronous dynamic intermittent safety control method of the coupled network is implemented.

[0058] By means of the above technical solution, an embodiment of the present application provides a method and system for asynchronous dynamic intermittent safety control of a coupled network. The method can obtain multiple attack signals including injection attack signals and replacement attack signals after establishing a dynamic model of a follower network, a target network and a state error variable, and set an intermittent controller according to the dynamic network model and the multiple attack signals, and then set a dynamic mechanism based on an exponential function to convert the state error variable into an interval control function. The interval control function is used to achieve safe mean square synchronization control between the follower network model and the target network model. The method can utilize a node-adaptive double deception attack probability model, based on the average intermittent control rate and the dynamic event trigger threshold coupling method, to construct an asynchronous anti-attack intermittent dynamic collaborative control strategy for complex coupled networks, which can alleviate the difficulties in modeling multiple attacks and the lack of coordination of control strategies.

[0059] The above description is only an overview of the technical solution of the present application. In order to more clearly understand the technical means of the present application, it can be implemented in accordance with the contents of the specification. In order to make the above and other purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are listed below. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0061] Figure 1 A directed topological graph of a complex coupled dynamic network provided in an embodiment of the present application;

[0062] Figure 2 Schematic diagram of the asynchronous dynamic intermittent safety control method for a coupled network provided in an embodiment of the present application;

[0063] Figure 3 A flow chart of the control method provided in the embodiment of the present application;

[0064] Figure 4 A schematic diagram of asynchronous non-periodic intermittent dynamic event triggering control provided by an embodiment of the present application;

[0065] Figure 5 An event trigger frequency diagram provided for an embodiment of the present application;

[0066] Figure 6 The error state change curve diagram provided in the embodiment of the present application;

[0067] Figure 7 Schematic diagram of the coupled network asynchronous dynamic intermittent safety control system provided in an embodiment of the present application. DETAILED DESCRIPTION

[0068] The present application will be described in detail below with reference to the accompanying drawings and in combination with embodiments. It should be noted that, unless there is a conflict, the embodiments and features in the embodiments of the present application can be combined with each other.

[0069] In the embodiments of this application, a complex dynamic network is a dynamic network structure formed by multi-node communication, data sharing, and collaborative control. Complex dynamic networks can be used to describe aircraft formations, smart grids, wireless sensor networks, mobile autonomous systems, industrial Internet of Things, and other fields.

[0070] In order to ensure the coordinated operation of multiple nodes in a complex dynamic network, synchronous control can be performed on the dynamic network. Figure 1 As shown, synchronous control is a control process that uses synchronous control theory to achieve a consistent state or behavior among multiple dynamic nodes in a network. A complex dynamic network can have multiple network nodes, which can be categorized based on their roles in the control process. For example, a network system can include follower nodes and leader nodes. Leader nodes issue control commands, while follower nodes respond to these commands and follow the commands. Therefore, the number of follower nodes is often smaller than the number of leader nodes. For example, nodes numbered 1, 2, 3, ..., 8 are called follower nodes. Follower nodes can also exchange data with each other to achieve synchronous control.

[0071] In a complex dynamic network, if the state variables of all nodes converge to the same state as time approaches infinity, the network is said to be synchronized. In some embodiments, synchronized control can be performed based on idealized assumptions: the communication links between network nodes are secure and reliable, the local data of sensors and actuators has not been tampered with, and the control process is not interfered with by malicious attacks.

[0072] However, as dynamic networks expand in scale and become more open, such as in 5G communications and cloud-edge-end collaborative architectures, collaboration between network nodes relies heavily on information exchange. This makes multiple deception attacks, such as false data injection, signal replay, and identity spoofing, a security threat to dynamic networks. Attackers can target the topology of coupled networks or node dynamics to tamper with transmitted data, disrupting network synchronization, reducing control efficiency, and even triggering cascading failures.

[0073] To improve the security of dynamic networks, some embodiments can implement continuous secure synchronization control against spoofing attacks. For example, secure synchronization control based on an idealized continuous control framework can be employed. However, this control approach struggles to address issues such as limited communication resources, asynchronous node responses, and dynamic heterogeneity of attacks in open networks. Furthermore, defense mechanisms lack tolerance for multiple coordinated attacks, and continuous control strategies can easily lead to resource overconsumption, making it difficult to meet the high-performance and robustness requirements of distributed coupled networks.

[0074] Since false data injection into communication channels can trigger persistent attacks, discrete control schemes can reduce the success rate of these attacks. Therefore, in some embodiments, secure synchronization control strategies based on discontinuous monitoring can also be used to synchronize complex dynamic networks. However, since discontinuous secure control focuses on a single attack scenario, namely the false data injection problem in the sensor-controller channel, secure synchronization control strategies based on discontinuous monitoring can target spoofing attacks in the controller-actuator channel.

[0075] Because complex dynamic networks can also be subject to dual-channel coordinated attacks, i.e., simultaneous attacks on both the sensor-controller and controller-actuator networks, in some embodiments, a pulse control model for dual-channel deception attacks can be constructed, and synchronous control can be achieved based on this model. However, due to the spatiotemporal coupling characteristics of cross-layer attack signals, theoretical bottlenecks exist in attack coupling modeling, defense strategy coordination, and dynamic stability analysis. Therefore, by constructing a pulse control model for dual-channel deception attacks, relying on a fixed-period trigger mechanism, it fails to achieve the coordinated design of dynamic trigger mechanisms and resource optimization, making it difficult to cope with the computing and communication resource constraints brought about by network scale expansion.

[0076] Intermittent control combines a flexible architecture with low computing resource consumption by alternating between start-stop control intervals and sleep intervals. Intermittent control can be triggered based on either clock cycles or events. Event-driven intermittent control dynamically triggers control actions based on error thresholds, optimizing resource efficiency by updating data on demand. Dynamic event triggering further introduces internal dynamic variables, significantly reducing communication overhead.

[0077] In view of the asynchronous characteristics of actual scenarios, in some embodiments, it is also possible to trigger control based on asynchronous non-periodic intermittent dynamic events. However, its application in coupled dynamic networks under network attacks is still limited, which are manifested as follows: asynchrony conflict, that is, the difference in the probability of nodes being subjected to deception attacks under network attacks makes the collaborative design of asynchronous intermittent control difficult; dynamic defense energy efficiency imbalance, that is, asynchronous non-periodic intermittent dynamic event triggering control does not consider the network topology reconstruction and dynamic resource allocation under attack destruction, and is difficult to adapt to large-scale coupled networks; insufficient cross-layer attack suppression, that is, the dynamic triggering mechanism is mostly targeted at a single attack scenario, and lacks the ability to respond elastically to dual-channel collaborative deception attacks on sensors-controllers and controllers-actuators.

[0078] In summary, the synchronization control methods described in the above embodiments assume a globally uniform attack probability, fail to account for node heterogeneity, and lack dynamic modeling for coordinated attacks between sensor-controller and controller-actuator channels. Consequently, modeling multiple attacks is difficult in the synchronization control process of complex dynamic networks.

[0079] Furthermore, asynchronous intermittent dynamic event-triggered control suffers from asynchronous conflicts under multiple attacks. This means that differences in node attack probabilities lead to control timing mismatches, making stability analysis difficult and convergence difficult during the inactive interval. Consequently, synchronous control strategies lack coordination. Furthermore, because the event-triggered mechanism frequently updates data under attack perturbations, the computational burden is excessive and it is difficult to adapt to the resource constraints of large-scale coupled networks. Consequently, synchronous control methods can lead to an imbalance between resources and security.

[0080] In order to solve the problems of difficulty in modeling multiple attacks and insufficient coordination of control strategies in security control methods, some embodiments of this application provide a coupled network asynchronous dynamic intermittent security control method, which can be applied to network systems. By constructing an attack-adaptive dynamic trigger control framework, it addresses the problem of coordinated optimization of asynchronous intermittent control and multiple attack defense, and realizes the safe and efficient operation of resource-constrained coupled networks. Figure 2 、 Figure 3 As shown, the method includes:

[0081] S101. Establish a coupled dynamic network model.

[0082] Before executing synchronous control, a coupled dynamic network model can be established. The coupled dynamic network model includes a following network model, a target network model, and a state error variable. The following network model is a dynamic model of the following node state relative to time.

[0083] In order to construct a follower network model, in some embodiments, the network system may first obtain the follower node state when establishing the coupled dynamic network model. The follower node state is a transposed representation of a matrix consisting of the node states of multiple follower nodes in the follower network. For example, the follower node state can be expressed as: , used to represent the i The status of a node.

[0084] After obtaining the status of the follower node, the network system can obtain the modeling data. The modeling data includes: a preset coefficient matrix, a nonlinear driving function f ( x i ( t )), coupling weight matrix , multiple attack signals And intermittent dynamic event trigger control input The preset coefficient matrix includes a first coefficient matrix and a second coefficient matrix, that is, the preset coefficient matrix includes the first coefficient matrix and the second coefficient matrix , the first coefficient matrix and the second coefficient matrix are both real matrices with appropriate dimensions.

[0085] Then, the following network model is established based on the modeling data and the following node state. In some embodiments, in order to establish the following network model, the network system can first calculate the product of the first coefficient matrix and the following node state to obtain the first model part.

[0086] For example, for the following node state x i ( t ), you can get the first coefficient matrix ; Then calculate the follower node status x i ( t ), you can get the first coefficient matrix , to obtain the first model part of the following network model, that is C x x i ( t ).

[0087] Then, an internal coupling strength coefficient and an adjacency matrix are obtained, and a second model portion is calculated based on the internal coupling strength coefficient, the adjacency matrix, and the follower node state. The second model portion is calculated to characterize the internal coupling strength of the follower network model, which can be calculated based on the internal coupling strength coefficient, the adjacency matrix, and the follower node state.

[0088] In some embodiments, the network system may first obtain a node combination state. The node combination state includes a first follower node state and a second follower node state, and the first follower node state and the second follower node state are respectively used to characterize the states of any two follower nodes belonging to different follower networks. Then the state difference between the first follower node state and the second follower node state is calculated. And the internal coupling data is calculated based on the state difference. The internal coupling data is the product of the adjacency matrix and the state difference, and the internal coupling data is used to characterize the internal coupling strength between the first follower node and the second follower node. Then the second model part is calculated based on the internal coupling data, and the second model part is the sum of the internal coupling data corresponding to all node combination states in the follower network.

[0089] When calculating the second model part, the network system can first obtain the node states corresponding to any two nodes in the follower network, that is, the first follower node state and the second follower node state , forming a node combination state. Then calculate the difference between the first follower node state and the second follower node state, that is, . And based on the coupling weight matrix Extract coupling weight b ij x , and calculate the product between the coupling weight and the above calculated difference to obtain the internal coupling data Then the sum of the internal coupling data is calculated to obtain the sum of the internal coupling data corresponding to the combined state of all nodes in the following network, that is, the second model part is .

[0090] After calculating the second model part, the following node state is input into the nonlinear driving function to obtain the following driving function value, and the product of the following driving function value and the second coefficient matrix is ​​calculated to obtain the third model part. x i ( t ) Input the nonlinear driving function and obtain the follow-up driving function value f ( x i ( t )), then based on the second coefficient matrix Calculate the third model part .

[0091] After calculating and obtaining the first model part, the second model part, and the third model part, the network system can generate a following network model based on the calculated model parts. The following network model is the sum of the first model part, the second model part, the third model part, the multiple attack signals, and the intermittent dynamic event trigger control input. That is, considering the mean square bounded safety synchronization control of a network of N coupled dynamic following nodes, the following network model of the i-th node is:

[0092] (1)

[0093] Where, i=1, 2, 3, ..., N; Indicates the state of the i-th follower node; d x represents the internal coupling strength coefficient; and Represents the preset coefficient matrix, which is a real matrix of appropriate dimension; represents the coupling weight matrix; Indicates multiple attack signals; represents the nonlinear driving function; Indicates asynchronous non-periodic intermittent dynamic event trigger control input.

[0094] The target network model is a dynamic model of the leader node state relative to time. To establish the target network model, in some embodiments, the network system may first obtain the leader node state when establishing the coupled dynamic network model. The leader node state is a transposed representation of a matrix consisting of the node states of multiple leader nodes in the target network. A preset coefficient matrix and a nonlinear driving function are then obtained and the leader node state is input into the nonlinear driving function to obtain a leader driving function value. Using the preset coefficient matrix as weights, a weighted sum of the leader node state and the leader driving function value is calculated to obtain the target network model.

[0095] For example, the dynamic model of the target network (leader node) can be expressed as:

[0096] (2)

[0097] in, Indicates the leader node status; and Represents the preset coefficient matrix, which is a real matrix of appropriate dimension; f ( y 0( t )) represents the nonlinear driving function.

[0098] The state error variable is the difference between the follower network model and the target network model. The state error variable is also a dynamic model used to characterize the change in state error over time. To establish a dynamic model corresponding to the state error variable, in some embodiments, when establishing a coupled dynamic network model, the network system can obtain the follower node state and the leader node state, and then establish a variable expression for the state error variable based on the follower node state and the leader node state. The variable expression is the difference between the follower node state and the leader node state; the variable expression is used to characterize the synchronization state error of the follower node relative to the leader node. Based on this variable expression, the follower network model and the target network model are combined to obtain the state error variable.

[0099] Let the synchronization state error variable of the i-th follower node relative to the target node (leader node) be , then by combining the above formula (1) and formula (2), and then combining the state error variable , the synchronization state error system of the i-th node relative to the target network is as follows:

[0100] (3)

[0101] in, ; d x represents the internal coupling strength coefficient; C x =( c ij x ) n×n and A x =( a ij x ) n×n Represents the preset coefficient matrix, which is a real matrix of appropriate dimension; represents the coupling weight matrix; is the Laplace matrix Parameter values ​​in ; Representing multiple attack signals, a deception attack function is mathematically defined. Its specific value can be obtained by monitoring attacks on network nodes. For multiple attack signals, the deception attack function is uncertain and unknown, and its acquisition is mathematically defined. Specifically, by defining a deception attack and characterizing it with mathematical variables that follow a random Bernoulli distribution, the attack variables are further introduced into a time-synchronized control model for complex dynamic networks to analyze their impact on data transmission between the controller and actuator.

[0102] For example, a multiple attack signal can be represented as:

[0103] ;

[0104] in, Represents the attack signal, which is the mathematical definition of a deception attack; or 1, indicating a Bernoulli-distributed random variable associated with a dynamic network; θ i ( t ) represents the first attack signal and is a bounded function.

[0105] Indicates a controller that is under deception attack, which can be based on event triggering mechanism and attack function The mathematical definition of is determined together. That is:

[0106] ;

[0107] Correspondingly, u i ( t ) indicates a controller that has not been subjected to a spoofing attack. That is:

[0108] ;

[0109] in, d x represents the internal coupling strength; Adjustable gain parameters for asynchronous intermittent control; express Synchronization error at time; represents a random variable with a value of 0 or 1. It takes a value of 1 when an attack occurs and a value of 0 when no attack occurs. It is k A quasi-periodic intermittent control cycle; It is i The first dynamic network k Interval control width; Indicates the i The first dynamic network k Intermittent non-controlled width; The part indicates the period of time when the system is activated during intermittent control. The event trigger interval is satisfied at the same time The time interval of the condition, Indicates the i A dynamic network in k An intermittent control and the specific time when the event occurs.

[0110] Therefore, given the topology structure for N dynamic networks, Used to represent the communication relationship between networks, where represents a non-empty vertex set, Representing the edge set, it can characterize the correlation characteristics between networks. represents the coupling weight matrix (adjacency matrix), where i and j belong to the edge set if and only if i and j belong to the edge set hour, ,otherwise . represents the Laplace matrix, where ,and .

[0111] For example, consider the mean square safe bounded synchronization control of a complex coupled dynamic network, which includes one target dynamic network and eight follower dynamic networks, and the dynamic model of the i-th follower dynamic network is:

[0112] (4);

[0113] Where, i =1, 2, 3, ..., 8; Indicates the i The state of a dynamic network; d x =1 indicates the internal coupling strength; the values ​​of the first coefficient matrix and the second coefficient matrix are:

[0114] , ;

[0115] The attack signal , where T represents the transpose of the vector; Indicates the asynchronous non-periodic intermittent dynamic event trigger control input to be designed.

[0116] Consider nonlinear functions ,and ,in, i =1, 2, 3, ..., 8; j =1, 2, 3, then the constraints can be met , .

[0117] remember l i1 = l i2 = l i3 =1, Represents the coupling weight matrix. Combined with the dynamic model of the target dynamic network:

[0118] (5);

[0119] Where, Indicates the status of the target network, , as well as Same as in formula (4), the initial state is .

[0120] Give the topology structure for 8 dynamic networks Used to represent the communication relationship between networks, the non-empty vertex set is , the edge set is , is used to characterize the correlation characteristics between networks. If there is an edge between two network nodes, they are considered neighbors. Therefore, the internal coupling weight matrix of the 8 dynamic network nodes is:

[0121] ;

[0122] S102: Acquire multiple attack signals.

[0123] After establishing a complex coupled dynamic network dynamics model under multiple attack effects, the network system can introduce multiple deception attack modeling, that is, obtain multiple attack signals. The multiple attack signals include injection attack signals and replacement attack signals. The injection attack signal is a function representation of the injection attack signals and the dynamic network random variables experienced by multiple follower nodes.

[0124] Regarding the injection attack signal, in some embodiments, when acquiring multiple attack signals, the network system may obtain the first attack signal and a Bernoulli distribution random variable suffered by any follower node, and then define the injection attack signal based on the first attack signal and the Bernoulli distribution random variable, thereby calculating the injection attack probability expectation matrix based on the injection attack signal. The injection attack signal is the sum of the products of the first attack signals and the Bernoulli distribution random variables corresponding to all nodes in the follower network.

[0125] It addresses the multiple attack problems of sensor-to-controller and controller-to-actuator channels under injection and replacement attacks. It is possible to define multiple attack signals injected into the following network model. :

[0126] (6);

[0127] in, Indicates multiple attack signals, which is the mathematical definition of deception attack; or 1, indicating a Bernoulli-distributed random variable associated with a dynamic network; θ i ( t ) represents the first attack signal, which is a predefined bounded function.

[0128] Assume that the Bernoulli distribution random variable takes the value of 1 when the attacker launches an attack and takes the value of 0 when the attacker does not launch an attack. are independent of each other, then:

[0129] ;

[0130] in, is a constant, and , represents the random variable at time t The probability of taking the value 1 is equal to a constant , Denotes that at time t, the random variable The probability of taking the value 0 is equal to the constant 1- β ij .matrix The mathematical expectation matrix is ,Right now:

[0131] (7);

[0132] Random variables via Bernoulli distribution The first attack signal with bounded function θ i ( t ) combined to define multiple attack signals .

[0133] The replacement attack signal is a functional representation of the replacement attack signal suffered by multiple follower nodes and a dynamic network random variable. Regarding the replacement attack signal, in some embodiments, when executing the acquisition of multiple attack signals, the network system may first acquire a second attack signal suffered by any follower node. The second attack signal is a transposed representation of the matrix constituting the follower node state when multiple follower networks are subjected to the replacement attack. The replacement attack signal is defined based on the second attack signal and the Bernoulli distribution random variable, and the replacement attack probability expectation matrix is ​​calculated based on the replacement attack signal. The replacement attack signal is the sum of the products of the second attack signals corresponding to all nodes in the follower network and the Bernoulli distribution random variable.

[0134] Define the replacement deception attack signal as ,remember By introducing Bernoulli distribution variables related to dynamic network controllers To describe the probability of a successful attack, assume that the random variable are independent of each other, i represents a positive integer, then:

[0135] ;

[0136] in, is a constant, Denotes that at time t, the random variable The probability of taking the value 1 is equal to a constant α i , Denotes that at time t, the random variable The probability of taking the value 0 is equal to the constant 1- α i .remember for expectations, namely:

[0137] (8);

[0138] For example, by introducing multiple deception attack modeling, the network system can be used to prevent multiple attacks on sensor-to-controller and controller-to-actuator channels under injection attacks and substitution attacks. and , I Represents the identity matrix with matching dimensions.

[0139] S103: Setting an intermittent controller according to the dynamic network model and the multiple attack signals.

[0140] After introducing multiple deception attack modeling and obtaining multiple attack signals, the network system can set up an asynchronous non-periodic intermittent dynamic event-triggered controller. Specifically, the intermittent controller is configured based on the dynamic network model and the multiple attack signals. The intermittent controller is an asynchronous non-periodic intermittent dynamic event-triggered controller, which is configured to converge the state expected value of the state error variable to a preset compact set.

[0141] In some embodiments, when setting the intermittent controller based on the dynamic network model and the multiple attack signals, the network system may first obtain a preset compact set, wherein the preset compact set is used to represent that the state expected value of the state error variable is less than or equal to a preset positive number within a preset control time period.

[0142] The problem of secure mean square bounded synchronization between the following network model and the target network model can be transformed into a tracking problem between each following dynamic network and the target network. In order to achieve secure tracking with the target network, the state expectation value of the state error variable of the following network model and the target network model can be made to converge to a compact set through secure anti-attack control. ,Right now:

[0143] (9);

[0144] in, is a positive number, The expectation of the state error variable is less than or equal to .

[0145] After obtaining the preset compact set, the dynamic network model can be divided into a control interval and a non-control interval. The control interval represents the state interval that satisfies the event trigger interval conditions during the intermittent control activation period. The instantaneous error is obtained by defining an event trigger instant and substituting the event trigger instant into the state error variable. The control data for the control interval is then set based on the preset asynchronous intermittent control adjustable gain parameter, the internal coupling strength coefficient, and the instantaneous error, in combination with the preset compact set.

[0146] The network system can be designed with the following asynchronous non-periodic intermittent dynamic event trigger controller:

[0147] (10);

[0148] in, Adjustable gain parameters for asynchronous intermittent control; It is k A quasi-periodic intermittent control cycle; It is i The first dynamic network k Interval control width; Indicates the i The first dynamic network k Intermittent non-controlled width; The part indicates the period of time when the system is activated during intermittent control. The event trigger interval is satisfied at the same time The time interval of the condition, Indicates the i A dynamic network in k An intermittent control and the specific time when the event occurs.

[0149] like Figure 4 As shown, the intermittent control sequence of the i-th node based on the event is:

[0150] ;

[0151] For example, for asynchronous non-periodic intermittent dynamic events triggering the controller:

[0152] (11);

[0153] In the formula, you can set , , express The synchronization error at the moment. Figure 5 As shown, the asynchronous control intervals for the 8 coupled networks are:

[0154] Coupling network 1: ;

[0155] Coupling network 2: ;

[0156] Coupling network 3: ;

[0157] Coupling network 4: ;

[0158] Coupling network 5: ;

[0159] Coupling network 6: ;

[0160] Coupling network 7: ;

[0161] Coupling network 8: .

[0162] S104 , setting a dynamic mechanism based on an exponential function, and converting the state error variable into an interval control function according to the intermittent controller and the dynamic mechanism.

[0163] An asynchronous non-periodic intermittent dynamic event-triggered controller and an event-dynamically triggered communication scheme are designed. Specifically, a dynamic mechanism is set up based on an exponential function. Furthermore, the state error variable is converted into an interval control function based on the intermittent controller and the dynamic mechanism. The interval control function is used to achieve secure mean square synchronization control between the follower network model and the target network model.

[0164] To convert the interval control function, in some embodiments, the network system can first obtain a preset exponential function. Then, the transmission interval error between the current data to be transmitted and the last triggered transmission data is calculated. A first value is calculated based on the transmission interval error and the state error variable. The first value is the difference between the square of the transmission interval error norm and the square of the state error variable norm. A conversion coefficient and an adjustable gain parameter for asynchronous intermittent control are then obtained, and a second value is calculated. The second value is the product of the first value, the adjustable gain parameter for asynchronous intermittent control, and the conversion coefficient. An event triggering mechanism is established based on the preset exponential function and the second value, and an event triggering instant and a dynamic adaptive variable are determined according to the event triggering mechanism. Consequently, the state error variable is converted into an interval control function based on the triggering instant and the dynamic adaptive variable.

[0165] Event trigger instant It can be determined by the following event triggering mechanism:

[0166] (12);

[0167] in, is a positive finite number, Indicates the error between the current data to be transmitted and the last triggered transmission data, then the dynamic adaptive variable Expressed as:

[0168] (13);

[0169] in, , is a positive finite number.

[0170] remember ,in Indicates the i A dynamic network, represents a natural number, , Indicates that in the interval The final trigger moment.

[0171] Under multiple deception attacks, the dynamic model corresponding to the state error variable formed by the follower network model and the target network model can be transformed into the following form under the action of intermittent control and dynamic mechanism:

[0172] (14);

[0173] Based on the above interval control function, the network system can achieve mean square bounded stability of the synchronization state error under the influence of multiple deception attacks based on the asynchronous non-periodic intermittent dynamic event triggering control method, that is, to finally achieve safe mean square synchronization control by following the network model and the target network model.

[0174] For example, in order to reduce the communication burden and save limited communication resources, based on the intermittent control mechanism introduced, based on the exponential function, considering the dynamic event triggering conditions, the event triggering instantaneous Determined by the following event triggering mechanism:

[0175] (15);

[0176] Therefore, the dynamic adaptive variable Designed to:

[0177] (16);

[0178] in, represents the initial value, is a positive finite number, Represents the exponential function. , , , Indicates the error between the current data to be transmitted and the data last triggered to be transmitted.

[0179] Therefore, under the action of the above-mentioned coupled network asynchronous dynamic intermittent security control method against multiple deception attacks, when the complex coupled dynamic network suffers from multiple deception attacks, the error system between each dynamic coupled network and the target dynamic network eventually achieves mean square bounded stability, that is, the mean square bounded security synchronization of the complex coupled dynamic network under the influence of multiple deception attacks is achieved, such as Figure 6 shown.

[0180] By applying the technical solutions of the above-mentioned embodiments, the asynchronous dynamic intermittent security control for coupled networks described in these embodiments can be based on a complex dynamic network attack model. This model simultaneously considers both edge-based injection-based spoofing attacks and node-based replacement-based spoofing attacks. By combining the differences in the mechanisms of different attack methods in the network, it assigns differentiated probabilities to each attack path, more realistically reflecting the heterogeneity of attacks. Through the collaborative design of asynchronous non-periodic intermittent control and dynamic event triggering conditions, it is implemented at the intersection of the control interval and the event triggering interval. That is, it responds to dynamic event triggers only within the activation window of the intermittent control, avoiding unnecessary control actions and achieving resource optimization. The trigger threshold is dynamically adjusted based on the attack probability, improving real-time fault tolerance against spoofing attacks and enhancing security. The dynamic event triggering control mechanism based on an exponential function can flexibly reduce the event triggering frequency while asynchronously decoupling the event triggering frequency and intermittent control activation time of each node, increasing the flexibility of the intermittent control width, ultimately achieving secure mean square synchronization of the entire complex coupled dynamic network. This mechanism is widely applicable in scenarios such as smart grids and multi-agent systems.

[0181] In some embodiments, as a specific implementation of the coupled network asynchronous dynamic intermittent safety control method described in the above embodiments, some embodiments of the present application also provide a coupled network asynchronous dynamic intermittent safety control system, such as Figure 7 As shown, the system includes:

[0182] A model building module is used to build a coupled dynamic network model, wherein the coupled dynamic network model includes a follower network model, a target network model, and a state error variable. The follower network model is a dynamic model of the follower node state relative to time; the target network model is a dynamic model of the leader node state relative to time; and the state error variable is the difference between the follower network model and the target network model.

[0183] An attack signal module is configured to obtain multiple attack signals, wherein the multiple attack signals include an injection attack signal and a replacement attack signal; the injection attack signal is a function representation of the injection attack signal suffered by multiple follower nodes and a dynamic network random variable; the replacement attack signal is a function representation of the replacement attack signal suffered by multiple follower nodes and a dynamic network random variable;

[0184] A setting module is configured to set an intermittent controller according to the dynamic network model and the multiple attack signals, wherein the intermittent controller is an asynchronous non-periodic intermittent dynamic event triggered controller; the controller is configured to make the state expected value of the state error variable converge to a preset compact set;

[0185] A control module is used to set a dynamic mechanism based on an exponential function, and to convert the state error variable into an interval control function according to the intermittent controller and the dynamic mechanism, wherein the interval control function is used to achieve safe mean square synchronization control between the follower network model and the target network model.

[0186] By applying the technical solutions of the above embodiments, the coupled network asynchronous dynamic intermittent safety control system provided by the above embodiments can establish a dynamic model of the follower network, the target network, and the state error variable through the model building module. Then, the attack signal module obtains multiple attack signals including the injection attack signal and the replacement attack signal, and the setting module sets the intermittent controller according to the dynamic network model and the multiple attack signals, so that the control module can set a dynamic mechanism based on the exponential function to convert the state error variable into an interval control function. The system can characterize the attack heterogeneity through the node differentiation probability association mechanism, and on this basis, build a joint security control framework for the sensor-controller and controller-actuator communication channels, overcome the collaborative design problem of the security controller under multiple deception attacks, and improve the limitations of the single attack mode and the static defense strategy.

[0187] The system can also be based on an anti-interference controller triggered by exponential dynamic events. By constructing auxiliary functionals and combining them with the averaging method theory, it can alleviate the analytical problem of the stability criterion of the dynamic system in the inactive interval of asynchronous intermittent control, achieve coordinated optimization of the trigger frequency and computational overhead under multiple deception attacks, and ensure the secure mean square bounded synchronous convergence of the networked system.

[0188] The system can also alleviate the problem of constructing stability criteria for asynchronous intermittent control under multiple deception attacks based on the core lemma of the average asynchronous intermittent control rate, improve the strong constraint assumptions on activation and sleep intervals, establish mean square bounded synchronization conditions, and systematically avoid the conservatism and computational redundancy problems caused by complex mathematical merging in existing intermittent control.

[0189] It should be noted that for other corresponding descriptions of the functional units involved in the coupled network asynchronous dynamic intermittent safety control system provided in the embodiment of the present application, reference can be made to the corresponding descriptions in the coupled network asynchronous dynamic intermittent safety control method provided in the above embodiment, and will not be repeated here.

[0190] The embodiment of the present application also provides a computer device, which can be specifically a personal computer, a server, a network device, etc. The computer device includes a bus, a processor, a memory and a communication interface, and may also include an input and output interface and a display device. The processor of the computer device is used to provide computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system, a computer program and a database. The internal memory provides an environment for the operation of the operating system and computer program in the non-volatile storage medium. The database of the computer device is used to store location information. The network interface of the computer device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, the steps in each method embodiment are implemented.

[0191] Those skilled in the art will understand that the structure of the above-mentioned computer device is only a partial structure related to the solution of the present application and does not constitute a limitation on the computer device to which the solution of the present application is applied. The specific computer device may include more or fewer components, or combine certain components, or have a different component arrangement.

[0192] In one embodiment, a computer-readable storage medium is further provided. The computer-readable storage medium may be non-volatile or volatile, and stores a computer program thereon. When the computer program is executed by a processor, the steps in the above-mentioned method embodiments are implemented.

[0193] In one embodiment, a computer program product is further provided, including a computer program, which implements the steps in the above method embodiments when executed by a processor.

[0194] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, stored data, displayed data, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties.

[0195] Those skilled in the art will understand that all or part of the processes in the above-mentioned embodiment methods can be implemented by instructing related hardware through a computer program. The computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods.

[0196] Any reference to a memory, database, or other medium used in the embodiments provided herein may include at least one of a non-volatile memory and a volatile memory. Non-volatile memory may include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc.

[0197] Volatile memory may include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM may be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0198] The database involved in each embodiment provided herein may include at least one of a relational database and a non-relational database. Non-relational databases may include, but are not limited to, distributed databases based on blockchain. The processor involved in each embodiment provided herein may be, but is not limited to, a general-purpose processor, a graphics processor, a digital signal processor, a programmable logic device, a data processing logic device based on quantum computing, and the like.

[0199] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0200] The above-described embodiments merely represent several implementation methods of the present application. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present application. It should be noted that a person of ordinary skill in the art may make various modifications and improvements without departing from the spirit of the present application, and these modifications and improvements fall within the scope of protection of the present application. Therefore, the scope of protection of the present application shall be determined by the appended claims.

Claims

1. A method for asynchronous dynamic intermittent safety control of a coupled network, characterized in that: The method comprises: Establishing a coupled dynamic network model, the coupled dynamic network model includes a follower network model, a target network model, and a state error variable, the follower network model is a dynamic model of the follower node state relative to time; the target network model is a dynamic model of the leader node state relative to time; the state error variable is the difference between the follower network model and the target network model; wherein establishing the coupled dynamic network model includes: obtaining the follower node state, the follower node state is the transposed representation of the matrix composed of the node states of multiple follower nodes in the follower network; obtaining modeling data, the modeling data including: a preset coefficient matrix, a nonlinear driving function, a coupling weight matrix, multiple attack signals, and an intermittent dynamic event triggering control input; the preset coefficient matrix includes a first coefficient matrix and a second coefficient matrix; establishing the follower network model according to the modeling data and the follower node state; Acquire multiple attack signals, wherein the multiple attack signals include an injection attack signal and a replacement attack signal; the injection attack signal is a function representation of the injection attack signal suffered by multiple follower nodes and a dynamic network random variable; the replacement attack signal is a function representation of the replacement attack signal suffered by multiple follower nodes and a dynamic network random variable; wherein acquiring multiple attack signals includes: acquiring a first attack signal suffered by any follower node and a Bernoulli distribution random variable; defining an injection attack signal based on the first attack signal and the Bernoulli distribution random variable, wherein the injection attack signal is the sum of the products of the first attack signals corresponding to all nodes in the follower network and the Bernoulli distribution random variable; and calculating an injection attack probability expectation matrix based on the injection attack signal; An intermittent controller is set according to the dynamic network model and the multiple attack signals, and the intermittent controller is an asynchronous non-periodic intermittent dynamic event triggered controller; the controller is used to make the state expected value of the state error variable converge to a preset compact set; wherein, setting the intermittent controller according to the dynamic network model and the multiple attack signals includes: obtaining a preset compact set, the preset compact set is used to characterize that the state expected value of the state error variable is less than or equal to a preset positive number within a preset control time period; dividing the dynamic network model into a control interval and a non-control interval, the control interval is used to represent a state interval that simultaneously satisfies the event trigger interval condition within the activation time period of intermittent control; defining an event trigger instant, and substituting the event trigger instant into the state error variable to obtain an instantaneous error; and setting intermittent control data of the control interval based on a preset asynchronous intermittent control adjustable gain parameter, an internal coupling strength coefficient, and the instantaneous error in combination with the preset compact set; A dynamic mechanism is set based on an exponential function, and the state error variable is converted into an interval control function according to the intermittent control data and the dynamic mechanism. The interval control function is used to achieve safe mean square synchronization control between the follower network model and the target network model.

2. The method according to claim 1, characterized in that Establishing the follower network model according to the modeling data and the follower node state includes: Calculating a product of the first coefficient matrix and the follower node state to obtain a first model part; Obtaining an inner coupling strength coefficient and an adjacency matrix, and calculating a second model part according to the inner coupling strength coefficient, the adjacency matrix and the follower node state; Inputting the follower node state into the nonlinear driving function to obtain a follower driving function value; Calculating the product of the follower driving function value and the second coefficient matrix to obtain a third model part; A following network model is generated, where the following network model is the sum of the first model part, the second model part, the third model part, the multiple attack signals, and the intermittent dynamic event triggering control input.

3. The method according to claim 2, characterized in that Calculating a second model part according to the inner coupling strength coefficient, the adjacency matrix and the follower node state includes: Acquire a node combination state, where the node combination state includes a first follower node state and a second follower node state, where the first follower node state and the second follower node state are respectively used to represent states of any two follower nodes belonging to different follower networks; Calculating a state difference between the first follower node state and the second follower node state; Calculating inner coupling data according to the state difference, the inner coupling data being the product of the adjacency matrix and the state difference, the inner coupling data being used to characterize the inner coupling strength between the first follower node and the second follower node; The second model part is calculated according to the in-coupling data, where the second model part is the sum of the in-coupling data corresponding to the combined states of all nodes in the follower network.

4. The method according to claim 1, wherein Establish coupled dynamic network models, including: Acquire a leader node state, where the leader node state is a transposed representation of a matrix consisting of node states of a plurality of the leader nodes in the target network; Acquire a preset coefficient matrix and a nonlinear driving function, wherein the preset coefficient matrix includes a first coefficient matrix and a second coefficient matrix; inputting the leader node state into the nonlinear driving function to obtain a leader driving function value; The preset coefficient matrix is ​​used as a weighted weight to calculate a weighted sum of the leader node state and the leader driving function value to obtain the target network model.

5. The method according to claim 1, characterized in that Acquire multiple attack signals, including: Obtaining a second attack signal suffered by any follower node, where the second attack signal is a transposed representation of a matrix of follower node states when multiple follower networks suffer a replacement attack; A replacement attack signal is defined according to the second attack signal and the Bernoulli distribution random variable, wherein the replacement attack signal is the sum of the products of the second attack signals corresponding to all nodes in the follower network and the Bernoulli distribution random variable; A replacement attack probability expectation matrix is ​​calculated based on the replacement attack signal.

6. The method according to claim 1, characterized in that Setting a dynamic mechanism based on an exponential function, and converting the state error variable into an interval control function according to the intermittent control data and the dynamic mechanism, comprises: Get the preset exponential function; Calculate the transmission interval error between the current data to be transmitted and the last triggered transmission data; Calculating a first value according to the transmission interval error and the state error variable, the first value being a difference between a square of a norm of the transmission interval error and a square of a norm of the state error variable; Obtaining a conversion coefficient and an asynchronous intermittent control adjustable gain parameter, and calculating a second value, where the second value is a product of the first value, the asynchronous intermittent control adjustable gain parameter, and the conversion coefficient; Constructing an event triggering mechanism according to the preset exponential function and the second value, and determining event triggering instantaneous and dynamic adaptive variables according to the event triggering mechanism; The state error variable is converted into an interval control function based on the trigger instant and the dynamic adaptive variable.

7. A coupled network asynchronous dynamic intermittent safety control system, characterized in that: The system comprises: A model building module is used to establish a coupled dynamic network model, wherein the coupled dynamic network model includes a follower network model, a target network model, and a state error variable. The follower network model is a dynamic model of the follower node state relative to time; the target network model is a dynamic model of the leader node state relative to time; and the state error variable is the difference between the follower network model and the target network model. Establishing the coupled dynamic network model includes: obtaining a follower node state, wherein the follower node state is a transposed representation of a matrix consisting of node states of multiple follower nodes in the follower network; obtaining modeling data, wherein the modeling data includes a preset coefficient matrix, a nonlinear driving function, a coupling weight matrix, multiple attack signals, and an intermittent dynamic event triggering control input; the preset coefficient matrix includes a first coefficient matrix and a second coefficient matrix; and establishing the follower network model according to the modeling data and the follower node state. An attack signal module is configured to obtain multiple attack signals, wherein the multiple attack signals include an injection attack signal and a replacement attack signal; the injection attack signal is a function representation of the injection attack signal suffered by multiple follower nodes and a dynamic network random variable; the replacement attack signal is a function representation of the replacement attack signal suffered by multiple follower nodes and a dynamic network random variable; wherein obtaining multiple attack signals includes: obtaining a first attack signal suffered by any follower node and a Bernoulli distribution random variable; defining an injection attack signal based on the first attack signal and the Bernoulli distribution random variable, wherein the injection attack signal is the sum of the products of the first attack signals corresponding to all nodes in the follower network and the Bernoulli distribution random variable; and calculating an injection attack probability expectation matrix based on the injection attack signal; a setting module for setting an intermittent controller according to the dynamic network model and the multiple attack signals, the intermittent controller being an asynchronous non-periodic intermittent dynamic event-triggered controller; the controller being configured to converge the state expected value of the state error variable to a preset compact set; wherein setting the intermittent controller according to the dynamic network model and the multiple attack signals comprises: obtaining a preset compact set, the preset compact set being configured to characterize that the state expected value of the state error variable is less than or equal to a preset positive number within a preset control time period; dividing the dynamic network model into a control interval and a non-control interval, the control interval being configured to represent a state interval that simultaneously satisfies an event trigger interval condition within an activation time period of intermittent control; defining an event trigger instant, and substituting the event trigger instant into the state error variable to obtain an instantaneous error; and setting intermittent control data of the control interval in combination with the preset compact set based on a preset asynchronous intermittent control adjustable gain parameter, an internal coupling strength coefficient, and the instantaneous error; A control module is used to set a dynamic mechanism based on an exponential function, and to convert the state error variable into an interval control function according to the intermittent control data and the dynamic mechanism, wherein the interval control function is used to achieve safe mean square synchronization control between the follower network model and the target network model.

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