Heterogeneous multi-agent dynamic event trigger output consistency control method and device under FDI attack, and storage medium

Abstract

The invention discloses a heterogeneous multi-agent dynamic event trigger output consistency control method and device under FDI attack and a storage medium wherein the heterogeneous multi-agent dynamic event trigger output consistency control method under FDI attack comprises the following steps: a heterogeneous multi-agent system receives FDI attack data; the FDI attack data triggers a trigger response of a dynamic event trigger mechanism introduced in a tracking state observer; self-adaptively compensating the influence of the FDI attack data on the heterogeneous multi-agent system through a self-adaptive state observer; fDI is false information injection. The invention discloses a heterogeneous multi-agent dynamic event trigger output consistency control method and device under FDI attack and a storage medium. The problem of output consistency of a heterogeneous multi-agent system under FDI attacks is solved, and a dynamic event triggering mechanism is introduced to save communication resources.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of multi-agent and estimation and malicious network attack processing, and particularly relates to a heterogeneous multi-agent dynamic event-triggered output consensus control method, equipment and storage medium under false data injection (FDI) attack. BACKGROUND

[0002] Multi-Agent Systems (MASs) can complete complex tasks that simple individuals cannot complete alone, or engage in dangerous production labor. Traditional multi-agent systems usually assume that agents are homogeneous, that is, all agents have the same dynamic characteristics. However, due to differences in physical composition, dynamic model and information processing capacity of agents, heterogeneous multi-agent systems have gradually become the focus of research.

[0003] For a single agent, it is usually unrealistic to directly measure all output information of a complex external system, and designing a distributed observer in MASs to cooperatively estimate the state of the external system becomes a more practical solution. The core idea of the distributed observer is that each local observer only obtains part of the output information of the external system, and through local communication with neighboring agents in the network, it compensates for the missing information, thereby asymptotically achieving global state omniscience.

[0004] Distributed control strategies rely on information exchange between neighboring agents in an open communication network. In networked control systems, data transmission and computing resources are limited, and frequent information updates can consume a large amount of bandwidth and increase system latency. To address these challenges, event-triggered mechanisms can reduce unnecessary information transmission and computing burden while still maintaining the desired control performance of MASs. Dynamic Event-Triggered Mechanism (DETM) is a more advanced triggering mechanism. Unlike traditional event-triggered mechanisms, the triggering function in DETM not only depends on the available system information, but also incorporates internal variables related to the system dynamics. With the introduction of internal dynamic variables, DETM can effectively reduce unnecessary information transmission and improve the average time interval between neighboring event triggers.

[0005] During network interaction, agents are vulnerable to network attacks from malicious attackers. The main purpose of FDI attacks is to mislead system components (such as estimators, filters, controllers, and actuators) to disrupt the normal operation of the system. Therefore, it is of great research significance and value to study an adaptive compensation method for heterogeneous multi-agent systems based on state observers and dynamic event-triggered mechanisms under FDI attacks. SUMMARY

[0006] The present application overcomes the deficiencies of the prior art, and provides a heterogeneous multi-agent dynamic event-triggered output consensus control method, device and storage medium under FDI attack; the output consensus problem of a heterogeneous multi-agent system under FDI attack is solved, and a dynamic event-triggered mechanism is introduced to save communication resources.

[0007] In one preferred embodiment of the present application, a heterogeneous multi-agent dynamic event-triggered output consensus control method under FDI attack comprises: The heterogeneous multi-agent system receives FDI attack data, and the FDI attack data triggers a trigger response of a dynamic event-triggered mechanism introduced in a tracking state observer; The influence of the FDI attack data on the heterogeneous multi-agent system is adaptively compensated by an adaptive state observer; FDI is false information injection.

[0008] In one preferred embodiment of the present application, the heterogeneous multi-agent system comprises a heterogeneous follower agent model and a leader agent model; The heterogeneous follower agent model comprises: ; Wherein, , , , respectively represent the state and control input and control output of the follower agent i; , and are the state matrix, input matrix and output matrix of the follower agent; The leader agent model comprises: ; Wherein, , , represent the state and control output of the leader agent; and are the state matrix and output matrix of the leader agent.

[0009] In one preferred embodiment of the present application, the heterogeneous follower agent model and the leader agent model satisfy the following conditions: The leader agent and the follower agent are connected to each other, and the connection of the leader agent and the follower agent satisfies that there is a directed spanning tree with the leader agent as the root node in the topological structure; And / or, the consistency of the outputs of the leader agent and the follower agent conforms to an output regulation equation; the output regulation equation is: ; wherein are two solutions of the output equation; And / or, the FDI attack occurs in the network channel of the sensor and the controller, the attack model of the system information description of the heterogeneous multi-agent system when subjected to the FDI attack is as follows: ; Wherein, And Respectively represent the FDI attack data injected into the follower agent control channel and the sensor channel, And Is the follower agent control input after the FDI attack and the follower agent control output.

[0010] In a preferred embodiment of the application, the tracking state observer comprises: ; Wherein, Z i (t) is the cumulative error of the leader agent estimation value under the dynamic event trigger mechanism; Is the estimation value of the follower to the leader state, Is the observation gain of the tracking state observer, Indicates the estimation value of the follower agent i at the kth trigger time; Indicates the k'th trigger time of agent j before the closest kth trigger time of agent i; When , it indicates that agent j can receive information from agent i; when , it indicates that the follower agent i can receive information from the leader.

[0011] In a preferred embodiment of the application, the tracking state observer further comprises a dynamic event trigger mechanism, and the dynamic event trigger mechanism comprises: ; Wherein, Is a dynamic threshold parameter, , , , All are positive scalar parameters; wherein Is a static weight parameter; Is a decay rate parameter; Is a driving weight parameter; The error in the dynamic event trigger includes: measurement error , ; Is the transpose of the measurement error, and T is the transpose symbol; Is the cumulative error; ; When the measurement error of the system is greater than the dynamic threshold of the system, an event trigger occurs; at the same time, the state at the triggering time is transmitted to the leader agent and the controller.

[0012] In a preferred embodiment of the present application, the adaptive state observer includes a compensation term for FDI attack added on the basis of the Luenberger state observer, which is used to weaken the influence of FDI attack on the estimated state information; the algorithm includes: ; wherein, , are the state estimation value and the output estimation value of the follower itself respectively; is a unit column vector, is the observation gain of the adaptive state observer; the compensation term is: ; wherein, is a scalar greater than zero, is a gain matrix, is an adaptive parameter; ; wherein, is a scalar greater than zero; The adaptive parameter judges whether an FDI attack occurs through the difference between the attacked output information and the output information estimation value; when the attack occurs, the adaptive compensation mechanism exerts an opposite effect to the FDI attack, weakening the influence of the attack on the estimated state information.

[0013] In a preferred embodiment of the present application, the gain parameters are set through variable substitution and least square method, and the gain parameters include the observer gains of the tracking state observer and the adaptive state observer, and the control gain of the controller.

[0014] In a preferred embodiment of the present application, the two observed state information of the tracking state observer and the adaptive state observer are introduced into the controller to control the heterogeneous multi-agent system, and the controller includes: ; wherein, and are control gains; is obtained through the Hurwitz matrix . .

[0015] In a preferred embodiment of the present application, a heterogeneous multi-agent dynamic event-triggered output consensus control device under FDI attack is used to realize the steps of a heterogeneous multi-agent dynamic event-triggered output consensus control method under FDI attack, which includes: an acquisition unit configured to acquire FDI attack data; a processing unit configured to trigger a response to a dynamic event-triggering mechanism introduced in a tracking state observer according to a heterogeneous multi-agent system receiving the FDI attack data; adaptively compensate for the influence of the FDI attack data on the heterogeneous multi-agent system through an adaptive state observer.

[0016] In a preferred embodiment of the present application, a storage medium for heterogeneous multi-agent dynamic event-triggered output consensus control under FDI attack is used to implement the steps of a heterogeneous multi-agent dynamic event-triggered output consensus control method under FDI attack.

[0017] Compared with the prior art, the present application has the following beneficial effects: The present application discloses a heterogeneous multi-agent dynamic event-triggered output consensus control method, device and storage medium under FDI attack, which solves the output consensus problem of a heterogeneous multi-agent system under FDI attack and introduces a dynamic event-triggering mechanism to save communication resources, thereby reducing the problems of state estimation distortion and excessive consumption of communication resources when the actual multi-agent is subjected to a network attack. BRIEF DESCRIPTION OF DRAWINGS

[0018] The present application will be further described below in conjunction with the drawings and examples.

[0019] Figure 1 A flowchart of the heterogeneous multi-agent dynamic event-triggered output consensus control method under FDI attack in the preferred embodiment of the present application is shown in the figure. Figure 2 A communication topology between agents in the preferred embodiment of the present application is shown in the figure. Figure 3 An agent data transmission structure in the preferred embodiment of the present application is shown in the figure. Figure 4 A tracking state observer in the preferred embodiment of the present application is shown in the figure. A tracking error diagram in the preferred embodiment of the present application is shown in the figure. Figure 5 A tracking state observer in the preferred embodiment of the present application is shown in the figure. A tracking error diagram in the preferred embodiment of the present application is shown in the figure. Figure 6 An adaptive state observer in the preferred embodiment of the present application is shown in the figure. An estimation error diagram in the preferred embodiment of the present application is shown in the figure. Figure 7 An adaptive state observer in the preferred embodiment of the present application is shown in the figure. An estimation error diagram in the preferred embodiment of the present application is shown in the figure. Figure 8 An adaptive state observer in the preferred embodiment of the present application is shown in the figure. Error estimation schematic diagram; Figure 9 Error estimation schematic diagram for leader-follower agent in preferred embodiment of the present application; Figure 10 Trigger sequence schematic diagram for dynamic event triggering in preferred embodiment of the present application; Figure 11 Schematic diagram of dynamic threshold variable in preferred embodiment of the present application; Figure 12 Structure schematic diagram of agent system for heterogeneous multi-agent dynamic event triggered output consensus control under false information injection attack in preferred embodiment of the present application. DETAILED DESCRIPTION

[0020] The technical solutions of the present application will be described in detail below with the aid of the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present application and the specific features in the embodiments are detailed descriptions of the technical solutions of the present application, and not limitations of the technical solutions of the present application. In the case of no conflict, the technical features in the embodiments of the present application and the embodiments can be combined with each other.

[0021] The term "and / or", only describes the association relationship of the associated objects, which means that there can be three relationships, for example, A and / or B, which can represent the three cases of A alone, A and B together, and B alone. In addition, the character " / ", generally represents that the associated objects before and after it are in an "or" relationship.

[0022] Embodiment one, a heterogeneous multi-agent dynamic event triggered output consensus control method under FDI attack, comprising: The heterogeneous multi-agent system receives FDI attack data, which triggers the trigger response of the dynamic event triggered mechanism introduced in the tracking state observer.

[0023] The influence of the FDI attack data on the heterogeneous multi-agent system is compensated by the adaptive state observer; FDI is false information injection.

[0024] Among them, the heterogeneous multi-agent system includes a heterogeneous follower agent model and a leader agent model; the heterogeneous follower agent model includes: ; wherein, , , , respectively represent the state and control input and control output of the follower agent i; and are the state matrix, input matrix and output matrix of the follower agent.

[0025] ​Wherein, the leader agent model comprises: ; Wherein, , , represent the state and control output of the leader agent; and are the state matrix and output matrix of the leader agent respectively.

[0026] Further, the heterogeneous follower agent model and the leader agent model satisfy the following conditions: Condition one, the leader agent and the follower agent are connected with each other, and the connection of the leader agent and the follower agent satisfies that there is a directed spanning tree with the leader agent as the root node in the topological structure; The consistency of the output of the leader agent and the follower agent conforms to the output regulation equation; the output regulation equation is: ; wherein are two solutions of the output equation; Condition two, the FDI attack occurs in the network channel of the sensor and the controller, and the attack model of the system information description of the heterogeneous multi-agent system when subjected to the FDI attack is: ; Condition three, and represent the FDI attack data injected into the control channel and the sensor channel of the follower agent, and are the control input of the follower agent and the control output of the follower agent after subjected to the FDI attack.

[0027] Specifically, the attack model satisfies the following conditions: when simulating the attack signal in the consistency task of the multi-agent system, the attack signal and its derivative are considered to be bounded, i.e., the energy is bounded, but no prior assumption is made on its distribution characteristics or form, which will be more in line with the actual situation and improve the generalizability.

[0028] Specifically, is controllable, is observable, is observable.

[0029] Specifically, the follower agent in the heterogeneous multi-agent system obtains the estimated state information of the leader agent through the tracking state observer.

[0030] Specifically, the tracking state observer comprises: ; Wherein, is the estimated value of the leader state by the follower, is the observation gain of the tracking state observer, denotes the estimated value at the kth trigger time of the follower agent i; denotes the k'th trigger time of agent j before the closest kth trigger time of agent i. When , it means that agent j can receive information from agent i; when , it means that follower agent i can receive information from the leader. Z i (t) is the cumulative error of the leader agent's estimated value under the dynamic event-triggered mechanism.

[0031] Specifically, the tracking state observer also contains a dynamic event-triggered mechanism, which includes: ; wherein, is a dynamic threshold parameter, , , , are all positive scalar parameters, wherein is a static weight parameter used to adjust the importance of the cumulative error term in the triggering condition. Increasing will make the triggering condition more difficult to meet, thereby further reducing the number of communications; is a decay rate parameter that determines the speed of natural decay of measurement error. The larger it is, the faster the measurement error decays; is a driving weight parameter that controls the influence of the driving term inside the right bracket on the change of measurement error; The error in the dynamic event trigger includes: measurement error , , is the transpose of the measurement error, is the transpose symbol; the cumulative error , ; When the measurement error of the system is greater than the dynamic threshold of the system, an event trigger occurs; at the same time, the state at the trigger time is transmitted to the leader agent and the controller.

[0032] Specifically, the adaptive state observer includes: on the basis of the Luenberger state observer, a compensation term for FDI attack is added to weaken the impact of FDI attack on the estimated state information; the algorithm includes: ; wherein, , are the state estimate value and output estimate value of the follower itself, respectively; is a unit column vector, is the observation gain of the adaptive state observer; Compensation term is: ; wherein, is a scalar and greater than zero, is a gain matrix, is an adaptive parameter; ; wherein, is a scalar and greater than zero; The adaptive parameter determines whether an FDI attack occurs through the difference between the output information of the attacked and the output information estimate value; when an attack occurs, the adaptive compensation mechanism applies an opposite effect to the FDI attack, weakening the influence of the attack on the estimated state information.

[0033] Working principle: The tracking state observer is constructed based on the dynamic model of the leader agent, and the observation accuracy is corrected in real time by fusing the error between the measured output state information of the neighbor agent and the estimated value of the tracking state observer, so that the follower agent can synchronously obtain the high-precision estimated state information of the leader agent, thereby solving the state synchronization lag problem of the heterogeneous system.

[0034] By introducing a dynamic event triggering mechanism in the tracking state observer, the communication frequency can be dynamically reduced in the process of agent communication, thereby better saving network resources, while ensuring that the system can respond in time through the triggering mechanism when attacked, and maintaining the consistency control goal. The dynamic event triggering mechanism adjusts the triggering threshold in real time by introducing a dynamic variable, wherein the triggering condition is dynamically calculated according to the difference between the current state error and the historical error; when the error exceeds the dynamic threshold, the communication update is triggered, which significantly reduces the transmission of redundant data to reduce network load, and at the same time, when an FDI attack is detected, the communication mechanism is forcibly triggered, thereby ensuring the stability of the system consistency control goal through fast response.

[0035] By adding an adaptive term in the observer, the influence of network attacks can be adaptively compensated, thereby improving the estimation accuracy. The adaptive state observer compensation is realized by adjusting the adaptive gain term in the observer online, specifically: when an FDI attack is detected, the adaptive term parameters are dynamically updated based on the characteristics of the attack signal, and the corrected state estimate value is used to replace the damaged state for closed-loop control; if no attack is detected, the observer is directly updated through the actual system state feedback, which ensures the estimation accuracy while avoiding system oscillation caused by excessive compensation.

[0036] The observation gain of the two state observers and the control gain of the controller are solved by an optimization algorithm, so that the system is stable. The observation values of the two state observers are used in the controller to realize the heterogeneous multi-agent leader-follower consensus control. And the design scheme of the multi-agent system is integrated and packaged to form an intelligent control system suitable for FDI attack defense. And it is applied to the heterogeneous multi-agent consensus control task in simulation or actual scene.

[0037] The resource efficiency of the application: the dynamic event triggering mechanism reduces network bandwidth occupation and energy consumption by dynamically adjusting the communication frequency, and is suitable for distributed systems with limited resources. Robustness against attacks: the adaptive state observer compensates the influence of FDI attacks in real time, and the gain parameters are solved by an optimization algorithm, which significantly improves the state estimation accuracy and control stability of the system under attack. Flexibility and versatility: the scheme supports the consistency of heterogeneous multi-agents (such as unmanned aerial vehicles, robots, etc.) specification Figure 3 Control can be extended to industrial Internet of Things, intelligent transportation and other practical scenarios. Fast response capability: the triggering mechanism and adaptive compensation work together to ensure that the system quickly switches to a safe mode when an attack occurs, avoiding attack propagation and system collapse.

[0038] In embodiment two, on the basis of embodiment one, the nonlinear terms in the nonlinear matrix inequality are replaced by linear terms by variable substitution, and then a linear matrix inequality is formed; for example: Where P and L1 are unknown quantities, which are replaced by Y through the above formula, and then converted to a linear term. Then the least squares method (the essence is an optimization algorithm, that is, the linear matrix inequality obtained by variable substitution is optimized to obtain the smallest Y) is used in MATLAB to obtain the gain parameters, including the observer gain of the tracking state observer and the adaptive state observer, and the control gain of the controller.

[0039] In embodiment three, on the basis of embodiment one or embodiment two, the two observation state information of the tracking state observer and the adaptive state observer are introduced into the controller to control the heterogeneous multi-agent system. The controller includes: ; Wherein, And are control gains; is obtained by the Hurwitz matrix . .

[0040] In embodiment four, on the basis of any one of embodiments one to three, the control protocol is constructed to realize simulation; considering six follower linear agents and one leader agent.

[0041] The state matrix is as follows: ; ; ; ; ; ; ; ; ; , ; where the description of the attack signal: ; ; the attack signal is added after 20s of the simulation start. From Fig. 4, Figure 5 it can be seen that the influence of the attack signal on the observation has been compensated by the adaptive compensation mechanism, and the error tends to zero.

[0042] In the setting, the Runge-Kutta method is used to realize the control protocol, the initial value is set, and the model option is prepared, so that the consistency control can be realized. The time domain closed loop expression of the system can be derived by theoretical method, and the sufficient condition for making the system stable can be obtained by Lyapunov stability theorem. A set of optimal solutions that meet the performance index are obtained by using LMIToolbox.

[0043] The results are shown in Figure 4 , Figure 5 , the observation error of the tracking state observer oscillates and converges, that is, the state observer can realize the tracking of the leader agent; from Figure 6 , Figure 7 , Figure 8 it can be seen that the adaptive state observer, for FDI attack, the estimation error tends to zero with time, that is, the adaptive mechanism can weaken the influence of FDI attack on estimation and improve the estimation accuracy. Figure 9 The output error of the leader agent and the follower agent is shown, which oscillates for a short time and finally converges to zero, so that the leader-follower output consistency of heterogeneous multi-agent under FDI attack is realized. Figure 10 The trigger sequence of the dynamic event trigger mechanism can be seen, which can avoid Zeno behavior. Figure 11 The trend of the change of the dynamic trigger parameter threshold in the dynamic event trigger is shown in the figure, and it can be seen that the trigger threshold tends to zero with time.

[0044] Embodiment five, a heterogeneous multi-agent dynamic event trigger output consistency control agent system under false information injection attack, comprising: a sampler, an event generator, a memory, a controller, an actuator, a system mathematical model, an attack detection device, the connection relationship is shown in Figure 12, the attack detection device is used for detecting attack, when detecting attack, the detection signal is input into the system mathematical model, the system mathematical model is also interconnected with the sampler, the memory, the actuator, the system mathematical model outputs the output result through the heterogeneous multi-agent dynamic event triggered output consensus control method under FDI attack in example one or example two, the sampler obtains the output structure of the system mathematical model, and the output structure is transmitted to the event generator, the event generator sends data and trigger signals to the controller, the controller outputs control signals to the actuator, and the actuator feeds back the control input to the system mathematical model, and the system mathematical model and the event generator realize data interaction with the memory.

[0045] Embodiment six, a kind of heterogeneous multi-agent dynamic event triggered output consensus control equipment under FDI attack, for realizing the steps of a kind of heterogeneous multi-agent dynamic event triggered output consensus control method under FDI attack of example one or example two, include: acquisition unit, the acquisition unit is used to obtain FDI attack data; processing unit, the processing unit is used to trigger the response of dynamic event trigger mechanism introduced in tracking state observer according to the FDI attack data received by heterogeneous multi-agent system; the influence of the FDI attack data on heterogeneous multi-agent system is compensated by adaptive state observer.

[0046] Embodiment seven, a kind of heterogeneous multi-agent dynamic event triggered output consensus control storage medium under FDI attack, for realizing the steps of a kind of heterogeneous multi-agent dynamic event triggered output consensus control method under FDI attack of example one or example two.

[0047] Working principle: The application discloses a false data injection (FDI) attack under a heterogeneous multi-agent dynamic event-triggered output consensus control method, and aims to solve the problems of inaccurate state estimation, waste of communication resources and difficulty in maintaining system consensus under the FDI attack in the prior art. The method comprises the following steps: when the controller and the sensor network channel are subjected to the FDI attack, an adaptive compensation mechanism of a state observer is constructed, a compensation term equivalent to the attack signal in reverse is generated in real time by using an output error, the disturbance of the attack on state estimation is dynamically counteracted, and the observation accuracy is improved; meanwhile, a dynamic event-triggered mechanism is designed, a communication threshold is dynamically adjusted based on the difference between system state error and historical data, data transmission is triggered only when the error exceeds the adaptive threshold or the attack is detected, and compared with the static event-triggered mechanism, the network communication load is further reduced; finally, the state estimation information after compensation is transmitted to the controller and the neighbor agent through the dynamic event-triggered mechanism, and high-robustness output consensus control of the heterogeneous multi-agent (such as a UAV and a robot) under the FDI attack is realized. The application has the advantages of attack resistance and resource efficiency, and is suitable for distributed system scenes such as industrial Internet of Things and intelligent transportation.

[0048] According to the ideal embodiments of the present application, the above description can be changed and modified in various ways without departing from the technical concept of the present application. The technical scope of the present application is not limited to the content of the specification, and must be determined by the scope of the claims.

Claims

1. A method for heterogeneous multi-agent dynamic event-triggered output consistency control under FDI attack, characterized in that, include: The heterogeneous multi-agent system receives FDI attack data, which triggers the dynamic event triggering mechanism introduced in the tracking state observer. The impact of the FDI attack data on the heterogeneous multi-agent system is adaptively compensated by an adaptive state observer; FDI refers to the injection of false information.

2. The heterogeneous multi-agent dynamic event-triggered output consistency control method under FDI attack as described in claim 1, characterized in that: The heterogeneous multi-agent system includes a heterogeneous follower agent model and a leader agent model; The heterogeneous follower agent model includes: ； in, , , , respectively represent the state, control input, and control output of the follower agent i; , and These are the state matrix, input matrix, and output matrix of the follower agent; The leader agent model includes: ； in, , This represents the state and control output of the leader agent; and These are the state matrix and output matrix of the leader agent, respectively.

3. The heterogeneous multi-agent dynamic event-triggered output consistency control method under FDI attack as described in claim 2, characterized in that: The heterogeneous follower agent model and leader agent model satisfy the following conditions: The leader agent and the follower agents are interconnected, and the connection between the leader agent and the follower agents satisfies the existence of a directed spanning tree in the topology with the leader agent as the root node. And / or, the consistency of the outputs of the leader agent and the follower agents conforms to the output regulation equation; the output regulation equation is: ;in These are the two solutions to the output equation; And / or, FDI attacks occur in the network channels of sensors and controllers. The attack model for describing the system information of a heterogeneous multi-agent system under an FDI attack is as follows: ； in, and These represent FDI attack data injected into the control channel and sensor channel of the follower agent, respectively. and It refers to the control input and control output of the follower agent after being attacked by FDI.

4. The heterogeneous multi-agent dynamic event-triggered output consistency control method under FDI attack as described in claim 3, characterized in that: The tracking state observer includes: ； Among them, Z i (t) is the cumulative error of the leader agent's estimated value under the dynamic event triggering mechanism; It is the followers' estimate of the leader's state. It is the observation gain of the tracking state observer. This represents the estimated value at the k-th triggering moment of follower agent i; This represents the k'th trigger moment of agent j before the kth trigger moment of agent i; when When, it means that agent j can receive information from agent i; when When this occurs, it means that the follower agent i is able to receive information from the leader.

5. The heterogeneous multi-agent dynamic event-triggered output consistency control method under FDI attack as described in claim 4, characterized in that: The tracking state observer also includes a dynamic event triggering mechanism, which includes: ； in, It is a dynamic threshold parameter. , , , All are positive scalar parameters; among them These are static weight parameters; It is the attenuation rate parameter; To drive the weight parameters; Errors in dynamic event triggering include: measurement errors. , ; The transpose of the measurement error is T, where T is the transpose sign. This is the cumulative error; ; When the system's measurement error exceeds the system's dynamic threshold, an event is triggered; at the same time, the state at the trigger moment is transmitted to the leader agent and the controller.

6. The heterogeneous multi-agent dynamic event-triggered output consistency control method under FDI attack as described in claim 5, characterized in that: The adaptive state observer includes: adding a compensation term against FDI attacks to the Romberg state observer to mitigate the impact of FDI attacks on the estimated state information; the algorithm includes: ； in, , These are the follower's own state estimate and output estimate, respectively; It is a unit column vector. The observation gain of the adaptive state observer; Compensation for: ； in, It is a scalar and greater than zero. It is the gain matrix. For adaptive parameters; ; in, It is a scalar and greater than zero; The adaptive parameters determine whether an FDI attack has occurred by measuring the difference between the attacked output information and the estimated output information. When an attack occurs, the adaptive compensation mechanism applies the opposite effect to the FDI attack, reducing the impact of the attack on the estimated state information.

7. The heterogeneous multi-agent dynamic event-triggered output consistency control method under FDI attack as described in claim 6, characterized in that: The gain parameters are set by variable substitution and least squares method. The gain parameters include the observer gain of the tracking state observer and the adaptive state observer, as well as the control gain of the controller.

8. The heterogeneous multi-agent dynamic event-triggered output consistency control method under FDI attack as described in claim 7, characterized in that: The observation state information from both the tracking state observer and the adaptive state observer is imported into the controller to control the heterogeneous multi-agent system. The controller includes: ； in, and All are control gain; Through the Herwitz matrix It can be concluded that; .

9. A heterogeneous multi-agent dynamic event-triggered output consistency control device under FDI attack, characterized in that, The steps for implementing the heterogeneous multi-agent dynamic event-triggered output consistency control method under FDI attack as described in any one of claims 1-8 include: Acquisition unit, the acquisition unit is used to acquire FDI attack data; The processing unit is used to trigger a response of the dynamic event triggering mechanism introduced in the tracking state observer based on the FDI attack data received by the heterogeneous multi-agent system. The impact of the FDI attack data on the heterogeneous multi-agent system is adaptively compensated by an adaptive state observer.

10. A storage medium for heterogeneous multi-agent dynamic event-triggered consistent control under FDI attack, characterized in that, The steps are for implementing the heterogeneous multi-agent dynamic event triggering output consistency control method under FDI attack as described in any one of claims 1-8.

Images