Coupling network asynchronous dynamic intermittent safety control method and system

Abstract

The embodiment of the invention provides a coupling network asynchronous dynamic intermittent safety control method and system, and the method comprises the steps: obtaining multiple attack signals comprising an injection attack signal and a replacement attack signal after building a dynamic model of a following network, a target network and a state error variable; and setting an intermittent controller according to the dynamic network model and the multiple attack signals, and setting a dynamic mechanism based on an exponential function to convert a state error variable into an interval control function. Wherein the interval control function is used for realizing security mean square synchronization control between the following network model and the target network model. According to the method, the asynchronous anti-attack intermittent dynamic cooperative control strategy oriented to the complex coupled network can be constructed based on an average intermittent control rate and dynamic event trigger threshold coupling method by utilizing a node self-adaptive dual spoofing attack probability model, and the problems of difficulty in multi-attack modeling and insufficient control strategy collaboration can be relieved.

Description

Technical Field

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

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

[0003] However, with the expansion of the scale and the enhancement of the openness of dynamic networks, such as 5G communication and cloud-edge-end collaborative architectures, the collaboration between network nodes highly depends on information interaction, which makes multiple deception attacks such as false data injection, signal replay, and identity disguise become security threats to dynamic networks. Attackers can target the topological structure or node dynamics of the coupled network and disrupt network synchronization, reduce control efficiency, or even trigger cascading failures by tampering with transmitted data. In coupled dynamic networks, distributed sensors and actuators rely on open channels for information interaction, resulting in control instructions and measurement data being vulnerable to deception attacks such as eavesdropping and tampering, seriously damaging network confidentiality, integrity, and synchronization performance. Deception attacks have strong concealment and can lurk for a long time by forging or manipulating data and induce cascading failures, posing a more profound threat.

[0004] To improve the security of dynamic networks, continuous security synchronous control can be carried out against deception attacks, such as security synchronous control based on an idealized continuous control framework, etc. However, this control method is difficult to cope with problems such as limited communication resources, asynchronous node responses, and heterogeneous attack dynamics in open networks. Moreover, the defense mechanism has insufficient tolerance for multiple collaborative attacks, and continuous control strategies are prone to cause excessive resource consumption, making it difficult to meet the high-performance and strong robustness requirements of distributed coupled networks. Summary of the Invention

[0005] In view of this, embodiments of this application provide a coupled network asynchronous dynamic intermittent security control method and system to solve the problems of difficult multiple attack modeling and insufficient coordination of control strategies in security control methods.

[0006] According to one aspect of this application, a coupled network asynchronous dynamic intermittent security control method is provided, and the method includes: A coupled dynamic network model is established. 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 states of follower nodes with respect to time; the target network model is a dynamic model of the states of leader nodes with respect to time; the state error variable is the difference between the follower network model and the target network model; Multiple attack signals are obtained. The multiple attack signals include an injection attack signal and a replacement attack signal. The injection attack signal is a functional representation of the injection attack signals suffered by multiple follower nodes and the dynamic network random variables; the replacement attack signal is a functional representation of the replacement attack signals suffered by multiple follower nodes and the dynamic network random variables; An intermittent controller is set according to the dynamic network model and the multiple attack signals. 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; A dynamic mechanism is set based on an exponential function, and the state error variable is transformed into an interval control function according to 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.

[0007] In some embodiments, establishing a coupled dynamic network model includes: The states of follower nodes are obtained. The states of follower nodes are represented by the transpose of a matrix composed of the node states of multiple follower nodes in the follower network; Modeling data is obtained. The modeling data includes: a preset coefficient matrix, a nonlinear driving function, a coupling weight matrix, multiple attack signals, and an intermittent dynamic event-triggered control input. The preset coefficient matrix includes a first coefficient matrix and a second coefficient matrix; The follower network model is established according to the modeling data and the states of follower nodes.

[0008] In some embodiments, establishing the follower network model according to the modeling data and the states of follower nodes includes: The product of the first coefficient matrix and the states of follower nodes is calculated to obtain a first model part; The internal coupling strength coefficient and the adjacency matrix are obtained, and a second model part is calculated according to the internal coupling strength coefficient, the adjacency matrix, and the states of follower nodes; The states of follower nodes are input into the nonlinear driving function to obtain a follower driving function value; The product of the follower driving function value and the second coefficient matrix is calculated to obtain a third model part; Generate a following network model, which 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-triggered control input.

[0009] In some embodiments, calculating the second model part according to the inner coupling strength coefficient, the adjacency matrix, and the following node state includes: Obtain the node combination state, which includes the first following node state and the second following node state. The first following node state and the second following node state are respectively used to represent the states of any two following nodes belonging to different following networks; Calculate the state difference between the first following node state and the second following node state; Calculate the inner coupling data according to the state difference. The inner coupling data is the product of the adjacency matrix and the state difference, and the inner coupling data is used to represent the inner coupling strength between the first following node and the second following node; Calculate the second model part according to the inner coupling data. The second model part is the sum of the inner coupling data corresponding to all node combination states in the following network.

[0010] In some embodiments, establishing a coupled dynamic network model includes: Obtain the leader node state, which is the transpose representation of the matrix composed of the node states of multiple leader nodes in the target network; Obtain a preset coefficient matrix and a nonlinear driving function. The preset coefficient matrix includes a first coefficient matrix and a second coefficient matrix; Input the leader node state into the nonlinear driving function to obtain the leader driving function value; Using the preset coefficient matrix as the weighted weight, calculate the weighted sum result of the leader node state and the leader driving function value to obtain the target network model.

[0011] In some embodiments, obtaining multiple attack signals includes: Obtain the first attack signal suffered by any following node and a Bernoulli distribution random variable; Define an injection attack signal according to the first attack signal and the Bernoulli distribution random variable. The injection attack signal is the sum of the product of the first attack signal corresponding to all nodes in the following network and the Bernoulli distribution random variable; Calculate the injection attack probability expectation matrix based on the injection attack signal.

[0012] In some embodiments, obtaining multiple attack signals includes: Obtain the second attack signal suffered by any follower node, where the second attack signal is the transposed representation of the state composition matrix of follower nodes when multiple follower networks are subjected to replacement attacks; Define the replacement attack signal according to the second attack signal and the Bernoulli distribution random variable, where 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; Calculate the replacement attack probability expectation matrix based on the replacement attack signal.

[0013] In some embodiments, setting an intermittent controller according to the dynamic network model and the multiple attack signals includes: Obtain a preset compact set, which is used to represent that within a preset control time period, the state expected value of the state error variable is less than or equal to a preset positive number; Divide the control interval and the non-control interval of the dynamic network model, where the control interval is used to represent the state interval that simultaneously satisfies the event trigger interval condition during the activation time period of intermittent control; Define the event trigger instant, and substitute the event trigger instant into the state error variable to obtain the instantaneous error; Based on the preset asynchronous intermittent control adjustable gain parameter, the internal coupling strength coefficient, and the instantaneous error, and in combination with the preset compact set, set the control data of the control interval.

[0014] In some embodiments, setting a dynamic mechanism based on an exponential function, and transforming the state error variable into an interval control function according to the intermittent controller and the dynamic mechanism includes: Obtain a preset exponential function; Calculate the transmission interval error between the current data to be transmitted and the data transmitted in the previous trigger; Calculate a first value according to the transmission interval error and the state error variable, where the first value is the difference between the square of the norm of the transmission interval error and the square of the norm of the state error variable; Obtain the conversion coefficient and the asynchronous intermittent control adjustable gain parameter, and calculate a second value, where the second value is the product of the first value, the asynchronous intermittent control adjustable gain parameter, and the conversion coefficient; Construct an event trigger mechanism according to the preset exponential function and the second value, and determine the event trigger instant and the dynamic adaptive variable according to the event trigger mechanism; Based on the trigger instant and the dynamic adaptive variable, transform the state error variable into an interval control function.

[0015] According to another aspect of the present application, there is provided a coupled network asynchronous dynamic intermittent safety control system, and the system includes: A model establishment module, configured to establish a coupled dynamic network model, where 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 with respect to time; the target network model is a dynamic model of the leader node state with respect to time; the state error variable is the difference between the follower network model and the target network model. An attack signal module, configured to obtain multiple attack signals, where the multiple attack signals include an injection attack signal and a replacement attack signal; the injection attack signal is a functional representation of multiple follower nodes being subjected to the injection attack signal and the dynamic network random variable; the replacement attack signal is a functional representation of multiple follower nodes being subjected to the replacement attack signal and the dynamic network random variable. A setting module, configured to set an intermittent controller according to the dynamic network model and the multiple attack signals, where the intermittent controller is an asynchronous aperiodic 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. A control module, configured to set a dynamic mechanism based on an exponential function, and convert the state error variable into an interval control function according to the intermittent controller and the dynamic mechanism, where the interval control function is used to achieve secure mean-square synchronization control between the follower network model and the target network model.

[0016] According to another aspect of the present application, there is provided a computer device, including a storage medium, a processor, and a computer program stored on the storage medium and executable on the processor. When the processor executes the program, the above-mentioned coupled network asynchronous dynamic intermittent security control method is implemented.

[0017] According to still another aspect of the present application, there is provided a storage medium, on which a computer program is stored. When the program is executed by a processor, the above-mentioned coupled network asynchronous dynamic intermittent security control method is implemented.

[0018] With the above technical solution, the embodiments of the present application provide a coupled network asynchronous dynamic intermittent security control method and system. After establishing the dynamic models of the follower network, the target network, and the state error variable, the method can obtain multiple attack signals including injection attack signals and replacement attack signals, set an intermittent controller according to the dynamic network model and the multiple attack signals, and then set a dynamic mechanism based on the exponential function to convert the state error variable into an interval control function. Among them, the interval control function is used to achieve secure mean square synchronization control between the follower network model and the target network model. The method can utilize the node adaptive double deception attack probability model, and construct an asynchronous anti-attack intermittent dynamic cooperative control strategy for complex coupled networks based on the coupling method of the average intermittent control rate and the dynamic event triggering threshold, which can alleviate the problems of difficult multiple attack modeling and insufficient coordination of control strategies.

[0019] The above description is only an overview of the technical solution of the present application. In order to be able to understand the technical means of the present application more clearly, it can be implemented according to the content of the description. And in order to make the above and other purposes, features and advantages of the present application more obvious and understandable, the specific embodiments of the present application are hereinafter specifically described. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The drawings described herein are used to provide a further understanding of the present application, and constitute a part of the present application. The schematic embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation to the present application. In the drawings: Figure 1 is a directed topology graph of a complex coupled dynamic network provided by an embodiment of the present application; Figure 2 is a schematic diagram of a coupled network asynchronous dynamic intermittent security control method provided by an embodiment of the present application; Figure 3 is a flowchart of the control method provided by an embodiment of the present application; Figure 4 is a schematic diagram of asynchronous non-periodic intermittent dynamic event triggering control provided by an embodiment of the present application; Figure 5 is an event triggering frequency diagram provided by an embodiment of the present application; Figure 6 is a curve graph of the change of the error state provided by an embodiment of the present application; Figure 7 is a schematic diagram of a coupled network asynchronous dynamic intermittent security control system provided by an embodiment of the present application. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0021] The present application will be described in detail below with reference to the drawings and in conjunction with the embodiments. It should be noted that, without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

[0022] In the embodiments of the present application, a complex dynamic network is a dynamic network structure formed by means of multi-node communication, data sharing, collaborative control, etc. The complex dynamic network can be used to describe fields such as aircraft formations, smart grids, wireless sensor networks, mobile autonomous systems, and industrial Internet of Things.

[0023] To ensure the collaborative operation of multiple nodes in the complex dynamic network, synchronous control can be performed on the dynamic network. As Figure 1 shown, synchronous control is a control process that enables multiple dynamic nodes in the network to reach a certain consistent state or behavior through synchronous control theory. Multiple network nodes can be provided in the complex dynamic network, and the network nodes can be classified according to their control roles in the control process. For example, the network system can include follower nodes and leader nodes. The leader node is used to issue control instructions, and the follower nodes execute following actions in response to the control instructions. Therefore, the number of follower nodes will be less than the number of leader nodes. For example, the nodes numbered 1, 2, 3, ……, 8 are called follower nodes, and the follower nodes can also transmit data to each other to achieve synchronous control.

[0024] In the complex dynamic network, if the state variables of all nodes tend to be consistent when the time approaches infinity, it is said that the network has achieved synchronization. In some embodiments, synchronous control can be performed based on idealized assumptions, that is, the communication links between network nodes are secure and reliable, the local data of sensors and actuators are not tampered with, and the control process is not interfered by malicious attacks.

[0025] However, with the expansion of the scale and the enhancement of the openness of the dynamic network, such as 5G communication, cloud-edge-end collaborative architecture, etc., the collaboration between network nodes highly depends on information interaction, which makes multiple deception attacks such as false data injection, signal replay, and identity disguise become security threats to the dynamic network. Attackers can target the topological structure or node dynamics of the coupled network and disrupt network synchronization, reduce control efficiency, or even cause cascading failures by tampering with the transmitted data.

[0026] To improve the security of the dynamic network, in some embodiments, continuous security synchronous control can be carried out against deception attacks. For example, security synchronous control based on an idealized continuous control framework, etc., but this control method is difficult to cope with problems such as limited communication resources, asynchronous node responses, and heterogeneous attack dynamics in open networks. Moreover, the defense mechanism has insufficient tolerance for multiple collaborative attacks, and the continuous control strategy is prone to cause resource overconsumption, making it difficult to meet the high-efficiency and strong robustness requirements of distributed coupled networks.

[0027] Since false data injection into the communication channel can trigger persistent attacks, and the discrete control scheme can reduce the success rate of attacks. Therefore, in some embodiments, the synchronization control of complex dynamic networks can also be based on a security synchronization control strategy with discontinuous monitoring. However, since discontinuous security control focuses on a single attack scenario, that is, the false data injection problem for the sensor-controller channel. The security synchronization control strategy based on discontinuous monitoring can address spoofing attacks on the controller-actuator channel.

[0028] Since complex dynamic networks can also be subject to dual-channel collaborative attacks, that is, simultaneously attacking "sensor-controller" and "controller-actuator". Therefore, in some embodiments, a pulse control model for dual-channel spoofing attacks can be constructed, and synchronization control can be achieved based on the pulse control model. However, due to the spatio-temporal coupling characteristics of cross-layer attack signals, there are theoretical bottlenecks in attack coupling modeling, defense strategy coordination, and dynamic stability analysis. Therefore, by constructing a pulse control model for dual-channel spoofing attacks and relying on a fixed-period triggering mechanism, it is impossible to achieve the co-design of a dynamic triggering mechanism and resource optimization, and it is difficult to cope with the computational and communication resource constraints brought about by network scale expansion.

[0029] Intermittent control has the advantages of a flexible architecture and low computational resource consumption by alternately starting and stopping control intervals and sleep intervals. Intermittent control can be triggered based on a clock cycle or event-driven. And event-driven intermittent control can dynamically trigger control actions based on an error threshold, optimize resource efficiency by updating data on demand, and the dynamic event triggering mechanism further introduces internal dynamic variables, significantly reducing communication overhead.

[0030] For the asynchronous characteristics of the actual scenario, in some embodiments, asynchronous non-periodic intermittent dynamic event-triggered control can also be used, but its application in coupled dynamic networks under network attacks still has limitations, which are manifested as: asynchronous conflicts, that is, the probability difference of nodes being subject to spoofing attacks under network attacks leads to difficulties in the co-design of asynchronous intermittent control; imbalance in dynamic defense energy efficiency, that is, asynchronous non-periodic intermittent dynamic event-triggered control does not consider the network topology reconstruction and resource dynamic allocation under attack damage, and it is difficult to adapt to large-scale coupled networks; insufficient suppression of cross-layer attacks, that is, the dynamic triggering mechanism mostly targets a single attack scenario and lacks the elastic response ability to dual-channel collaborative spoofing attacks on sensor-controller and controller-actuator.

[0031] Considering the synchronization control methods described in the above embodiments, since the spoofing attack model assumes a globally unified attack probability, does not consider node heterogeneity, and lacks dynamic modeling of dual-channel collaborative attacks on sensor-controller and controller-actuator. Therefore, in the process of synchronization control of complex dynamic networks, there is a problem of difficulty in multi-attack modeling.

[0032] Moreover, due to the asynchronous conflict in asynchronous intermittent dynamic event-triggered control under multiple attacks, that is, the difference in node attack probabilities leads to a mismatch in control timing, and there are also difficulties in stability analysis, and it is difficult for the non-activated interval to converge. Therefore, the coordination of the control strategy of the synchronous control method is insufficient. In addition, because the event-triggered mechanism frequently updates data under attack disturbances, resulting in an excessive computational burden and difficulty in adapting to the resource constraint requirements of large-scale coupled networks, the synchronous control method will lead to an imbalance between resources and security.

[0033] To solve the problems of difficult modeling of multiple attacks and insufficient coordination of control strategies in security control methods, some embodiments of this application provide an asynchronous dynamic intermittent security control method for coupled networks. The method can be applied to a network system. By constructing an attack-adaptive dynamic trigger control framework, it can address the problem of collaborative optimization of asynchronous intermittent control and multiple attack defenses, and achieve the safe and efficient operation of resource-constrained coupled networks. As Figure 2 、 Figure 3 shown, the method includes: S101. Establish a coupled dynamic network model.

[0034] Before performing synchronous control, a coupled dynamic network model can be established first. Among them, the coupled dynamic network model includes a follower network model, a target network model, and a state error variable. The follower network model is the dynamic model of the follower node state with respect to time.

[0035] To construct the follower network model, in some embodiments, the network system can obtain the follower node state when establishing the coupled dynamic network model. Among them, the follower node state is represented by the transpose of the matrix composed 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 state of the i th node.

[0036] After obtaining the follower node state, the network system can obtain the modeling data. The modeling data includes: a preset coefficient matrix, a nonlinear drive function f ( x i ( t )), a coupling weight matrix , a multiple attack signal , and an intermittent dynamic event-triggered control input . Among them, 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 , and both the first coefficient matrix and the second coefficient matrix are real matrices with appropriate dimensions.

[0037] Then, based on the modeling data and the follower node states, the follower network model is established. In some embodiments, to establish the follower network model, the network system may first calculate the product of the first coefficient matrix and the follower node states to obtain a first model part.

[0038] For example, for the follower node states x i ( t ), the first coefficient matrix can be obtained ; then calculate the follower node states x i ( t ), the first coefficient matrix can be obtained , to obtain the first model part of the follower network model, that is C x x i ( t ).

[0039] Then, obtain the internal coupling strength coefficient and the adjacency matrix, and calculate a second model part based on the internal coupling strength coefficient, the adjacency matrix, and the follower node states. Among them, calculating the second model part is used to characterize the internal coupling strength of the follower network model, and it can be obtained by calculating the internal coupling strength coefficient, the adjacency matrix, and the follower node states.

[0040] In some embodiments, the network system may first obtain the node combination states. Among them, the node combination states include the first follower node state and the 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 calculate the state difference between the first follower node state and the second follower node state. And calculate the internal coupling data 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 calculate the second model part 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.

[0041] When calculating the second model part, the network system may 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 , to form a node combination state. Then calculate the difference between the first follower node state and the second follower node state, that is . And extract the coupling weight based on the coupling weight matrix b ijx , and calculate the product between the coupling weight and the above calculated difference to obtain the internal coupling data Then the internal coupling data is summed up 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 .

[0042] 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. That is, the network model is obtained by inputting the following node state into the nonlinear driving function to obtain the following driving function value. x i ( t ) Input the nonlinear driving function and obtain the follow-up driving function value f ( x i ( t )), and then based on the second coefficient matrix Calculate the third model part .

[0043] After the first model part, the second model part and the third model part are calculated, the network system can generate a following network model according to 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 N coupled dynamic following node networks, the following network model of the i-th node is: (1) Wherein, 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 triggered control input.

[0044] The target network model is a dynamic model of the leader node state with respect to time. To establish the target network model, in some embodiments, when the network system executes the establishment of the coupled dynamic network model, it may first obtain the leader node state. The leader node state is represented by the transpose of the matrix formed by the node states of multiple leader nodes in the target network. Then, obtain the preset coefficient matrix and the nonlinear driving function, and input the leader node state into the nonlinear driving function to obtain the leader driving function value. Then, using the preset coefficient matrix as the weighting weight, calculate the weighted sum result of the leader node state and the leader driving function value to obtain the target network model.

[0045] For example, the dynamic model of the target network (leader node) can be expressed as: (2) Where, represents the leader node state; and represent the preset coefficient matrix, which is a real matrix of appropriate dimension; f ( y 0 ( t ) ) represents the nonlinear driving function.

[0046] The state error variable is the difference between the follower network model and the target network model. The state error variable is also a kind of dynamic model, which is used to characterize the change of the state error with respect to time. To establish the dynamic model corresponding to the state error variable, in some embodiments, when the network system establishes the coupled dynamic network model, it can obtain the follower node state and the leader node state, and then establish a variable expression of the state error variable according to the follower node state and the leader node state. Where the variable expression is the difference between the follower node state and the leader node state; the variable expression is used to characterize the synchronous state error of the follower node relative to the leader node. Then, based on the variable expression, combine the follower network model and the target network model to obtain the state error variable.

[0047] Let the synchronous 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 synchronous state error system of the i-th node relative to the target network can be obtained as follows: (3) Where, ; d x represents the internal coupling strength coefficient; C x = ( cij x ) n×n and A x =( a ij x ) n×n represents a preset coefficient matrix, which is a real matrix of appropriate dimension; represents the coupling weight matrix; is the Laplacian matrix the parameter value in; represents a multi - attack signal, which is a deception attack function defined by mathematical methods. Its specific value can be obtained by monitoring the attacks suffered by network nodes. For the multi - attack signal, the deception attack function has uncertain unknownness, and its acquisition is defined by mathematical methods. That is, by giving the definition of the deception attack and introducing a mathematical variable subject to a random Bernoulli distribution to characterize it, and further introducing the attack variable into the complex dynamic network - setting time - synchronization control model to analyze its impact on the data transmission between the controller and the actuator.

[0048] For example, the multi - attack signal can be expressed as: ; where represents the attack signal, which is the mathematical definition of the deception attack; or 1, represents a Bernoulli - distribution random variable related to the dynamic network; θ i ( t ) represents the first attack signal, which is a bounded function.

[0049] represents the controller under deception attack, which can be jointly determined based on the event - trigger mechanism and the mathematical definition of the attack function That is: ; Correspondingly, u i ( t ) represents the controller without deception attack. That is: ; where d x represents the internal coupling strength; is the adjustable gain parameter for asynchronous intermittent control; represents the synchronization error at time; represents a random variable taking values of 0 or 1, which takes the value of 1 when an attack occurs and 0 when no attack occurs; is the k th pseudo-periodic intermittent control period; is the i th intermittent control width of the k th dynamic network; represents the i th intermittent non-control width of the k th dynamic network; The part represents the time interval during which the system simultaneously satisfies the event trigger interval condition within the activation time period of intermittent control, and represents the specific time of the th intermittent control and event occurrence of the i th dynamic network. k

[0050] Therefore, a topological graph structure is given for N dynamic networks, which is used to represent the communication relationship between networks, where represents a non-empty vertex set, represents an edge set, and the correlation characteristics between networks can be characterized. represents a coupling weight matrix (adjacency matrix), where, if and only if i and j belong to the edge set , otherwise . represents a Laplacian matrix, where , and .

[0051] For example, consider the mean-square secure bounded synchronization control of a complex coupled dynamic network, which includes 1 target dynamic network and 8 follower dynamic networks, and the dynamic model of the i th follower dynamic network is: i = 1, 2, 3,..., 8; represents the state of the i th dynamic network; d x = 1 represents the internal coupling strength; the values of the first coefficient matrix and the second coefficient matrix are respectively: , ; Then the attack signal , where T represents the transpose of the vector; represents the asynchronous aperiodic intermittent dynamic event-triggered control input to be designed.

[0052] Consider the non-linear function , and , where,​i = 1, 2, 3, ……, 8; j = 1, 2, 3, then the constraint conditions can be satisfied , .

[0053] Denote l i1 = l i2 = l i3 = 1, denotes the coupling weight matrix. Combining with the dynamic model of the target dynamic network: (5); In the formula, denotes the state of the target network, , and is the same as that in formula (4), and the initial state is .

[0054] The topological graph structures are given for 8 dynamic networks used to represent the communication relationship between networks, and the non-empty vertex set is , and the edge set is , which is used to characterize the correlation characteristics between networks. If there is an edge connecting two network nodes, they are regarded as neighbors. Therefore, the internal coupling weight matrices of the 8 dynamic network connections are: ; S102. Obtain multiple attack signals.

[0055] After establishing the dynamic model of the complex coupled dynamic network under multiple attack effects, the network system can introduce multiple deception attack modeling, that is, obtain multiple attack signals. Among them, 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 suffered by multiple follower nodes and the random variables of the dynamic network.

[0056] For the injection attack signal, in some embodiments, when the network system obtains multiple attack signals, it can obtain the first attack signal suffered by any follower node and the Bernoulli distribution random variable, and then define the injection attack signal according to the first attack signal and the Bernoulli distribution random variable, so as to calculate the injection attack probability expectation matrix based on the injection attack signal. Among them, 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.

[0057] Regarding the problem of multiple attacks on the sensor-to-controller and controller-to-actuator channels under injection attacks and replacement attacks, multiple attack signals following the injection in the network model can be defined. : (6); Wherein, represents the multiple attack signal, which is a mathematical definition of spoofing attacks; or 1, representing a Bernoulli distribution random variable related to the dynamic network; θ i ( t ) represents the first attack signal, which is a predefined bounded function.

[0058] Assume that the Bernoulli distribution random variable takes the value of 1 when the attacker launches an attack and 0 when the attacker does not launch an attack. The random variables are independent of each other, then: ; Wherein, is a constant, and , represents that the probability that the random variable takes the value of 1 at time t is equal to the constant , represents that at time t, the probability that the random variable takes the value of 0 is equal to the constant 1 - β ij . The mathematical expectation matrix of the matrix is , that is: (7); Through the combination of the Bernoulli distribution random variable and the bounded function first attack signal θ i ( t ), the multiple attack signal is defined.

[0059] The replacement attack signal is a functional representation of the replacement attack signals suffered by multiple follower nodes and the dynamic network random variable. For the replacement attack signal, in some embodiments, when the network system executes to obtain the multiple attack signal, it can first obtain the second attack signal suffered by any follower node. The second attack signal is the transpose representation of the matrix formed by the states of the follower nodes when multiple follower networks suffer replacement attacks. Define the replacement attack signal according to the second attack signal and the Bernoulli distribution random variable, and calculate the replacement attack probability expectation matrix based on the replacement attack signal. 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.

[0060] Define the replacement spoofing attack signal as , denoted as . By introducing a Bernoulli distribution variable related to the dynamic network controller to describe the probability of successful attack. Assume that the random variables are independent of each other, and i represents a positive integer, then: ; where is a constant, represents that at time t, the probability that the random variable takes the value of 1 is equal to the constant α i , represents that at time t, the probability that the random variable takes the value of 0 is equal to the constant 1 - α i . Denote as the expectation of , that is: (8); For example, when modeling multiple spoofing attacks, when the network system addresses the problem of multiple attacks on the sensor-to-controller and controller-to-actuator channels under injection attacks and replacement attacks, and , I represents an identity matrix with dimension matching.

[0061] S103. Set an intermittent controller according to the dynamic network model and the multiple attack signal.

[0062] After obtaining the multiple attack signal through introducing multiple spoofing attack modeling, the network system can set an asynchronous aperiodic intermittent dynamic event-triggered controller, that is, set an intermittent controller according to the dynamic network model and the multiple attack signal. Among them, the intermittent controller is an asynchronous aperiodic 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.

[0063] In some embodiments, when the network system sets an intermittent controller according to the dynamic network model and the multiple attack signal, it can first obtain a preset compact set. Among them, the preset compact set is used to characterize that within a preset control time period, the state expected value of the state error variable is less than or equal to a preset positive number.

[0064] The problem of secure mean-square bounded synchronization between the follower network model and the target network model can be transformed into the tracking problem of each follower dynamic network and the target network. To achieve secure tracking with the target network, the state error variable of the follower network model and the target network model can be made to converge to a compact set through secure anti-attack control , that is: (9); where is a positive number, denotes that the expectation of the state of the state error variable is less than or equal to .

[0065] After obtaining the preset compact set, the control interval and the non-control interval of the dynamic network model can be divided for the dynamic network. Among them, the control interval is used to represent the state interval that simultaneously satisfies the event trigger interval condition during the activation time period of the intermittent control. By defining the event trigger instant and substituting the event trigger instant into the state error variable, the instantaneous error is obtained; then, based on the preset asynchronous intermittent control adjustable gain parameter, the internal coupling strength coefficient, and the instantaneous error, combined with the preset compact set, the control data of the control interval is set

[0066] The network system can design an asynchronous non-periodic intermittent dynamic event-triggered controller in the following form: (10); where is the asynchronous intermittent control adjustable gain parameter; is the k th quasi-periodic intermittent control period; is the i th intermittent control width of the k th dynamic network; represents the i th intermittent non-control width of the k th dynamic network; The part represents the time interval within the activation time period of the intermittent control of the system that simultaneously satisfies the event trigger interval condition, represents the specific time of the i th dynamic network at the k th intermittent control and event occurrence.

[0067] As shown in Figure 4 , the intermittent control sequence of the ith node based on events is: ; For example, for the asynchronous non-periodic intermittent dynamic event-triggered controller: (11); In the formula, by setting , , represents the synchronization error at the moment. Then as Figure 5 shown, the asynchronous control intervals for 8 coupled networks are respectively: Coupled network 1: ; Coupled network 2: ; Coupled network 3: ; Coupled network 4: ; Coupled network 5: ; Coupled network 6: ; Coupled network 7: ; Coupled network 8: .

[0068] S104. Set a dynamic mechanism based on the exponential function, and convert the state error variable into an interval control function according to the intermittent controller and the dynamic mechanism.

[0069] Design an asynchronous aperiodic intermittent dynamic event-triggered controller, design an event dynamic trigger communication scheme, that is, set a dynamic mechanism based on the exponential function, and convert the state error variable into an interval control function according to the intermittent controller and the dynamic mechanism. Among them, the interval control function is used to achieve secure mean-square synchronization control between the following network model and the target network model.

[0070] To convert the interval control function, in some embodiments, the network system can first obtain a preset exponential function. Then calculate the transmission interval error between the currently to-be-transmitted data and the data triggered for transmission last time, and then calculate a first value according to the transmission interval error and the state error variable. The first value is the difference between the square of the norm of the transmission interval error and the square of the norm of the state error variable. Then obtain the conversion coefficient and the asynchronous intermittent control adjustable gain parameter, and calculate a second value. The second value is the product of the first value, the asynchronous intermittent control adjustable gain parameter, and the conversion coefficient. Construct an event trigger mechanism according to the preset exponential function and the second value, and determine the event trigger instant and the dynamic adaptive variable according to the event trigger mechanism. Thus, based on the trigger instant and the dynamic adaptive variable, convert the state error variable into an interval control function.

[0071] Event trigger instant It can be determined by the following event-triggering mechanism: (12); Among them, is a positive finite number, represents the error between the current data to be transmitted and the data triggered for transmission last time, then the dynamic adaptive variable is expressed as: (13); Among them, , is a positive finite number.

[0072] Denote , where represents the i th dynamic network, represents a natural number, , represents the last triggering instant in the interval .

[0073] Under the multi-deception attack, 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: (14); Based on the above interval control function, the network system can achieve mean-square bounded stability of the synchronous state error based on the asynchronous aperiodic intermittent dynamic event-triggering control method under the influence of the multi-deception attack, that is, the follower network model and the target network model finally achieve secure mean-square synchronous control.

[0074] For example, in order to reduce the communication burden and save limited communication resources, based on the introduced intermittent control mechanism, considering the dynamic event-triggering condition based on the exponential function, then the event-triggering instant is determined by the following event-triggering mechanism: (15); Therefore, the dynamic adaptive variable is designed as: (16); Among them, represents the initial value, is a positive finite number, represents the exponential function. , , , represents the error between the current data to be transmitted and the data triggered for transmission last time.

[0075] Therefore, under the action of the above asynchronous dynamic intermittent security control method for a coupled network against multiple spoofing attacks, when a complex coupled dynamic network suffers from multiple spoofing attacks, the error system between each dynamic coupled network and the target dynamic network finally achieves mean-square bounded stability, that is, realizes mean-square bounded secure synchronization of the complex coupled dynamic network under the influence of multiple spoofing attacks, as Figure 6 shown.

[0076] By applying the technical solution of the above embodiment, the coupled network asynchronous dynamic intermittent security control described in the above embodiment can be based on a complex dynamic network attack model, which simultaneously considers edge-based injection spoofing attacks and node-based replacement spoofing attacks. Combining the differences in the action mechanisms of different attack methods in the network, different probabilities are assigned to each attack path, which more realistically reflects the heterogeneity of the attacks. Through the collaborative design of asynchronous aperiodic intermittent control and dynamic event-triggering conditions, it is achieved in the intersection part of the control interval and the event-triggering interval, that is, only respond to dynamic event-triggering within the activation window of the intermittent control, avoiding unnecessary control actions to optimize resources. Dynamically adjust the triggering threshold according to the attack probability, improve the real-time fault tolerance ability against spoofing attacks, and enhance security. The dynamic event-triggering control mechanism based on the exponential function can flexibly reduce the event-triggering frequency, and at the same time make the event-triggering frequency of each node and the activation time of the intermittent control asynchronous, increasing the flexibility of the intermittent control width, and finally realizing the secure mean-square synchronization of the entire complex coupled dynamic network, which can be widely applied to scenarios such as smart grids and multi-agent systems.

[0077] In some embodiments, as a specific implementation of the coupled network asynchronous dynamic intermittent security control method described in the above embodiment, some embodiments of the present application also provide a coupled network asynchronous dynamic intermittent security control system, as Figure 7 shown, the system includes: A model establishment module, configured to establish a coupled dynamic network model, where 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 with respect to time; the target network model is a dynamic model of the leader node state with respect to time; the state error variable is the difference between the follower network model and the target network model; An attack signal module, configured to obtain multiple attack signals, where the multiple attack signals include an injection attack signal and a replacement attack signal; the injection attack signal is a function representation of multiple follower nodes suffering from injection attack signals and dynamic network random variables; the replacement attack signal is a function representation of multiple follower nodes suffering from replacement attack signals and dynamic network random variables; A setting module, configured to set an intermittent controller according to the dynamic network model and the multiple attack signals, where the intermittent controller is an asynchronous aperiodic intermittent dynamic event-triggered controller; the controller is configured to converge the state expected value of the state error variable to a preset compact set; A control module, configured to set a dynamic mechanism based on an exponential function, and convert the state error variable into an interval control function according to the intermittent controller and the dynamic mechanism, where the interval control function is used to achieve secure mean-square synchronization control between the following network model and the target network model.

[0078] By applying the technical solutions of the above embodiments, the coupled network asynchronous dynamic intermittent security control system provided by the above embodiments, the system can establish dynamic models of a following network, a target network, and a state error variable by a model establishment module. Then, a multiple attack signal including an injection attack signal and a replacement attack signal is obtained through an attack signal module, and an intermittent controller is set by the setting module according to the dynamic network model and the multiple attack signals, so that the control module can set a dynamic mechanism based on an exponential function to convert the state error variable into an interval control function. The system can characterize attack heterogeneity through a node differential probability association mechanism, and on this basis, construct a joint security control framework for sensor-controller and controller-actuator communication channels, overcome the problem of collaborative design of security controllers under multiple spoofing attacks, and improve the limitations of single attack mode and static defense strategy.

[0079] The system can also be based on an exponential-type dynamic event-triggered anti-interference controller. By constructing an auxiliary functional and combining the averaging method theory, the analytical problem of the dynamic system stability criterion in the asynchronous intermittent control non-active interval is alleviated, and the co-optimization of the triggering frequency and the computational overhead is achieved under multiple spoofing attacks, ensuring the secure mean-square bounded synchronous convergence of the networked system.

[0080] The system can also be based on the core lemma of the average asynchronous intermittent control rate, alleviate the problem of constructing the asynchronous intermittent control stability criterion under multiple spoofing attacks, improve the strong constraint assumptions on the active and dormant intervals, establish a mean-square bounded synchronization condition, and systematically avoid the conservatism and computational redundancy problems caused by complex mathematical merging in existing intermittent control.

[0081] It should be noted that for other corresponding descriptions of each functional unit involved in the coupled network asynchronous dynamic intermittent security control system provided by the embodiments of the present application, reference can be made to the corresponding descriptions in the coupled network asynchronous dynamic intermittent security control method provided by the above embodiments, which will not be elaborated here.

[0082] The embodiments of the present application further provide a computer device, which can specifically be 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 further include an input / output interface and a display device. Among them, 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 the 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 through a network connection. When the computer program is executed by the processor, it realizes the steps in the method embodiments.

[0083] Those skilled in the art can understand that the structure of the above computer device is only a part of the 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 some components, or have different component arrangements.

[0084] In one embodiment, a computer-readable storage medium is further provided. The computer-readable storage medium can be non-volatile or volatile, and stores a computer program. When the computer program is executed by the processor, it realizes the steps in the above method embodiments.

[0085] In one embodiment, a computer program product is further provided, including a computer program. When the computer program is executed by the processor, it realizes the steps in the above method embodiments.

[0086] 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 for analysis, stored data, displayed data, etc.) involved in the present application are all information and data authorized by the user or fully authorized by all parties.

[0087] Those of ordinary skill in the art can understand that all or part of the processes of implementing the above method embodiments can be completed by instructing relevant 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 may include the processes of the above method embodiments.

[0088] Among them, any reference to a memory, database, or other medium used in the embodiments provided by this application may include at least one of non-volatile and volatile memories. Non-volatile memories may include read-only memory (ROM), magnetic tapes, floppy disks, flash memories, optical memories, high-density embedded non-volatile memories, resistive random access memories (ReRAM), magnetoresistive random access memories (MRAM), ferroelectric random access memories (FRAM), phase change memories (PCM), graphene memories, and the like.

[0089] Volatile memories may include random access memory (RAM) or external cache memories, etc. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM), etc.

[0090] The databases involved in the embodiments provided by this application may include at least one of relational databases and non-relational databases. Non-relational databases may include distributed databases based on blockchain, etc., without limitation. The processors involved in the embodiments provided by this application may be general-purpose processors, graphics processors, digital signal processors, programmable logics, data processing logics based on quantum computing, etc., without limitation.

[0091] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, 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, it should be considered as the scope described in this specification.

[0092] The above-described embodiments merely represent several implementation manners of this application. Their descriptions are relatively specific and detailed, but they should not be construed as limiting the patent scope of this application. It should be noted that for those of ordinary skill in the art, without departing from the concept of this application, several modifications and improvements can still be made, and these all belong to the protection scope of this application. Therefore, the protection scope of this application should be subject to the appended claims.

Claims

1. An asynchronous dynamic intermittent safety control method for a coupling network, characterized in that The method includes: Establishing a coupled dynamic network model, which 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 with respect to time; the target network model is a dynamic model of the leader node state with respect to time; the state error variable is the difference between the follower network model and the target network model. Obtaining a multiple attack signal, which includes an injection attack signal and a replacement attack signal. The injection attack signal is a function representation of multiple follower nodes suffering from an injection attack signal and a dynamic network random variable; the replacement attack signal is a function representation of multiple follower nodes suffering from a replacement attack signal and a dynamic network random variable. Setting an intermittent controller according to the dynamic network model and the multiple attack signal. 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. 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. The interval control function is used to achieve secure 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 a coupled dynamic network model, including: Obtaining the follower node state, which is the transpose representation of a matrix composed of the node states of multiple follower nodes in the follower network. Obtaining modeling data, which includes: a preset coefficient matrix, a nonlinear driving function, a coupling weight matrix, a multiple attack signal, and an intermittent dynamic event-triggered 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.

3. The method according to claim 2, wherein Establishing the follower network model according to the modeling data and the follower node state, including: Calculating the product of the first coefficient matrix and the follower node state to obtain a first model part. Obtaining an internal coupling strength coefficient and an adjacency matrix, and calculating a second model part according to the internal 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. Generating a follower network model, which is the sum of the first model part, the second model part, the third model part, the multiple attack signal, and the intermittent dynamic event-triggered control input.

4. The method according to claim 3, wherein Calculating the second model part according to the internal coupling strength coefficient, the adjacency matrix, and the follower node state, including: Obtaining a node combination state, which includes a first follower node state and a second follower node state. The first follower node state and the second follower node state are respectively used to represent the states of any two follower nodes belonging to different follower networks. Calculating the state difference between the first follower node state and the second follower node state. Calculate the internal coupling data according to the state difference, where 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; Calculate the second model part according to the internal coupling data, where the second model part is the sum of the internal coupling data corresponding to the combined states of all nodes in the follower network.

5. The method according to claim 1, wherein Establish a coupled dynamic network model, including: Obtain the leader node state, where the leader node state is the transpose representation of the matrix composed of the node states of multiple leader nodes in the target network; Obtain a preset coefficient matrix and a nonlinear driving function, where the preset coefficient matrix includes a first coefficient matrix and a second coefficient matrix; Input the leader node state into the nonlinear driving function to obtain the leader driving function value; Calculate the weighted sum result of the leader node state and the leader driving function value with the preset coefficient matrix as the weighted weight to obtain the target network model.

6. The method according to claim 1, characterized in that Obtain multiple attack signals, including: Obtain the first attack signal suffered by any follower node and a Bernoulli distribution random variable; Define an injection attack signal according to the first attack signal and the Bernoulli distribution random variable, where the injection attack signal is the sum of the product of the first attack signal corresponding to all nodes in the follower network and the Bernoulli distribution random variable; Calculate the injection attack probability expectation matrix based on the injection attack signal.

7. The method according to claim 6, wherein Obtain multiple attack signals, including: Obtain the second attack signal suffered by any follower node, where the second attack signal is the transpose representation of the matrix composed of the follower node states when multiple follower networks are subject to replacement attacks; Define a replacement attack signal according to the second attack signal and the Bernoulli distribution random variable, where the replacement attack signal is the sum of the product of the second attack signal corresponding to all nodes in the follower network and the Bernoulli distribution random variable; Calculate the replacement attack probability expectation matrix based on the replacement attack signal.

8. The method according to claim 1, wherein Set an intermittent controller according to the dynamic network model and the multiple attack signals, including: Obtain a preset compact set, where 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; Divide the control interval and the non-control interval of the dynamic network model, where the control interval is used to represent the state interval that satisfies the event trigger interval condition simultaneously during the activation time period of the intermittent control; Define the event trigger instant, and substitute the event trigger instant into the state error variable to obtain the instantaneous error; Set the control data of the control interval based on a preset asynchronous intermittent control adjustable gain parameter, the internal coupling strength coefficient, and the instantaneous error, in combination with the preset compact set.

9. The method according to claim 1, wherein Set a dynamic mechanism based on an exponential function, and convert the state error variable into an interval control function according to the intermittent controller and the dynamic mechanism, including: Obtain a preset exponential function; Calculate the transmission interval error between the current data to be transmitted and the data transmitted at the previous trigger; Calculate a first value based on the transmission interval error and the state error variable, where the first value is the difference between the square of the norm of the transmission interval error and the square of the norm of the state error variable; Obtain a conversion coefficient and an asynchronous intermittent control adjustable gain parameter, and calculate a second value, where the second value is the product of the first value, the asynchronous intermittent control adjustable gain parameter, and the conversion coefficient; Construct an event-triggering mechanism based on the preset exponential function and the second value, and determine the event-triggering instant and the dynamic adaptive variable according to the event-triggering mechanism; Based on the triggering instant and the dynamic adaptive variable, transform the state error variable into an interval control function.

10. A coupled network asynchronous dynamic intermittent safety control system, characterized in that, The system includes: A model establishment module for establishing a coupled dynamic network model, where the coupled dynamic network model includes a follower network model, a target network model, and a state error variable. The follower network model is the dynamic model of the follower node state with respect to time; the target network model is the dynamic model of the leader node state with respect to time; the state error variable is the difference between the follower network model and the target network model; An attack signal module for obtaining multiple attack signals, where the multiple attack signals include an injection attack signal and a replacement attack signal; the injection attack signal is a function representation of multiple follower nodes suffering from an injection attack signal and a dynamic network random variable; the replacement attack signal is a function representation of multiple follower nodes suffering from a replacement attack signal and a dynamic network random variable; A setting module for setting an intermittent controller according to the dynamic network model and the multiple attack signals, where the intermittent controller is an asynchronous aperiodic intermittent dynamic event-triggering controller; the controller is used to make the state expected value of the state error variable converge to a preset compact set; A control module for setting a dynamic mechanism based on an exponential function, and transforming the state error variable into an interval control function according to the intermittent controller and the dynamic mechanism, where the interval control function is used to achieve secure mean-square synchronization control between the follower network model and the target network model.

Images