A layered self-triggered fixed-hitch aperiodic intermittent secure synchronization control method for deception attacks

Abstract

The application discloses a layered self-triggered fixed containment non-periodic intermittent security synchronization control method for deception attack, first constructs a leader-follower multi-agent dynamics model, and divides followers into a containment layer only connected with leaders and a follower layer relying on neighborhood interaction based on a fixed containment strategy; a non-periodic intermittent containment control scheme is designed for the containment layer, a special self-triggered mechanism is matched, control is only applied in a control interval, control quantity is zero in a non-control interval, and a self-triggered function is used to autonomously predict a sampling time; a Bernoulli additive deception attack mathematical model is established for the communication edge in the follower layer, a distributed self-triggered consensus control law is designed under the condition that attack disturbance exists, and control input is only refreshed at a self-triggered update time. The application realizes multi-agent mean square bounded safe synchronization under a random deception attack environment, and can be widely applied to collaborative control scenes of resource-limited industrial control, power information physical systems and the like.

Description

Technical Field

[0001] This invention relates to a hierarchical self-triggered fixed restraint non-periodic intermittent security synchronization control method for deception attacks, belonging to the field of multi-agent control technology. Background Technology

[0002] Cyber-physical networks (CPR), as a new generation of complex networks, are characterized by the deep integration of physical and network components. Through network components, remote control and computing can be accessed via physical devices, and different physical devices can also communicate conveniently through shared network components. Critical infrastructure such as power grids, transportation systems, and oil pipelines are typical examples of CPR systems. The high degree of integration and collaboration between physical and network components makes the system more flexible and efficient, but it also makes it particularly vulnerable to malicious attacks.

[0003] In the field of cooperative control of multi-agent systems, leader-follower synchronization control is a typical and widely used synchronization mode, aiming to ensure that the state trajectories of all followers track the state trajectory of the leader. However, continuous control of large-scale complex agent systems is often accompanied by high consumption of communication and computing resources. How to reduce resource consumption while ensuring synchronization performance has become a fundamental problem that urgently needs to be solved in this field.

[0004] To reduce control costs, intermittent control effectively reduces control resource consumption by applying control actions within the control interval and shutting off control inputs in the non-control interval. Compared to periodic intermittent control, aperiodic intermittent control allows for more flexible width configurations of the control and non-control intervals, making it more suitable for practical operating scenarios such as wind power generation. To further conserve resources, researchers combined intermittent control with restraint control, applying control only to a few nodes within the control interval, forming a multi-layered resource-saving mechanism of "intermittent + restraint + self-triggering".

[0005] However, existing intermittent control schemes still have significant limitations: single-control-node schemes have excessively high control update frequencies, making engineering implementation difficult; switching control schemes requires acquiring real-time error information from all nodes, resulting in high implementation costs; and existing intermittent triggering strategies still require continuous monitoring of the state trajectory, leading to substantial hardware overhead. Therefore, designing a fixed-control aperiodic intermittent control scheme—which selects a fixed node for control within the intermittent interval and combines it with a self-triggering mechanism to avoid continuous monitoring, while achieving coordinated design of control gain and triggering parameters—has become a technical challenge in this field.

[0006] Regarding triggering mechanisms, event-triggered control requires continuous monitoring of the state trajectory, resulting in high hardware overhead. Self-triggered control, on the other hand, uses the current system state information to predict the next trigger moment, effectively solving the bandwidth and energy consumption limitations. Existing research combines self-triggered control with intermittent control, attempting to reduce control costs while minimizing monitoring burden. However, existing intermittent triggering strategies still require continuous monitoring of the state trajectory in engineering implementation to determine whether triggering conditions are met, resulting in high consumption of communication and computing resources, making it difficult to meet engineering requirements in resource-constrained scenarios.

[0007] Deception attacks induce systems to accept false information by tampering with, injecting, or replaying data, thereby compromising the authenticity and integrity of the data. Aperiodic intermittent control allows for discontinuous inputs and instantaneous transitions, which can effectively describe certain characteristics of deception attacks that cause state transitions. However, if a non-layered control architecture is adopted, control and protection must be applied to the actuator-sensor channels of all physical layer nodes, resulting in a large attack exposure surface and high anti-attack costs.

[0008] To address the aforementioned issues, a layered control architecture offers an effective solution. By dividing the network into a restraining layer and a follower layer, and applying control only to the actuator-sensor channels of the follower layer nodes, the attack exposure surface can be effectively reduced, converging the potential attack scope from global to local, thereby lowering the risk of attack. Simultaneously, protective measures only need to be deployed on the controlled node channels, significantly reducing the cost of anti-attack measures. However, constructing a mathematical model within the layered framework that accurately characterizes the features of spoofing attacks, particularly modeling the random attack characteristics of communication edges within the follower layer, and performing corresponding secure synchronization theory analysis, still presents technical challenges.

[0009] In summary, the existing technology has at least the following shortcomings:

[0010] (1) Existing intermittent control schemes lack deep integration of fixed restraint and non-periodic intermittent control, often requiring dynamic switching of restraint nodes or reliance on periodic intermittent control, resulting in complex controller structure, high implementation cost, and poor engineering feasibility.

[0011] (2) In the existing trigger-intermittent joint control method, the triggering condition still requires continuous monitoring of the system state trajectory (such as continuous detection error threshold), which fails to make full use of the advantage of the self-triggering mechanism that only relies on historical sampling information, and the communication and computing resources are still relatively large.

[0012] (3) Existing research on secure synchronization is mostly carried out under a non-layered architecture, which requires protection of all node channels and has a large attack exposure surface; while under a layered framework, there is a lack of accurate mathematical models for spoofing attacks on the communication edge of the follow layer, as well as corresponding non-periodic intermittent secure synchronization control strategies.

[0013] (4) Existing methods are highly conservative in the parameter design of control interval width, restraint conditions and triggering conditions, and fail to make full use of the relaxed scheduling capability given by the average non-periodic intermittent control law, resulting in poor adaptability of the follower layer network with different topologies and dynamic characteristics and redundant synchronization performance.

[0014] Therefore, how to design a non-periodic intermittent control strategy under a layered framework, effectively control and protect only the actuator-sensor channel of the following layer node, ensure the system's secure synchronization performance under deception attack environment, and significantly reduce resource consumption and control costs has become a key technical problem that urgently needs to be solved in this field. Summary of the Invention

[0015] This invention provides a layered, self-triggered, fixed-restraint, non-periodic, intermittent security synchronization control method for deception attacks, in order to solve the problems existing in the prior art.

[0016] The technical solutions adopted in this invention are as follows:

[0017] A layered, self-triggered, fixed-restraint, non-periodic intermittent security synchronization control method for deception attacks includes the following steps:

[0018] S1: Establish a multi-agent system consisting of a leader and followers, and establish a dynamic model of the multi-agent system. The dynamic model includes a leader dynamic model and a follower dynamic model. The leader dynamic model is used to describe the evolution of the leader's state vector, and the follower dynamic model is used to describe the evolution of the follower's state vector. The follower dynamic model contains the control input to be designed.

[0019] S2: A fixed restraint strategy is used to induce the followers to differentiate into a restraint layer and a follower layer. The followers who have a direct information connection with the leader, only receive information from the leader, and whose control input generation does not depend on the neighbor interaction information constitute the restraint layer. The followers in the restraint layer remain fixed throughout the process. The followers who do not have a direct information connection with the leader and depend on the local neighbor interaction constitute the follower layer.

[0020] S3: Design a self-triggering driven aperiodic intermittent control input for each follower in the restraint layer. The aperiodic intermittent control input is generated within the control interval based on the synchronization error between the follower and the leader in the restraint layer and the intermittent restraint control gain. The control input is zero outside the control interval. The sampling time of each follower in the restraint layer within the control interval is independently predicted and generated by the self-triggering mechanism.

[0021] S4: Establish a Bernoulli random spoofing attack model for each follower in the follower layer to characterize the behavior of the attacker injecting additive spoofing attack signals into the state data in a Bernoulli random manner through the internal communication edges of the follower layer.

[0022] S5: Design a self-triggered distributed consensus control input for each follower in the follower layer. This input consists of a distributed coupling term based on the difference in neighbor states and an additive spoofing attack signal superimposed on it. The control input of each follower in the follower layer is updated only at the self-triggered moment and remains constant between adjacent self-triggered moments.

[0023] Furthermore, in S1, the leader dynamic model is as follows:

[0024] ,

[0025] The follower dynamic model is as follows:

[0026] ,

[0027] in, Represents the leader's state vector. Indicates the first A follower state vector, Indicates the first A follower's control input, Represents a diagonal real matrix. Represents a real matrix. Let represent a nonlinear function that satisfies the Lipschitz condition. Indicates the follower index and , This indicates the total number of followers.

[0028] Furthermore, in S2, information exchange between followers participating in neighbor communication is achieved through a communication topology, which is represented by the graph. Description, in which For all followers to gather, the first Each follower corresponds to a node , Let be the set of edges. It is an adjacency matrix. Represents a node To the node The connection weights; followers in the follower layer achieve local neighbor interaction through the communication topology, and the Laplace matrix of the communication topology. diagonal elements Represents a node in-degree, off-diagonal elements This represents the negative of the adjacency weight.

[0029] Furthermore, based on the result that followers are induced to differentiate into restraining layers and following layers, the Laplace matrix is ​​decomposed into a block form:

[0030] ,

[0031] in, This represents the coupling matrix between followers in the restraint layer. This represents the coupling influence matrix between followers in the restraint layer and followers in the follower layer. This represents the coupling influence matrix between followers in the following layer and followers in the restraining layer. This represents the matrix representing the internal coupling relationships between followers in the follower layer. This indicates the number of followers in the restraint layer.

[0032] Furthermore, the synchronization error is defined as:

[0033] ,

[0034] in, Indicates the first The synchronization error between followers and leaders Represents the follower state vector. This represents the leader's state vector.

[0035] Furthermore, in S3, the input for the restraining aperiodic intermittent control is:

[0036] ,

[0037] in, Indicates the first layer of restraint A fixed-restraint, non-periodic, intermittent control input for a follower. This indicates the intermittent restraint control gain. Indicates synchronization error. Indicates the first One control interval, Indicates the first One non-control interval, Indicates the first The first follower in the Sampling times within a control interval.

[0038] Furthermore, for each follower in the restraint layer, the self-triggering mechanism calculates the difference between the synchronization error of the follower at the current sampling time and the synchronization error at the current time, compares the difference with the synchronization error, and independently predicts and generates the next sampling time based on preset triggering conditions.

[0039] Furthermore, in S3, the sampling time is independently predicted and generated by the self-triggering function of the restraint layer, and the self-triggering function of the restraint layer is:

[0040] ,

[0041] in, This indicates the self-triggering function of the restraint layer. Indicates the first The next self-triggered moment for a follower. Indicates the first The current self-triggering moment of a follower , This represents a constant related to the dynamic model parameters and triggering matrix of a multi-agent system. This represents a function related to the current state of the restraint layer triggering constant and synchronization error. Let ln denote the Euclidean norm, and ln denote the natural logarithm.

[0042] Furthermore, in S4, for the first layer in the following layer... A follower establishes a Bernoulli random spoofing attack model for the follower layer communication edge, and the additive spoofing attack signal is:

[0043] ,

[0044] in, This represents the additive deception attack signal suffered by the i-th follower in the following layer. Let be a Bernoulli random variable, used to characterize the attack state of the communication link between the i-th follower and the j-th follower. This indicates that the communication edge is subjected to a deception attack at time t. This indicates that no attack has occurred; Let j be a bounded attack function, describing the waveform of the fake data injected by the attacker; the summation index j iterates through all other followers in the follower layer that have a communication connection with the i-th follower, and it is agreed that if there is no connection, then ;each They are statistically independent, and their mathematical expectation This represents the probability that the corresponding communication edge is attacked; furthermore, to avoid the influence of self-loops, it is stipulated that the diagonal elements satisfy... .

[0045] Furthermore, in S5, the input for the self-triggered distributed consistency control is:

[0046] ,

[0047] in, Indicates following the layer number A follower-triggered distributed consensus control input Indicates coupling strength. Represents the elements of the adjacency matrix. Indicates the first The first follower and his neighbor The state vector difference between each follower This indicates a deceptive attack signal. Let represent the set of neighboring followers of the i-th follower.

[0048] Furthermore, in S5, the self-triggering time is independently predicted and generated by the self-triggering function of the follower layer, and the self-triggering function of the follower layer is:

[0049] ,

[0050] in, This indicates a self-triggering function of the following layer. Indicates the first The next self-triggered moment for a follower. Indicates the first The current self-triggering moment of a follower , This represents a constant related to the dynamic model parameters of a multi-agent system and the upper bound of the attack function. This represents a function related to the trigger constant of the follower layer and the current error state. This represents the Euclidean norm.

[0051] The present invention has the following beneficial effects:

[0052] (1) This invention employs a fixed restraint strategy, directly differentiating followers into a restraint layer and a follower layer, eliminating the need for pre-designing a complex network hierarchy. Any fixed restraint strategy applied to large-scale complex agents can spontaneously form a clear hierarchical network topology. Restraint layer nodes only receive leader information and do not participate in neighbor communication; follower layer nodes rely solely on local interactions. This structure overcomes the limitation of traditional restraint control requiring pre-defined network structures, providing a clear topological foundation for differentiated control design.

[0053] (2) Based on the aforementioned hierarchical characteristics, the restraint layer nodes only receive leader information and do not participate in neighbor communication. Therefore, the risk of their actuator-sensor channels being exposed to communication network attacks is significantly lower than that of the follower layer nodes. The main threat of spoofing attacks is concentrated on the communication edges between follower layer nodes and their associated actuator-sensor channels. Therefore, this invention only needs to apply security control and protection to the actuator-sensor channels of the follower layer nodes to converge the attack exposure surface from all nodes globally to a local subset of follower layer nodes. Compared to the traditional non-hierarchical architecture that requires equal protection for all node channels, this invention significantly reduces the overall system attack risk, while greatly reducing the communication bandwidth, encryption computing, and real-time monitoring resources required for security protection, thus improving the security and deployability of large-scale intelligent agent systems in resource-constrained scenarios.

[0054] (3) This invention introduces a self-triggering mechanism in both the restraint layer and the follower layer: each node in the restraint layer independently predicts the next sampling time based solely on historical sampling information through the restraint layer self-triggering function; each node in the follower layer also independently predicts the next control drive time based solely on local historical information through the follower layer self-triggering function. This mechanism eliminates the need for continuous monitoring of the system state trajectory or real-time listening to neighbor interaction information. All control updates are strictly limited to execution at the self-triggering prediction time, thereby fundamentally avoiding the overhead of continuous monitoring and periodic communication, significantly reducing the consumption of hardware sampling, communication bandwidth, and computing resources, and improving the engineering feasibility of the method in resource-constrained scenarios.

[0055] (4) This invention employs aperiodic intermittent control for the restraint layer, with control input applied only within the control interval and zero outside the control interval. Compared to continuous control schemes, this approach effectively reduces control execution time and energy consumption. Furthermore, the fixed restraint strategy applies restraint control only to the restraint layer nodes, while the follower layer nodes achieve synchronization through self-triggered distributed consistency control, eliminating the need for frequent switching of restraint nodes or obtaining real-time error information from all nodes, further reducing control implementation costs.

[0056] (5) The average non-periodic intermittent control rate scheme proposed in this invention allows each control interval to have a flexible control width, abandoning the strict fixed requirements for control period or control width in traditional methods. This scheme is more relaxed in terms of both restraint conditions and trigger conditions, significantly reducing the design conservatism of the controller, enabling the control strategy to adapt to complex networks with different dynamic characteristics and topologies, and improving the versatility and engineering applicability of the method.

[0057] (6) This invention establishes a Bernoulli random spoofing attack model for each follower in the follower layer and embeds the attack signal into the distributed consensus control input. Through the synergistic effect of the self-triggered aperiodic intermittent control strategy of the restraint layer and the follower layer, the system can still ensure that the synchronization error between each follower and the leader converges in a bounded manner under random spoofing attacks, achieving mean-square bounded synchronization. This scheme provides theoretical protection and an engineering feasible path for the secure operation of complex cyber-physical networks under attack environments. Attached Figure Description

[0058] Figure 1 This is a time evolution diagram of the state trajectories of three fixed restraint nodes in a 7-node network in the example.

[0059] Figure 2 This is a time evolution diagram of the state trajectories of the four nodes in the follower layer within the 7-node network in the example.

[0060] Figure 3 This is a tracking error state curve between the 7-node network and the leader in the example.

[0061] Figure 4 This is a diagram showing the triggering time of the self-triggered mechanism for restraint layer nodes 1, 2, and 3 in the example.

[0062] Figure 5 This is a diagram showing the triggering time of the self-triggered mechanism for following layer nodes 4, 5, 6, and 7 in the example. Detailed Implementation

[0063] The invention will now be further described with reference to the accompanying drawings.

[0064] This specific implementation method is verified using a multi-agent system comprising one leader and seven followers. It follows the hierarchical, self-triggered, fixed-restraint, non-periodic, intermittent secure synchronization control method for deception attacks proposed in this invention, fully realizing secure synchronization of the system under random deception attacks. The specific steps include:

[0065] First, a dynamic model of a multi-agent system including leaders and followers is established. The leader's dynamic model is as follows:

[0066] ;

[0067] The follower dynamic model is as follows: ;

[0068] in, Indicates the first The state of a follower , Take the third-order identity matrix , Take the real matrix nonlinear functions Satisfying the Lipschitz condition, specifically in the form of: j=1,2,3, the leader's initial state is set to .

[0069] Information exchange between followers is achieved through communication topology, which is represented by a graph. describe, For the gathering of all followers, Let be the set of edges. It is an adjacency matrix. Represents a node To the node Connection weights.

[0070] Corresponding Laplace matrix Constructed based on node in-degree and adjacency weight, diagonal elements The in-degree of node i, and the non-diagonal element. The Laplace matrix, which is the negative of the adjacency weights, is specifically defined in this embodiment as follows:

[0071] .

[0072] A fixed restraint strategy is used to induce the seven followers to differentiate into a restraint layer and a follower layer. The first three followers are selected to form the restraint layer, and the number of followers in the restraint layer is s. p =3, this part of the followers have a direct information connection with the leader, only receive information from the leader and do not participate in neighbor communication, and remain fixed throughout the control process.

[0073] The remaining four followers form the follower layer. These followers have no direct informational connection with the leader, but only interact locally with their neighboring followers through the communication topology. Based on this layering, the Laplace matrix is ​​decomposed into a block-based form:

[0074] ,

[0075] in, This represents the coupling matrix between followers in the restraint layer. This represents the coupling influence matrix between followers in the restraint layer and followers in the follower layer. This represents the coupling influence matrix between followers in the following layer and followers in the restraining layer. This represents the internal coupling matrix between followers in the follower layer. Since the restraint layer does not receive interaction information from its neighbors in the follower layer... It is a zero matrix.

[0076] For each follower in the restraint layer, a fixed aperiodic intermittent control input is designed, and the synchronization error is defined as follows: The specific form of the control input is as follows:

[0077] ,

[0078] in, Indicates the first layer of restraint A fixed-restraint, non-periodic, intermittent control input for a follower. This indicates the intermittent restraint control gain. Indicates synchronization error. Indicates the first One control interval, Indicates the first One non-control interval, Indicates the first The first follower in the Sampling times within a control interval.

[0079] Intermittent restraint control gain Take the diagonal matrix The intermittent control interval satisfies The average non-periodic intermittent control rate was 0.7. Indicates the first The first follower in the Sampling times within a control interval.

[0080] The sampling time of each follower in the restraint layer within the control interval is independently predicted and generated by a self-triggering mechanism, defining the measurement error. The triggering condition is The trigger constant Trigger matrix Take the diagonal matrix .

[0081] The sampling time is calculated by the self-trigger function of the restraint layer:

[0082] ,

[0083] in Lipschitz constant matrix ,

[0084] ,

[0085] , .

[0086] This self-triggering mechanism does not require continuous monitoring of the state trajectory; it can predict the next sampling time solely based on the synchronization error at the current sampling time.

[0087] It should be noted that the deception attack considered in this invention is an additive perturbation attack based on communication edge injection. Since the restraint layer nodes only receive leader information and do not participate in communication interactions with follower layer nodes, their control channels do not have applicable scenarios for communication edge attacks. If a restraint layer node is attacked, it is essentially an attack on the node's own sensors / actuators, which does not fall within the scope of communication edge attacks defined in this invention, and is therefore excluded. Furthermore, although follower layer nodes have a topological connection with the restraint layer, the information flow is unidirectional from the restraint layer to the follower layer; the restraint layer does not receive any information from the follower layer. Therefore, there is no cross-layer reverse attack path, and this invention does not introduce a feedback channel from the follower layer to the restraint layer in the controller design. Based on the above-mentioned layered characteristics and the assumption of unidirectional information flow, this invention only establishes a deception attack model for the communication edges within the follower layer. This assumption conforms to the typical scenario in actual engineering where leader / restraint nodes are usually deployed in relatively secure areas, while follower nodes are exposed to an open network environment, and has clear engineering rationale.

[0088] A Bernoulli random spoofing attack model is established for each follower in the follower layer to characterize the additive spoofing attack signal injected through the communication edges within the follower layer. The additive spoofing attack signal is... The summation is performed on other followers in the follower layer that are connected to the i-th follower by a communication edge. Let be a Bernoulli random variable. A value of 1 indicates that the communication edge between the i-th follower and the j-th follower in the follower layer has been attacked, and a value of 0 indicates that it has not been attacked. They are statistically independent, parameters And satisfy the diagonal element .

[0089] In this embodiment, the following layer nodes are renumbered as 1–4 (corresponding to the original nodes 4–7), and the attack function... The expected attack matrix within the corresponding follower layer is:

[0090] .

[0091] For each follower in the follower layer, design a self-triggered distributed consensus control input. The control input is:

[0092] ,

[0093] Coupling strength , Indicates following the layer number A follower-triggered distributed consensus control input Indicates coupling strength. Represents the elements of the adjacency matrix. Indicates the first The first follower and his neighbor The state vector difference between each follower This indicates a deceptive attack signal. Let represent the set of neighboring followers of the i-th follower.

[0094] Define sampling error The triggering condition is The triggering constant η F =0.2, trigger matrix ϕ F Pick: .

[0095] In the follower layer, the control input of each follower is updated only at the self-trigger time. The control input remains constant between adjacent self-trigger times, eliminating the need for continuous monitoring of neighbor interaction information. The self-trigger time is independently predicted and generated by the self-trigger function of the follower layer.

[0096] ,

[0097] in , , , ,

[0098] , , ,in Indicates using (i.e., 7-3=4) dimensional identity matrix and event triggering matrix The Kronecker product, where D is the matrix representation of the Lipschitz constant, Representation matrix The Kronecker product with the 4-dimensional identity matrix.

[0099] The seven-node multi-agent system was simulated and verified using the control and attack modeling process described above. Figure 1 The figure shows the state trajectory evolution curves of the three restraint layer followers over time. It can be seen that the state of the restraint layer followers quickly and stably tracks the state of the leader.

[0100] Figure 2 The figure shows the state trajectory evolution curves of four followers over time. Under the influence of deception attacks and self-triggered control, the state of the followers gradually becomes consistent and they track the leader.

[0101] Figure 3 The figure shows the tracking error state curves between all followers and the leader. The synchronization error converges quickly to a bounded range, achieving mean square bounded synchronization.

[0102] Figure 4The diagram shows the trigger interval distribution of the self-triggering mechanism of the three followers in the restraint layer. The triggering times are discrete and the intervals are reasonable, which effectively reduces the control update frequency.

[0103] Figure 5 The diagram shows the trigger interval distribution of the self-triggering mechanism for the four followers in the follower layer. The triggering time is generated independently, without the need for global synchronization, which significantly reduces the consumption of communication and computing resources while ensuring synchronization performance.

[0104] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements without departing from the principle of the present invention, and these improvements should also be considered within the scope of protection of the present invention.

Claims

1. A layered, self-triggered, fixed-restraint, non-periodic, intermittent security synchronization control method for deception attacks, characterized in that: Includes the following steps: S1: Establish a multi-agent system consisting of a leader and followers, and establish a dynamic model of the multi-agent system. The dynamic model includes a leader dynamic model and a follower dynamic model. The leader dynamic model is used to describe the evolution of the leader's state vector, and the follower dynamic model is used to describe the evolution of the follower's state vector. The follower dynamic model contains the control input to be designed. S2: A fixed restraint strategy is used to induce the followers to differentiate into a restraint layer and a follower layer. The followers who have a direct information connection with the leader, only receive information from the leader, and whose control input generation does not depend on the neighbor interaction information constitute the restraint layer. The followers in the restraint layer remain fixed throughout the process. The followers who do not have a direct information connection with the leader and depend on the local neighbor interaction constitute the follower layer. S3: Design a self-triggering driven aperiodic intermittent control input for each follower in the restraint layer. The aperiodic intermittent control input is generated within the control interval based on the synchronization error between the follower and the leader in the restraint layer and the intermittent restraint control gain. The control input is zero outside the control interval. The sampling time of each follower in the restraint layer within the control interval is independently predicted and generated by the self-triggering mechanism. S4: Establish a Bernoulli random spoofing attack model for each follower in the follower layer to characterize the behavior of the attacker injecting additive spoofing attack signals into the state data in a Bernoulli random manner through the internal communication edges of the follower layer. S5: Design a self-triggered distributed consensus control input for each follower in the follower layer. This input consists of a distributed coupling term based on the difference in neighbor states and an additive spoofing attack signal superimposed on it. The control input of each follower in the follower layer is updated only at the self-triggered moment and remains constant between adjacent self-triggered moments.

2. The layered self-triggered fixed restraint non-periodic intermittent security synchronization control method for deception attacks as described in claim 1, characterized in that: In S1, the leader dynamic model is as follows: ， The follower dynamic model is as follows: ， in, Represents the leader's state vector. Indicates the first A follower state vector, Indicates the first A follower's control input, Represents a diagonal real matrix. Represents a real matrix. Let represent a nonlinear function that satisfies the Lipschitz condition. Indicates the follower index and , This indicates the total number of followers.

3. The layered self-triggered fixed restraint non-periodic intermittent security synchronization control method for deception attacks as described in claim 2, characterized in that: In S2, information exchange between followers participating in neighbor communication is achieved through a communication topology, which is represented by the graph. Description, in which For all followers to gather, the first Each follower corresponds to a node , Let be the set of edges. It is an adjacency matrix. Represents a node To the node Connection weights; Followers in the follower layer achieve local neighbor interaction through the communication topology, and the Laplace matrix of the communication topology... diagonal elements Represents a node in-degree, off-diagonal elements This represents the negative of the adjacency weight.

4. The layered self-triggered fixed restraint non-periodic intermittent security synchronization control method for deception attacks as described in claim 3, characterized in that: Based on the result that followers are induced to differentiate into a restraining layer and a following layer, the Laplace matrix is ​​decomposed into a block form: ， in, This represents the coupling matrix between followers in the restraint layer. This represents the coupling influence matrix between followers in the restraint layer and followers in the follower layer. This represents the coupling influence matrix between followers in the following layer and followers in the restraining layer. This represents the matrix representing the internal coupling relationships between followers in the follower layer. This indicates the number of followers in the restraint layer.

5. The layered self-triggered fixed restraint non-periodic intermittent security synchronization control method for deception attacks as described in claim 1, characterized in that: The synchronization error is defined as: ， in, Indicates the first The synchronization error between followers and leaders Represents the follower state vector. This represents the leader's state vector.

6. The layered self-triggered fixed restraint non-periodic intermittent security synchronization control method for deception attacks as described in claim 1, characterized in that: In S3, the non-periodic intermittent control input for restraint is: ， in, Indicates the first layer of restraint A fixed-restraint, non-periodic, intermittent control input for a follower. This indicates the intermittent restraint control gain. Indicates synchronization error. Indicates the first One control interval, Indicates the first One non-control interval, Indicates the first The first follower in the Sampling times within a control interval.

7. The layered self-triggered fixed restraint non-periodic intermittent security synchronization control method for deception attacks as described in claim 6, characterized in that: For each follower in the restraint layer, the self-triggering mechanism calculates the difference between the synchronization error of the follower at the current sampling time and the synchronization error at the current time, compares the difference with the synchronization error, and independently predicts and generates the next sampling time based on preset triggering conditions.

8. The layered self-triggered fixed restraint non-periodic intermittent security synchronization control method for deception attacks as described in claim 7, characterized in that: In S3, the sampling time is independently predicted and generated by the self-triggering function of the restraint layer, and the self-triggering function of the restraint layer is: ， in, This indicates the self-triggering function of the restraint layer. Indicates the first The next self-triggered moment for a follower. Indicates the first The current self-triggering moment of a follower , This represents a constant related to the dynamic model parameters and triggering matrix of a multi-agent system. This represents a function related to the current state of the restraint layer triggering constant and synchronization error. Let ln denote the Euclidean norm, and ln denote the natural logarithm.

9. The layered self-triggered fixed restraint non-periodic intermittent security synchronization control method for deception attacks as described in claim 1, characterized in that: In S4, for the first in the following layer A follower establishes a Bernoulli random spoofing attack model for the follower layer communication edge, and the additive spoofing attack signal is: ， in, This represents the additive deception attack signal suffered by the i-th follower in the following layer. Let be a Bernoulli random variable, used to characterize the attack state of the communication link between the i-th follower and the j-th follower. This indicates that the communication edge is subjected to a deception attack at time t. This indicates that no attack has occurred; Let j be a bounded attack function, describing the waveform of the fake data injected by the attacker; the summation index j iterates through all other followers in the follower layer that have a communication connection with the i-th follower, and it is agreed that if there is no connection, then ;each They are statistically independent, and their mathematical expectation This represents the probability that the corresponding communication edge is attacked; furthermore, to avoid the influence of self-loops, it is stipulated that the diagonal elements satisfy... .

10. The layered self-triggered fixed restraint non-periodic intermittent security synchronization control method for deception attacks as described in claim 9, characterized in that: In S5, the input for the self-triggered distributed consistency control is: ， in, Indicates following the layer number A follower-triggered distributed consensus control input Indicates coupling strength. Represents the elements of the adjacency matrix. Indicates the first The first follower and his neighbor The state vector difference between each follower This indicates a deceptive attack signal. Let represent the set of neighboring followers of the i-th follower.

11. The layered self-triggered fixed restraint non-periodic intermittent security synchronization control method for deception attacks as described in claim 10, characterized in that: In S5, the self-triggering time is independently predicted and generated by the self-triggering function of the follower layer. The self-triggering function of the follower layer is: ， in, This indicates a self-triggering function of the following layer. Indicates the first The next self-triggered moment for a follower. Indicates the first The current self-triggering moment of a follower , This represents a constant related to the dynamic model parameters of a multi-agent system and the upper bound of the attack function. This represents a function related to the trigger constant of the follower layer and the current error state. This represents the Euclidean norm.

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