Pulse control method and system for multi-agent system under double-channel attack

Abstract

The application provides a kind of double-channel attack under multi-agent system pulse control method and system, it is related to system control technical field.The method comprises: constructing follower-follower, leader-follower double-channel attack processing model in multi-agent system;Bernoulli random variable is used to describe the random occurrence of false data injection in the double-channel attack processing model;According to the distributed event trigger mechanism, the preset condition of tracking error and sampling tracking error is judged at the first pulse moment Trigger information update, generate distributed pulse control signal;The distributed pulse control signal is subjected to symmetric input saturation constraint processing, and the control input is obtained and applied to the follower.The application solves the technical problem that the prior art cannot realize multi-agent system stable cooperative control under double-channel random deception attack condition, and achieves the beneficial effect of reducing the number of sampling updates while maintaining tracking performance.

Description

Technical Field

[0001] This invention relates to the field of system control technology, specifically to a pulse control method and system for a multi-agent system under dual-channel attack. Background Technology

[0002] With the rapid development of communication networks, embedded computing, and distributed sensing technologies, Multi-Agent Systems (MASs) have been widely applied in engineering fields such as UAV formations, smart grid scheduling, distributed sensor networks, and collaborative robots due to their advantages of distributed cooperation, high robustness, and easy scalability. Leader-follower consistency, as a core issue in multi-agent cooperative control, aims to achieve global cooperative behavior by enabling all follower states to track the leader's state within a finite timeframe through local information exchange among agents.

[0003] The open and interconnected nature of networked multi-agent systems makes them vulnerable to malicious network attacks. Among these, deception attacks (false data injection attacks) are a major threat to the secure and stable operation of the system due to their high degree of concealment and destructive power. Deception attacks do not interrupt communication links but mislead controller decisions by tampering with or forging communication data, severely damaging the system's collaborative tracking performance. Existing research mainly focuses on single-channel attacks or ideal communication environments, and research on differentiated modeling and resilient control of leader-follower channels and follower-follower channels simultaneously subjected to random deception attacks is still insufficient.

[0004] In summary, existing multi-agent system cooperative control technologies cannot solve the problem of maintaining stable cooperative control after a dual-channel random spoofing attack, and are insufficient to meet the requirements of safe, efficient, stable, and cooperative control in practical engineering scenarios such as UAV swarms and smart grids. Therefore, there is an urgent need for a control method for multi-agent systems that can adapt to dual-channel spoofing attacks. Summary of the Invention

[0005] This invention addresses the shortcomings of existing multi-agent systems in maintaining stable and coordinated control after a dual-channel random deception attack by providing a pulse control method and system for multi-agent systems under dual-channel attacks.

[0006] In a first aspect, embodiments of the present invention provide a pulse control method for a multi-agent system under dual-channel attacks, characterized by comprising: constructing a dual-channel attack processing model of follower-follower and leader-follower in the multi-agent system; using Bernoulli random variables to describe the random occurrence of false data injection in the dual-channel attack processing model; based on the distributed event triggering mechanism in the multi-agent system, updating the tracking error and sampling tracking error of the data in the multi-agent system at the first pulse moment by performing a preset condition judgment triggering information update to generate a distributed pulse control signal; and performing symmetric input saturation constraint processing on the distributed pulse control signal to obtain a control input and apply it to the followers.

[0007] In conjunction with the first aspect, embodiments of the present invention provide a first possible implementation of the first aspect, wherein the leader and followers in the multi-agent system are configured with the following dynamic model:

[0008] in, The leader's state at time t. for The first derivative, , It is an m-dimensional vector space; —The state of follower i at time t. for The first derivative, , Let i be an m-dimensional vector space; i is the follower label; —A given nonlinear vector function; —A given nonlinear vector function; constant This refers to system time delay; The control input for the followers; the set of followers is denoted as . .

[0009] In conjunction with the first aspect, this invention provides a second possible implementation of the first aspect, wherein constructing a dual-channel attack processing model for follower-follower and leader-follower in a multi-agent system includes: receiving interaction information in the leader-follower communication channel and the follower-follower communication channel in the multi-agent system; injecting false data into the interaction information to influence the model, and modeling it as a dual-channel deception attack model, wherein the false data injection influence in the follower-follower communication channel is used to characterize the situation where the relative information received by the follower from neighboring followers is contaminated, and the false data injection influence in the leader-follower communication channel is used to characterize the situation where the leader information received by the follower is contaminated.

[0010] In conjunction with the first aspect, this invention provides a third possible implementation of the first aspect, wherein the use of Bernoulli random variables to describe the random occurrence of spoofing in the dual-channel attack processing model includes: For follower-follower communication channels Indicates injection into the follower Spurious data in the received relative information from neighbors; based on Bernoulli random variables Describe whether an attack has occurred in the follower-follower communication channel; when When, it indicates from the follower To followers Communication information is affected by false data Pollution; when When, it indicates that the channel is not under attack at the current moment; wherein, The probability distribution is as follows:

[0011] in, For probability labeling, This indicates the probability of an attack occurring in a follower-follower channel. For leader-follower communication channels Indicates injection into the follower The received leader information contained false data, based on Bernoulli random variables. Describe whether an attack occurred in the leader-follower communication channel; when , indicating followers The obtained leader information was Pollution; when This indicates that the leader's information transmission has not been attacked; wherein the... The probability distribution is as follows:

[0012] in The probability of an attack occurring in the leader-follower channel.

[0013] In conjunction with the first aspect, this embodiment of the invention provides a fourth possible implementation of the first aspect, wherein, based on the distributed event triggering mechanism, during the process of triggering information updates by judging the tracking error and sampling tracking error of the data in the multi-agent system at the first pulse moment: For any follower Its state tracking error relative to the leader is: Its stacking error vector is: ,in For followers The most recent sampling status, The sampling tracking error for the leader's most recent sampled state is: ,and The set of followers is denoted as , This is a transpose operation; At the pulse moment The event triggering condition for the distributed event triggering mechanism is as follows:

[0014] in For vector norm, For preset trigger parameters, if the conditions are not met, the current sampled information will not support subsequent control updates, and... Triggering new information transmission, For pulse timing: .

[0015] In conjunction with the first aspect, this embodiment of the invention provides a fifth possible implementation of the first aspect, wherein in the step of performing symmetrical input saturation constraint processing on the distributed pulse control signal to obtain the control input: When a new information transmission is triggered by an event based on the aforementioned distributed event triggering mechanism, the distributed pulse control signal u under the distributed control protocol in the multi-agent system... i (t) is:

[0016] in; For the members in the weighted adjacency matrix of the followers, Connect the members in the leader connection matrix; Pulse control input after symmetrical input saturation constraint for:

[0017] in For the Dirac impulse function, Let be a symmetric saturating function, where the set of followers is denoted as . , This refers to the pulse moment.

[0018] In conjunction with the first aspect, this embodiment of the invention provides a sixth possible implementation of the first aspect, which further includes: determining a control gain and event triggering parameters that satisfy the sufficient condition of mean-square bounded consistency based on the system time delay of the multi-agent system, the probability of follower-follower communication channel attack, the probability of leader-follower communication channel attack, the input saturation bound, and event triggering parameters; generating the distributed pulse control signal based on the control gain and event triggering parameters, so that the multi-agent system achieves leader-follower mean-square bounded consistency under dual-channel spoofing attacks and input saturation constraints.

[0019] Secondly, embodiments of the present invention also provide a multi-agent system, comprising: a leader module, at least two follower modules, wherein the leader module and the follower modules construct a follower-follower communication channel and a leader-follower communication channel, a dual-channel attack processing module, an event triggering condition evaluation module, a pulse controller module, and an input saturation execution module; wherein the dual-channel attack processing module is configured to describe the random occurrence of attacks by using Bernoulli random variables for spurious data injected in the follower-follower channel and spurious data injected in the leader-follower channel, respectively; the event triggering condition evaluation module is configured to update the tracking error and sampling tracking error of the data described in the dual-channel attack processing module at the first pulse moment according to a distributed event triggering mechanism; the pulse controller module is configured to generate a distributed pulse control signal according to the trigger information update instruction; and the input saturation execution module is configured to perform symmetrical input saturation constraint processing on the pulse control signal and output control input to the follower modules.

[0020] Thirdly, embodiments of the present invention also provide an electronic device, including: at least one processor; and at least one memory communicatively connected to the processor, wherein: the memory stores program instructions executable by the processor, and the processor can execute the control method described above in the embodiments of the present invention by calling the program instructions.

[0021] Fourthly, embodiments of the present invention also provide a computer-readable storage medium storing computer instructions that cause the computer to perform the control method described above in the embodiments of the present invention.

[0022] The present invention provides a pulse control method and system for multi-agent systems under dual-channel attacks. It distinguishes between follower-follower and leader-follower dual-channel deception attacks, uses Bernoulli random variables to describe the random occurrence characteristics of the attack, which is closer to real adversarial scenarios. By performing symmetrical input saturation constraint processing on the distributed pulse control signal, the control input is obtained and then applied to the followers to achieve stable and coordinated control of the multi-agent system under dual-channel attacks. This meets the requirements of safe, efficient, stable and coordinated control in practical engineering scenarios such as UAV swarms and smart grids.

[0023] Furthermore, this invention deeply integrates the distributed event triggering mechanism with pulse control, triggering sampling updates only when the tracking error exceeds a preset threshold; this reduces the communication burden while maintaining a smaller tracking error; and this invention also directly embeds the symmetrical input saturation constraint into the pulse control loop, taking into account the requirements of communication saving, attack suppression, and actuator limitation, thus comprehensively realizing the stable and coordinated control of a multi-agent system under dual-channel attacks.

[0024] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention are realized and obtained in accordance with the structures particularly pointed out in the description, claims and drawings.

[0025] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0026] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a flowchart illustrating a pulse control method for a multi-agent system under dual-channel attack, as provided in Embodiment 1 of the present invention. Figure 2 This is a schematic diagram of the structure of the multi-agent system provided in Embodiment 2 of the present invention; Figure 3a This is a schematic diagram of the first state component of the state trajectory of the leader and follower under event-triggered pulse control in Embodiment 4 of the present invention; Figure 3b This is a schematic diagram of the second state component of the state trajectory of the leader and follower under event-triggered pulse control in Embodiment 4 of the present invention; Figure 4This is a schematic diagram of the follower tracking error norm under a deception attack in Embodiment 4 of the present invention; Figure 5a This is a schematic diagram illustrating the comparison of the global tracking error norm in Embodiment 4 of the present invention; Figure 5b This is a schematic diagram showing the comparison of tracking error norms within a locally magnified range of 5 ≤ t ≤ 25 s in Embodiment 4 of the present invention; Figure 6 This is a schematic diagram of the structure of the electronic device according to Embodiment 5 of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0029] Current multi-agent systems cannot address the shortcomings of maintaining stable collaborative control after a dual-channel random deception attack. Therefore, this invention provides a pulse control method and system for multi-agent systems under dual-channel attacks. This method can distinguish between follower-follower and leader-follower dual-channel deception attacks, uses Bernoulli random variables to describe the random occurrence characteristics of the attack, and more closely approximates real-world adversarial scenarios to achieve stable collaborative control of the multi-agent system. A distributed event triggering mechanism is deeply integrated with pulse control, triggering sampling updates only when the tracking error exceeds a preset threshold. This reduces communication burden while maintaining a smaller tracking error. Symmetrical input saturation constraints are directly embedded into the pulse control loop, simultaneously addressing the requirements of communication savings, attack suppression, and actuator limitation, thus achieving stable collaborative control of the multi-agent system under dual-channel attacks.

[0030] To facilitate understanding of this embodiment, a pulse control method for a multi-agent system under dual-channel attack, disclosed in Embodiment 1 of the present invention, will be described in detail first.

[0031] Example 1 This embodiment uses UAV formation cooperative patrol as a specific application scenario to fully disclose the control method of the multi-agent system of the present invention. This embodiment selects a multi-agent system consisting of one leader UAV (numbered 0) and five follower UAVs (numbered 1 to 5). Each UAV is equipped with a Global Positioning System (GPS) / Inertial Measurement Unit (IMU) integrated navigation module and a data transmission radio. The leader flies along a preset route, and the followers exchange status information through a communication network to maintain formation. The system communication and computation are integrated with time delays. .

[0032] Reference Figure 1 , Figure 1 This is a flowchart illustrating a pulse control method for a multi-agent system under a dual-channel attack, as provided in Embodiment 1 of the present invention. The method provided in Embodiment 1 includes: Step 100: Construct a dual-channel attack handling model for follower-follower and leader-follower systems in a multi-agent system. In this embodiment, a communication topology and dynamics model of a multi-agent system is first established, and a dual-channel deception attack handling model is constructed based on this model.

[0033] Communication topology modeling: The set of followers is denoted as The communication relationships between followers are formed by an undirected connected graph. Description, in which For a weighted adjacency matrix, For the members in the weighted adjacency matrix of the followers: if the followers Able to receive followers The information, ;otherwise ;and Followers The neighbor set is .picture The Laplacian matrix is ​​denoted as ,in , The communication relationship between leaders and followers is represented by a diagonal matrix. express, Connect the members in the leader matrix: if the followers If you can directly obtain information about the leader, then ,otherwise .

[0034] Dynamics model: The leader and followers adopt the following model with time delay. Nonlinear dynamic model:

[0035]

[0036] in and Representing the leader's state and the followers respectively. The state (in this embodiment, we take) The state vector represents the position in three-dimensional space. ), for The first derivative, , Given an m-dimensional vector space, for The first derivative, , Let i be an m-dimensional vector space; i is the follower label; constant. This refers to system time delay; and Given a nonlinear vector function; For followers The control input to be designed; the set of followers is denoted as In other embodiments of the present invention, the above-described markings may represent the same meaning.

[0037] Dual-channel spoofing attack model: The attacker does not interrupt the communication link, but injects false data during transmission. The first type of attack occurs in the follower-follower communication channel: [The text abruptly ends here, likely due to an incomplete sentence or missing information.] Indicates injection into the follower The second type of attack occurs in the leader-follower communication channel: [The text abruptly shifts to a seemingly unrelated topic about spoofed data in neighbor information.] Indicates injection into the follower The received leader information contains false data. In this embodiment, and The values ​​of each component are set in Within the range, the typical offset of simulated GPS location spoofing attacks is used to establish a descriptive model of the false data information transmitted in the dual channels of follower-follower and leader-follower communication, based on the tampered false information injected into the leader-follower communication channel and the follower-follower communication channel used in these spoofing attacks.

[0038] Step 101: Use Bernoulli random variables to describe the random occurrence of spoofing in the dual-channel attack processing model. In this embodiment, since actual attacks are intermittent and random, Bernoulli random variables are used to probabilistically model the random occurrence characteristics of attacks.

[0039] Follower-follower channel model: In this embodiment, a Bernoulli random variable is introduced. Description from followers To followers Did an attack occur in the communication channel? This indicates that the communication information is affected by false data. pollute; This indicates that the device is not currently under attack. Its probability distribution is as follows:

[0040] in This represents the probability of an attack occurring in a follower-follower channel. In this embodiment, the attack probability between adjacent followers (with a spacing of approximately 5m) is taken as... The attack probability of cross-wing links (spacing approximately 10m) is taken as... . For probability labeling.

[0041] Leader-Follower Channel Model: This embodiment introduces Bernoulli random variables. Describe whether an attack occurred in the leader-follower channel: Indicates follower The obtained leader information was pollute; This indicates that the leader's information was transmitted normally. Its probability distribution is as follows:

[0042] in This represents the probability of an attack occurring in the leader-follower channel. In this embodiment, only follower 1 and follower 5 can directly receive leader information. ),Pick .

[0043] Based on the above modeling, the attacked control information is respectively from and This indicates that the random spoofing data injection in the two types of channels is characterized accordingly.

[0044] Preferably, in the multi-agent system of this embodiment, the process of constructing a dual-channel attack processing model for follower-follower and leader-follower in the multi-agent system can be as follows: in the multi-agent system, receiving interaction information in the leader-follower communication channel and the follower-follower communication channel; injecting false data into the interaction information to influence the model, and modeling it as a dual-channel deception attack model, wherein the false data injection influence in the follower-follower communication channel is used to characterize the situation where the relative information received by the follower from neighboring followers is contaminated, and the false data injection influence in the leader-follower communication channel is used to characterize the situation where the leader information received by the follower is contaminated.

[0045] Step 102: Based on the distributed event triggering mechanism in a multi-agent system, at the first pulse moment... The tracking error and sampling tracking error of the data in the multi-agent system are used to trigger information updates based on preset conditions, and distributed pulse control signals are generated. In this embodiment, since each follower does not need to update its transmission state at every candidate moment, a distributed event-triggered mechanism is designed to save communication and control update resources. In this embodiment, the first pulse moment refers to either "any candidate pulse moment" or "any current candidate pulse moment," and should not be misunderstood as referring only to... The pulse moment of time. In various embodiments of the present invention, the first pulse moment is also disclosed in this way, and will not be described again hereafter.

[0046] Preferably, the pulse time sequence: Let the pulse time sequence be... satisfy and The interval between adjacent pulses is constrained to be This embodiment takes (Preventing Zeno, behavior) (Maximum safety interval).

[0047] Tracking error and sampling tracking error: In this embodiment, for any follower The state tracking error relative to the leader is defined as:

[0048] The stacking error vector is , . This is a transpose operation.

[0049] remember For followers The most recently available sampling state, If the leader's most recently available sampled state is used, then the followers... The sampling tracking error is defined as:

[0050] The stacked sampling tracking error vector is .

[0051] Event triggering condition: In this embodiment, at the pulse moment The event triggering condition is set as follows:

[0052] in For preset trigger parameters, This is the vector norm. In this embodiment, we take... , If the above conditions are not met, the current sampling information is insufficient to support subsequent control updates. Triggering a new information transmission:

[0053] After triggering, the sampling and tracking error is refreshed to If the conditions are met, the system maintains the current sampling state and does not perform an update.

[0054] In this embodiment, the event triggering mechanism operates as shown in the following typical moments: when the formation is stable ( , If the true error does not change significantly (still exists) If the data is within the specified range, no update will be triggered; however, if an attacker suddenly injects false data, causing... Increased sharply to (Exceeding the upper limit) If the upper bound condition of the norm is not met, an information update is immediately triggered, and a correction response is initiated.

[0055] Preferably, in the multi-agent system of this embodiment, the distributed event triggering mechanism can also update the preset condition judgment triggering information at any current candidate pulse moment (i.e., the first pulse moment) regarding the tracking error of the follower relative to the leader in the multi-agent system and the sampling tracking error corresponding to the most recent available sampling state. Based on the updated sampling state, follower-follower communication topology, leader-follower connection relationship, and the attacked information item in the dual-channel attack processing model, a distributed pulse control signal is generated. In this embodiment, the first pulse moment is "any candidate pulse moment" or "any current candidate pulse moment," and should not be misunderstood as referring only to... The pulse moment of a moment.

[0056] Step 103: Perform symmetrical input saturation constraint processing on the distributed pulse control signal to obtain the control input, which is then applied to the follower. In this embodiment, the brushless DC motors and electronic speed controllers of each follower drone have clearly defined maximum thrust output limits (maximum thrust per axis). Saturation constraints must be applied before the control signal enters the actuator.

[0057] Distributed pulse control signal: In this embodiment, when the event triggering condition determines that the control input needs to be updated, the distributed pulse control signal before the saturation constraint... for:

[0058] The meanings of each symbol are consistent with the steps described above. , The control signal consists of four parts: (1) the consistency error term among followers. (2) Leader tracking error term. (3) Follower-follower channel attack information item (4) Leader-follower channel attack information item .in; For the members in the weighted adjacency matrix of the followers, Connect the members in the leader matrix.

[0059] Symmetrical input saturation constraint: In this embodiment, the distributed pulse control signal... Symmetrical input saturation constraint processing is performed to obtain pulse control input. :

[0060] in The Dirac pulse function modulates the continuous control signal only at the pulse moment. A discrete pulse that takes effect instantaneously; For a symmetric saturation function, it is defined as:

[0061] In this embodiment, the horizontal direction ( , (Axis) Saturation Upper Limit Take Vertical direction ( (Axis) Taking gravity compensation requirements into account .

[0062] Taking the initial formation of the formation as an example: the calculated value of the distributed control signal of follower 5 is... , All exceeded The upper limit, after being subject to symmetric saturation constraints, is reduced to , The direction of the control input remains unchanged, and only the amplitude is limited within a safe range ("maintain direction, limit amplitude").

[0063] Preferably, in this embodiment, the multi-agent system can further determine the control gain and event triggering parameters that satisfy the sufficient condition of mean-square bounded consistency based on the system time delay, the probability of follower-follower communication channel attack, the probability of leader-follower communication channel attack, the input saturation bound, and the event triggering parameters; and generate the distributed pulse control signal based on the control gain and event triggering parameters to enable the multi-agent system to achieve leader-follower mean-square bounded consistency under dual-channel spoofing attacks and input saturation constraints. Mean-square bounded consistency condition: In this embodiment, a Lyapunov-Krasovskii functional is constructed based on Lyapunov stability theory and time delay correlation estimation. ,in Measuring the energy of instantaneous tracking error, and These are the cumulative error energy and the error rate of change functionals for the time delay interval, respectively, used for compensation. The impact of time delay on stability. Through differential analysis of the Lyapunov function under mathematical expectation, and by using Jensen's integral inequality to handle the time delay term and sector bounded conditions to handle saturated nonlinearity, sufficient conditions in the form of Linear Matrix Inequality (LMI) can be established. When this LMI condition holds, there exists a constant. , , so that:

[0064] in A positive definite matrix The smallest eigenvalue. When At that time, the mean square steady-state upper bound of the tracking error is The closed-loop system achieves mean-squared bounded consistency between leaders and followers. In this embodiment, under a scenario with equal attack probability, the mean-squared error bound is... (Root mean square error approximately) This meets the accuracy requirements for drone formation patrols.

[0065] In this first embodiment, by distinguishing between follower-follower and leader-follower dual-channel deception attacks, a Bernoulli random variable is used to describe the random occurrence characteristics of the attack, which more closely resembles the stable collaborative control of a multi-agent system in a real adversarial scenario. Furthermore, a distributed event triggering mechanism is deeply integrated with pulse control, triggering sampling updates only when the tracking error exceeds a preset threshold; this reduces communication burden while maintaining a smaller tracking error. In this embodiment, symmetric input saturation constraints can be directly embedded into the pulse control loop, simultaneously addressing the requirements of communication savings, attack suppression, and actuator limitation, thus achieving stable collaborative control of a multi-agent system under dual-channel attacks.

[0066] Example 2 Reference Figure 2 , Figure 2 This is a schematic diagram of the structure of a multi-agent system provided in Embodiment 2 of the present invention. Embodiment 2 of the present invention discloses a multi-agent system 200, which includes: a leader module 201, a first follower module 202, and a second follower module 203. The leader module 201 and the first follower module 202 establish a leader-follower communication channel 204, and the first follower module 202 and the second follower module 203 establish a follower-follower communication channel 205. Other components include a dual-channel attack processing module 206, an event triggering condition evaluation module 207, a pulse controller module 208, and an input saturation execution module 209. The dual-channel attack processing module 206 is configured to describe the random occurrence of attacks using Bernoulli random variables for the false data injected into the follower-follower communication channel 205 and the false data injected into the leader-follower communication channel 204, respectively. The event triggering condition evaluation module 207 is configured to update the triggering information based on the tracking error and sampling tracking error of the data described in the dual-channel attack processing module 206 at the first pulse moment, according to the distributed event triggering mechanism. The pulse controller module 208 is configured to generate a distributed pulse control signal based on the triggering information update instruction. The input saturation execution module 209 is configured to perform symmetrical input saturation constraint processing on the pulse control signal and output the control input to the first follower module 202.

[0067] In this embodiment, the multi-agent system 200, and its constituent modules 201 (leader module 201, first follower module 202, second follower module 203, leader-follower communication channel 204, follower-follower communication channel 205, dual-channel attack processing module 206, event triggering condition evaluation module 207, pulse controller module 208, and input saturation execution module 209) will be described in detail with a practical and complete example.

[0068] This embodiment uses UAV formation collaborative reconnaissance as a specific application scenario. A multi-agent system 200 is deployed in a three-drone formation consisting of one leader UAV (numbered 0, which includes a leader module 201) and two follower UAVs (numbered 1 and 2, which include a first follower module 202 and a second follower module 203, respectively, and will not be described further below). The three UAVs fly in a horizontal "I" formation. The leader UAV 0 is responsible for autonomously flying according to a preset reconnaissance route. Follower UAVs 1 and 2 are located to the left and right rear of the leader, respectively, and obtain flight status information of the leader and neighboring UAVs through onboard data radio communication to maintain a predetermined formation spacing. Each UAV is equipped with a GPS / IMU integrated navigation module, a 5.8GHz data radio, an onboard flight control computer, and a brushless DC motor actuator. The system control objective is to ensure that the position tracking errors of the followers and leader converge to a bounded set under dual-channel deception attacks and input saturation constraints, thus maintaining the formation reconnaissance configuration.

[0069] The formation system parameters in this embodiment are as follows:

[0070] Leader Module 201 The leader module 201 provides a reference trajectory and state baseline for the formation. In this embodiment, the leader drone 0... It flies at a constant speed along a preset reconnaissance route, and its own state vector is taken as , representing the eastward position, northward position, and flight altitude (unit: m), respectively. The leader module 201 broadcasts its real-time status information to the first follower module 202 and the second follower module 203 via an onboard 5.8GHz data radio.

[0071] Preferably, in this embodiment, the dynamic model constructed by the leader module 201, the first follower module 202, and the second follower module 203 is as follows:

[0072]

[0073] in For followers state; constant The system time delay is taken; the nonlinear function is taken as... Characterizing air damping velocity decay, Characterizes time-delay coupling caused by wake disturbances from neighboring aircraft; This is the control input to be designed.

[0074] First follower module 202 and second follower module 203 The first follower module 202 (corresponding to follower UAV 1) and the second follower module 203 (corresponding to follower UAV 2) are located to the left and right rear of the leader UAV 0, respectively. They receive status information from the leader-follower communication channel 204 and the follower-follower communication channel 205. The event trigger condition evaluation module 207 determines whether to trigger an update. The pulse controller module 208 generates control signals, which are then constrained by the input saturation execution module 209 and applied to their respective flight control actuators. The function of the first follower module 202 is to maintain a predetermined left rear formation offset from the leader. direction , direction , direction The function of the second follower module 203 is to maintain the predetermined right rear formation offset from the leader. direction , direction , direction The initial positions of the two follower modules are set as follows:

[0075] Both the first follower module 202 and the second follower module 203 include a complete functional chain: a complete signal processing and closed-loop control process from receiving data through the communication channel, through the dual-channel attack processing module 206, the event triggering condition evaluation module 207, the pulse controller module 208, to the input saturation execution module 209. To simplify the disclosure of the present invention, this embodiment fully discloses the complete functional chain of the first follower module 202. The complete functional chain of the second follower module 203 is similar to that of the first follower module 202 and will not be described in detail here.

[0076] Follower-Follower Communication Channel 205 and Leader-Follower Communication Channel 204 In this embodiment, the leader-follower communication channel 204 is a 5.8GHz data radio broadcast link for the leader module 201 to broadcast status information to the first follower module 202 and the second follower module 203. The follower-follower communication channel 205 is a 5.8GHz data radio direct link for exchanging relative position information between the first follower module 202 and the second follower module 203.

[0077] Communication topology: follower set Weighted adjacency matrix ,in (The two followers communicate with each other) Leader Connection Matrix In this embodiment, both followers are within the leader's communication coverage area. The Laplacian matrix is:

[0078] Dual-channel attack processing module 206 The dual-channel attack processing module 206 is responsible for modeling and processing spoofing attacks in the communication link. In the UAV swarm reconnaissance scenario of this embodiment, the attacker intercepts communication data packets in the 5.8GHz band and injects forged GPS location information by deploying a ground jamming station. In this embodiment, the attack does not interrupt the communication link, but injects false data during transmission.

[0079] Type 1 Attack – Follower-Follower Communication Channel 205 Attack: [Instructions] Indicates injection into the follower module The received neighbor relative information contains spurious data. In this embodiment, the amplitude of each component of the spurious data is taken as... This simulates typical deception biases of GPS positioning signals by ground-based jamming stations.

[0080] The second type of attack—the leader-follower communication channel 204 attack: [Instructions / Description] Indicates injection into the follower module The magnitude of the false data in the received leader information is consistent with the above.

[0081] Random attack modeling: In this embodiment, a Bernoulli random variable is used to describe the random occurrence of the attack. For follower-follower communication channel 205:

[0082] in Indicates from followers To followers Communication is affected by false data Contamination. In this embodiment, the attack probability is taken when the distance between the two followers is approximately 30m. .

[0083] For leader-follower communication channel 204:

[0084] in Indicates follower The obtained leader information was Pollution. This embodiment takes The probability of a channel attack between followers is lower than that between followers, because the leader is usually located at the front of the formation and has a higher data transmission power.

[0085] Preferably, in the multi-agent system 200 of this embodiment, the process of constructing the follower-follower and leader-follower dual-channel attack processing model in the multi-agent system 200 can be as follows: in the multi-agent system, receiving the interaction information in the leader-follower communication channel and the follower-follower communication channel; injecting false data into the interaction information to influence the model, and modeling it as a dual-channel deception attack model, wherein the false data injection influence in the follower-follower communication channel is used to characterize the situation where the relative information received by the follower from neighboring followers is contaminated, and the false data injection influence in the leader-follower communication channel is used to characterize the situation where the leader information received by the follower is contaminated.

[0086] Preferably, in this embodiment, a differentiated attack intensity setting can be introduced. Because follower 1 and follower 2 are located to the left and right rear of the leader respectively, their communication distances from the leader differ slightly, resulting in different levels of attack exposure.

[0087] Event Triggering Condition Evaluation Module 207 The event triggering condition evaluation module 207 determines whether to trigger information transmission and control updates based on a distributed event triggering mechanism. In this embodiment, based on the distributed event triggering mechanism, a preset condition judgment is performed on the tracking error and sampling tracking error of the data described in the dual-channel attack processing module at the first pulse moment to trigger information updates. In this embodiment, the first pulse moment is either "any candidate pulse moment" or "any current candidate pulse moment," and should not be misunderstood as referring only to... The pulse time of time. In this embodiment, let the pulse time sequence be... satisfy .

[0088] Preferably, in the multi-agent system of the present invention, the distributed event triggering mechanism can also perform a preset condition judgment to update the tracking error of the follower relative to the leader and the sampling tracking error corresponding to the most recent available sampling state at any candidate pulse moment (i.e. the first pulse moment), and generate a distributed pulse control signal based on the updated sampling state, follower-follower communication topology, leader-follower connection relationship and the attacked information item in the dual-channel attack processing model.

[0089] Tracking error versus sampling tracking error: For any follower module Its state tracking error relative to the leader module 201 is Stacked error vectors (dimension) ).remember and The following modules are respectively The sampling tracking error is based on the most recent sampled state of the leader module 201. Stacked as .

[0090] Event triggering condition: at the pulse moment The event trigger condition evaluation module 207 performs the following determination:

[0091] In this embodiment, the following is taken , If the conditions are not met, an information update will be triggered:

[0092] In this embodiment, The settings provide approximately The relative variation tolerance is multiple times, which is applicable to the tracking error fluctuations caused by wind disturbances and other factors during UAV formation reconnaissance flights.

[0093] The trigger determination process is explained below using the specific timing of this embodiment:

[0094] Pulse controller module 208 The pulse controller module 208 generates a distributed pulse control signal when the event triggering condition evaluation module 207 determines that an update is needed. The distributed pulse control signal before saturation constraint... for:

[0095] in , The meanings of each item are as follows: (1) The first item is the consistency error between followers, which makes the two followers maintain a 20m expected formation distance; (2) The second item is the leader tracking error, which drives each follower to tend towards the leader state; (3) The third item is the follower-follower channel attack signal; (4) The fourth item is the leader-follower channel attack signal.

[0096] In this embodiment, the pulse controller module 208 calculates based on the sampling status data received by the data transmission radio. Taking the initial stage of formation as an example, assume the sampling and tracking error of the first follower module 202... Furthermore, there has been no attack yet, and the sampling and tracking error of the second follower module 203 is... Then the consistency term between the two followers is Leader tracking item is , (Converted into thrust through subsequent gain).

[0097] Input saturation execution module 209 The input saturation execution module 209 performs symmetrical input saturation constraint processing on the distributed pulse control signal generated by the pulse controller module 208. In this embodiment, the pulse control input... for:

[0098] in For the Dirac impulse function, It is a symmetric saturated function:

[0099] In this embodiment, the maximum saturation upper limit of the single-axis maximum thrust of the UAV brushless DC motor is taken as... Taking the first follower module 202 during the formation phase as an example, the thrust control signal output by the pulse controller module 208 is: (Exceeding the upper limit), the input saturation execution module 209 reduces it to The control direction remains unchanged, only the amplitude is limited, ensuring the safe operation of the motor.

[0100] The input saturation execution module 209 inputs the processed pulse control input. The dynamic equations injected into the first follower module 202 drive the follower UAV to complete position adjustment and attitude tracking.

[0101] A preferred embodiment: A preferred detailed implementation of the event triggering condition evaluation module 207 is as follows.

[0102] In this preferred embodiment, the event triggering condition evaluation module 207 includes a tracking error and sampling tracking error acquisition submodule and a judgment submodule.

[0103] The tracking error and sampling tracking error acquisition submodule (not shown) is configured as follows: for any follower module Obtain the state tracking error relative to the leader module. Stacked error vectors ; obtain and The following modules are respectively The most recent sampled state of the leader module, and the sampling tracking error. ,and .

[0104] The judgment submodule (not shown) is configured to: at the pulse moment The judgment is performed based on the event triggering conditions:

[0105] in For preset trigger parameters (in this preferred embodiment, the parameters are taken as follows): , If the conditions are not met, then in Triggering a new information transmission: , .

[0106] A preferred embodiment of the input saturation execution module 209 is detailed below.

[0107] In this preferred embodiment, the input saturation execution module 209 includes a distributed pulse control signal acquisition submodule (not shown), an input saturation constraint generation submodule (not shown), and an output submodule (not shown).

[0108] The distributed pulse control signal acquisition submodule is configured to acquire distributed pulse control signals from the pulse controller module 208. :

[0109] in , .

[0110] The input saturation constraint generation submodule is configured to perform symmetrical input saturation constraint processing, with pulse-controlled input. for:

[0111] in For the Dirac impulse function, It is a symmetric saturation function, and in this preferred embodiment, the upper limit of saturation is taken as... The output submodule is configured to input the saturated-constrained pulse control. Output to the first follower module 202.

[0112] In this second embodiment, mean square bounded consistency is preferably further achieved.

[0113] Preferably, in this embodiment, the control gain and event triggering parameters that satisfy the sufficient condition of mean-square bounded consistency can be further determined based on the system delay of the multi-agent system 200, the probability of follower-follower communication channel attack, the probability of leader-follower communication channel attack, the input saturation limit, and the event triggering parameters; the distributed pulse control signal is generated based on the control gain and event triggering parameters so that the multi-agent system can achieve leader-follower mean-square bounded consistency under dual-channel spoofing attack and input saturation constraint.

[0114] In this preferred embodiment, based on Lyapunov stability theory and time-delay correlation estimation, the mean-square bounded consistency condition of the leader-follower relationship in the multi-agent system 200 is satisfied. A Lyapunov-Krasovskii functional is constructed. ,in , , Let be the positive definite matrix to be solved. Through Lyapunov analysis under mathematical expectation and solving linear matrix inequalities, the closed-loop system is verified in terms of attack probability. , Under the baseline scenario, the mean square bounded consistency condition is satisfied, and the root mean square tracking error converges to... This meets the accuracy requirements for drone formation reconnaissance.

[0115] Through the collaborative work of the aforementioned modules, the UAV formation multi-agent system 200 in this embodiment distinguishes between follower-follower and leader-follower dual-channel deception attacks. It employs Bernoulli random variables to describe the random occurrence characteristics of the attack, more closely mimicking the stable collaborative control of a multi-agent system in real-world adversarial scenarios. Furthermore, it deeply integrates a distributed event triggering mechanism with pulse control, triggering sampling updates only when the tracking error exceeds a preset threshold. This reduces communication burden while maintaining a smaller tracking error, achieving stable formation reconnaissance control and verifying the engineering feasibility of this invention in UAV formation applications.

[0116] In this second embodiment, the second follower module 203 can also perform similar processing as the first follower module 202, and output control input is sent to the second follower module 203 to control it. Therefore, the similar technical processing scheme in the second follower module 203 will not be described again.

[0117] Example 3 This embodiment three uses the event-triggered pulses of six two-dimensional UAVs under a dual-channel deception attack to reveal a method for controlling a multi-agent system.

[0118] The drone system settings in this embodiment are as follows: Taking a cooperative flight system consisting of six two-dimensional planar motion drones as an example, one drone acts as the leader, and the other five drones act as followers. The leader drone is designated UAV0, and the five follower drones are designated UAV1. UAV2 UAV3 UAV4 UAV5

[0119] Each UAV moves in a two-dimensional plane, and its state vector is defined as:

[0120] in, and Let x and y represent the horizontal and vertical coordinates of the i-th UAV in the two-dimensional plane, respectively. The leader is in a certain state. The follower state is .

[0121] The system objective is: to counter dual-channel deception attacks. Under the constraints of communication time delay and actuator input saturation, the two-dimensional positions of the five follower drones are gradually made to track the position of the leader drone, i.e.:

[0122] In other words, the follower drones are not required to be perfectly aligned with the leader's position instantaneously, but rather, under the conditions of cyberattacks and physical constraints, they must ultimately remain within an allowable margin of error near the leader.

[0123] The communication topology settings in this embodiment are as follows: The five followers use a ring communication structure. Specifically, UAV1 and UAV2 UAV5 communication; UAV2 and UAV1 UAV3 communication; UAV3 and UAV2 UAV4 communication; UAV4 and UAV3 UAV5 communication; UAV5 and UAV4 UAV1 communication

[0124] The adjacency matrix between followers is taken as:

[0125] The corresponding Laplacian matrix is:

[0126] The leader UAV0 only sends messages directly to UAV1 and UAV2, UAV3... UAV4 UAV5 does not directly receive leader information, but indirectly obtains the leader's movement trends through localized communication among followers. Therefore, the leader information access matrix is ​​taken as follows:

[0127] Right now:

[0128] The two-dimensional UAV motion model in this embodiment is as follows: The two-dimensional motion model of the leader UAV0 is as follows:

[0129] The two-dimensional motion model of the follower UAVi is as follows:

[0130] in, For communication and system response time delay; This represents the nonlinear motion term caused by the current state of the drone; This indicates the effect of time delay on the drone's motion; Control input for the follower UAVi

[0131] In this embodiment, the two-dimensional nonlinear function is taken as:

[0132]

[0133] Time delay:

[0134] This means that the drone controller is influenced by the state information from 0.25 seconds ago when calculating the current control input, which more closely reflects the communication latency in a real drone swarm. The coexistence of sensing delay and processing delay

[0135] The initial two-dimensional coordinates and leader task in this embodiment are as follows: Suppose the two-dimensional coordinates of the six drones at the start of the mission are as follows, in meters:

[0136] The leader UAV0 performs a two-dimensional cruise mission, for example, moving along the following reference directions:

[0137] That is, the leader moves in the northeast direction in a two-dimensional plane. The follower drone does not know the complete trajectory in advance, but obtains the status information of the leader or neighboring drones through local communication and tracks them according to the event-triggered pulse control protocol.

[0138] The specific data example of the dual-channel spoofing attack in this embodiment is as follows: This invention considers two types of deception attacks. The first type is follower-follower channel spoofing attacks, where the attacker tampers with the data received by a follower from its neighboring followers. For example, when UAV1 receives coordinate information from UAV5, an attacker could inject false data into the communication link, causing UAV1 to mistakenly believe that UAV5's position has shifted.

[0139] The second type is the leader-follower channel spoofing attack, in which the attacker tampers with the status information sent by the leader UAV0 to UAV1 or UAV2, causing the followers to receive incorrect leader coordinates.

[0140] At a certain candidate pulse moment Assume the actual two-dimensional coordinates of each UAV are as follows:

[0141] The following deception attack occurs at this time:

[0142] in, This indicates that the follower-follower communication link was subjected to a spoofing attack at that moment. This indicates that no attack has occurred; This indicates that the leader-follower communication link has been compromised by a deception attack.

[0143] For example, UAV1 should have received the coordinates of UAV5:

[0144] But due to UAV5 When the UAV1 channel is attacked, the equivalent information received by UAV1 becomes:

[0145] Meanwhile, UAV1 should have received the coordinates of the leader UAV0:

[0146] However, after the leader-follower channel is attacked, the equivalent coordinates of the leader received by UAV1 are:

[0147] This demonstrates that the deception attack did not sever the communication link, but rather tampered with the transmitted data while the link remained connected, causing the follower drone to calculate control inputs based on incorrect information.

[0148] The workflow of this embodiment is disclosed as follows: Leader UAV0 processing flow The primary role of the leader UAV0 is to execute task trajectories and provide reference information to some followers. The processing procedure is as follows:

[0149] First, UAV0 generates a two-dimensional reference trajectory based on the mission plan, for example, from... Cruise in the northeast direction Subsequently, UAV0 obtains its current two-dimensional state through its own positioning function:

[0150] At the candidate pulse time UAV0 will display the current or most recent sampled state. Send to directly connected followers UAV1 and UAV2 because Therefore, only UAV1 and UAV2 can directly receive leader information.

[0151] If the leader-follower communication link is not compromised by a spoofing attack, then UAV1 and UAV2 will receive the following information:

[0152] If the leader-follower communication link is compromised by a spoofing attack, the follower will receive the following information:

[0153] in, Fake data injected into the leader-follower channel

[0154] It should be noted that in this embodiment, the leader UAV0 itself does not perform tracking control, nor does it need to correct its own trajectory based on the status of other UAVs. Its main processing steps include: status acquisition Trajectory Execution Status broadcast and communication interface output

[0155] Follower UAVi's processing flow For any follower UAVi, the processing includes state acquisition. Neighbor information reception Construction of relative error under attack Event trigger judgment Pulse control calculation Seven steps of input saturation processing and actuator operation

[0156] Step 1: Collect its own two-dimensional state UAVi obtains its current status through location services:

[0157] Simultaneously save the sampled state at the most recent trigger time:

[0158] Step 2: Receive information from neighbors and leaders UAVi receives the state information of its neighbor, follower UAVj. If link If not attacked, then receive If the link is attacked, the following will be received:

[0159] If UAV is directly connected to the leader, that is It also receives leader information. If the leader-follower link is attacked, then the following will be received:

[0160] Step 3: Construct relative error information affected by the attack The follower UAV constructs relative error information affected by the attack based on neighbor and leader information:

[0161] The first term represents the relative information of the follower-follower channel, and the second term represents the relative information of the leader-follower channel.

[0162] Step 4: Execute event trigger judgment Define the current tracking error as:

[0163] Define the most recent sampling tracking error as:

[0164] At the candidate pulse time The follower UAVi checks whether the event triggering condition is met:

[0165] and:

[0166] in, and Preset trigger parameters In this embodiment, the following can be adopted:

[0167] If the above conditions are met, it means that the currently saved sampling information can still be used for control calculations, and the system will not perform new state transmissions, thereby saving communication resources.

[0168] If the above conditions are not met, it indicates that the current error change is already significant, and the original sampling information is insufficient to support effective control. In this case, a new sampling transmission is triggered.

[0169] Step 5: Calculate the pulse control input When a control update is required, UAVi calculates the pulse control quantity based on the attacked relative error information:

[0170] Where K is the control gain. In this embodiment, the following is taken:

[0171] The actual control input of the follower is in the form of pulses:

[0172] Step 6: Input saturation processing Considering the physical limitations of drone actuators, such as the maximum thrust of the motor. Since the maximum speed correction and maximum attitude adjustment are limited, symmetrical saturation processing is required before the control input is applied to the UAV actuators.

[0173] Let the maximum allowable amplitude of the two-dimensional control input be:

[0174] Then the following restrictions are imposed on each control component:

[0175] Step 7: Actuator action and update drone motion The saturated control input is converted into speed correction for the drone. Attitude or position correction commands are issued and applied to the UAV actuators. After the actuator is activated, the two-dimensional state of UAVi continues to evolve according to the following model:

[0176] The following is an example of a complete calculation of UAV1 in this embodiment.

[0177] by Taking UAV1 at a given time as an example, UAV1's neighbors are UAV2 and UAV5, and UAV1 can directly receive information from the leader UAV0.

[0178] UAV1's current coordinates are:

[0179] The actual coordinates of its neighbors and leaders are:

[0180] At that moment, UAV1 was subjected to a follower-follower channel spoofing attack when receiving information from UAV5:

[0181] Meanwhile, UAV1 is vulnerable to leader-follower channel spoofing attacks when receiving information from the leader UAV0:

[0182] Therefore, the attacked relative error information constructed by UAV1 is:

[0183] The controller calculates the unsaturated control input:

[0184] Because the input to the drone actuator is limited, symmetrical saturation processing is performed:

[0185] Therefore, at this pulse moment, the final two-dimensional correction input executed by UAV1 is:

[0186] This input causes UAV1 to make a bounded correction to the upper right in the two-dimensional plane, thus continuing to track the leader UAV0, while avoiding excessive control input that could exceed the actuator's capabilities due to a deception attack.

[0187] The following is an example of a complete calculation of UAV2 in this embodiment.

[0188] UAV2's neighbors are UAV1 and UAV3, and UAV2 can also directly receive information from its leader, UAV0. UAV2's current coordinates are:

[0189] exist At a certain moment, UAV2 was subjected to a spoofing attack when receiving information from UAV3:

[0190] However, UAV2 was not attacked when receiving leader information, that is:

[0191] Therefore, the attacked relative error information constructed by UAV2 is:

[0192] The unsaturated control input is:

[0193] After symmetrical saturation treatment:

[0194] Therefore, the control input executed by UAV2 at that moment is:

[0195] This input indicates that UAV2 primarily corrects upwards along the longitudinal direction, while making a smaller correction laterally.

[0196] In summary, in this embodiment, six two-dimensional drones constitute a leader-follower multi-agent system. The leader UAV0 is responsible for generating and executing the two-dimensional cruise trajectory and sending its own status to UAV1 and UAV2. Followers UAV1 to UAV5 each act according to their own status Relative error information is constructed from neighbor states and the available leader state.

[0197] During communication, attackers may inject false data into the follower-follower channel. It is also possible to inject false data into the leader-follower channel. After acquiring relative error information affected by the attack, the follower drone does not perform control updates at every sampling moment. Instead, it first determines whether the current sampling information is still valid based on event triggering conditions. If the sampled information is still valid, the previous control-related information is kept unchanged to reduce communication and computational overhead; if the event triggering condition is not met, the sampling state is updated and a new pulse control input is calculated.

[0198] Before the control input is applied to the UAV actuator, it needs to be processed by a symmetric saturation function to ensure that the two-dimensional correction does not exceed the allowable range of the UAV actuator. Ultimately, the saturated pulse control input acts on the dynamics of the follower drone, enabling it to withstand dual-channel deception attacks. Even under time delay and input saturation constraints, it can still gradually approach the leader drone, achieving leader-follower mean-square bounded consistency, enabling multi-agent systems to maintain stable collaborative control, and deeply integrating distributed event triggering mechanism with pulse control, triggering sampling update only when the tracking error exceeds a preset threshold, thus reducing communication burden while maintaining a smaller tracking error.

[0199] Example 4 In this embodiment, the pulse control of the present invention is applied to a leader-follower multi-agent system consisting of a leader and five followers (follower 1, follower 2, follower 3, follower 4, and follower 5) under a dual-channel attack. The following numerical simulations demonstrate the authenticity of the beneficial effects of the present invention. A communication channel exists between the leader and followers 1 and 2. The nonlinear function in the multi-agent system is taken as:

[0200] Time Delay = 0.25 s. The event trigger parameter is set to... = 0.10、 = 0.85, θ1 = 0.10, θ2 = 0.28; the pulse control gain and saturation limit are set to 0.45 and 0.18, respectively. The deception attack probabilities of the follower-follower channel and the leader-follower channel are set to 0.12 and 0.10, respectively. The simulation step size is 0.005s, and the total simulation time is 25s.

[0201] Figure 3a This is a schematic diagram of the first state component of the state trajectory of the leader and follower under event-triggered pulse control in Embodiment 4 of the present invention. Figure 3b This is a schematic diagram of the second state component of the state trajectories of the leader and follower under event-triggered pulse control in Embodiment 4 of the present invention. All trajectories are drawn on a unified simulation mesh, therefore the left and right limits at the same pulse moment are not additionally marked in the figure. It can be seen that although both communication channels are injected with deceptive information, the follower state can still gradually approach the leader state and eventually remain within a small bounded neighborhood. Figure 3a , Figure 3bThe table shows the state trajectories of the leader, follower 1, follower 2, follower 3, follower 4, and follower 5, respectively.

[0202] Figure 4 This diagram illustrates the follower tracking error norm under a deception attack in Embodiment 4 of the present invention. The error decays rapidly in the initial stage and then remains bounded, its trend consistent with the mean-square boundedness principle. The dashed line in the diagram represents the theoretical boundedness calculated based on the selected theorems. Figure 4 middle, Follower 1 state error; Follower 2 state error; Follower 3-state error; Follower 4-state error; Follower 5 state error; Black dashed line: Theoretical boundary, with coordinate axis labels: Vertical axis : No. Term error The 2-norm (the magnitude of synchronization error among nodes in a multi-agent system) Horizontal axis: time (unit: seconds) This figure shows the convergence curve of the synchronization error of 5 followers in a multi-agent system. The norm value decays over time, indicating that the agents gradually achieve synchronization.

[0203] Figure 5a This is a schematic diagram of the global tracking error norm comparison in Embodiment 4 of the present invention; Figure 5b This is a schematic diagram showing the comparison of tracking error norms within a locally magnified range of 5 ≤ t ≤ 25 s in Embodiment 4 of the present invention; Figure 5a and Figure 5b The global tracking error norm under different control schemes was compared. 2. Among them, Figure 5a The overall convergence process is presented. It can be observed that all control schemes can compress the tracking error to a bounded region; the steady-state error is minimized under attack-free conditions, which also indirectly demonstrates that deception attacks weaken cooperative tracking performance. Further comparison shows that, under the same attack environment, the event-triggered scheme proposed in this invention has a smaller tracking error compared to existing periodic pulse control benchmarks.

[0204] To more clearly illustrate the differences in the steady-state phase, Figure 5b shows a locally magnified result within the interval t ∈ [5, 25] s. It can be seen that the method of this invention maintains a relatively low tracking error level in the steady-state phase; the figure also shows the theoretical boundary as a reference for the actual error evolution. Figure 5a and Figure 5bThe diagram is divided into three parts: event-triggered control scheme + under attack conditions, event-triggered control scheme + ideal under-attack conditions, and existing periodic intermittent control scheme + under attack conditions; and a dashed line: the theoretical upper limit. The coordinate axes are labeled as follows: vertical axis. :error The L2 norm (control system error norm), horizontal axis: time (unit: seconds), where the L2 norm... The curve represents a mathematical index used by the control system to characterize the magnitude of the system error. The lower the curve, the smaller the system error and the better the convergence performance. The curve changes in the figure: the value decreases over time, which means that the system error gradually converges. The convergence speed of the traditional yellow scheme with attack is significantly worse than the control method proposed in this invention.

[0205] The simulation results in this embodiment further compare the communication / update burden of the method of this invention with that of existing periodic pulse control methods. For the event-triggered scheme of this invention, there are 133 candidate pulse moments, while actual sampling updates occur only 54 times; in contrast, the periodic pulse control method needs to update the sampling information at all 133 candidate moments. Therefore, while maintaining bounded tracking performance, the scheme of this invention reduces the number of sampling updates by approximately 59.4%, demonstrating a better communication saving effect.

[0206] Example 5 Figure 6 This is a schematic diagram of the structure of the electronic device according to Embodiment 5 of the present invention. Figure 6 The preferred embodiment of the electronic device of the present invention shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of this application.

[0207] like Figure 6 As shown, the electronic device is presented in the form of a general-purpose computing device. The components of the electronic device may include, but are not limited to: one or more processors 610, memory 630, and communication bus 640 connecting different system components (including memory 630 and processing unit 610).

[0208] Communication bus 640 represents one or more of several bus architectures, including a memory bus or memory controller, a peripheral bus, a graphics acceleration port, a processor, or a local bus using any of the various bus architectures. For example, these architectures include, but are not limited to, Industry Standard Architecture (ISA) buses, Micro Channel Architecture (MAC) buses, Enhanced ISA buses, Video Electronics Standards Association (VESA) local buses, and Peripheral Component Interconnect (PCI) buses.

[0209] Electronic devices typically include a variety of computer-readable media. These media can be any available media that can be accessed by the electronic device, including volatile and non-volatile media, and removable and non-removable media.

[0210] Memory 630 may include computer system readable media in the form of volatile memory, such as random access memory (RAM) and / or cache memory. The electronic device may further include other removable / non-removable, volatile / non-volatile computer system storage media. Memory 630 may include at least one program product having a set (e.g., at least one) of program modules configured to perform the functions of the embodiments of this application.

[0211] A program / utility having a set (at least one) of program modules can be stored in memory 630. Such program modules include—but are not limited to—an operating system, one or more application programs, other program modules, and program data. Each or some combination of these examples may include an implementation of a network environment. The program modules typically perform the functions and / or methods described in the embodiments of this application.

[0212] Processor 610 executes various functional applications and data processing by running programs stored in memory 630, such as implementing embodiments of this application. Figure 1 The control method provided in the illustrated embodiment.

[0213] This application provides a non-transitory computer-readable storage medium that stores computer instructions, which cause the computer to execute embodiments of this application. Figure 1 The method provided in the illustrated embodiment.

[0214] The aforementioned computer-readable storage medium may be any combination of one or more computer-readable media. A computer-readable medium may be a computer-readable signal medium or a computer-readable storage medium. A computer-readable storage medium may be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of computer-readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), or flash memory, optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this document, a computer-readable storage medium may be any tangible medium that contains or stores a program that may be used by or in connection with an instruction execution system, apparatus, or device.

[0215] Computer-readable signal media may include data signals propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals may take various forms, including—but not limited to—electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media may also be any computer-readable medium other than computer-readable storage media, which can send, propagate, or transmit programs for use by or in connection with an instruction execution system, apparatus, or device.

[0216] Program code contained on a computer-readable medium may be transmitted using any suitable medium, including—but not limited to—wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0217] Computer program code for performing the operations of the embodiments of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a Local Area Network (LAN) or a Wide Area Network (WAN), or it can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0218] The foregoing has described specific embodiments of the present invention. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps described in the claims may be performed in a different order than that shown in the embodiments and may still achieve the desired results. Furthermore, the processes depicted in the drawings do not necessarily require the specific or sequential order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0219] In the description of the embodiments of the present invention, the terms "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In the embodiments of the present invention, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in a suitable manner in any one or more embodiments or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in the embodiments of the present invention, as well as the features of the different embodiments or examples.

[0220] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of embodiments of the present invention, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0221] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing custom logic functions or processes, and the scope of preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of the invention pertain.

[0222] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0223] In the embodiments provided in this invention, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the system embodiments described above are merely illustrative. For instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, modules, or units, and may be electrical, mechanical, or other forms.

[0224] Furthermore, in the various embodiments of the present invention, the functional units can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0225] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the implementation methods of the present invention, and should be understood that the scope of protection of the present invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of the present invention.

Claims

1. A pulse control method for a multi-agent system under dual-channel attack, characterized in that, include: Construct a dual-channel attack handling model for follower-follower and leader-follower systems in a multi-agent system; Bernoulli random variables are used to describe the random occurrence of spoofing in the dual-channel attack handling model. Based on the distributed event triggering mechanism in the multi-agent system, the tracking error and sampling tracking error of the data in the multi-agent system are updated with preset conditions at the first pulse moment to generate a distributed pulse control signal. The distributed pulse control signal is subjected to symmetrical input saturation constraint processing to obtain the control input, which is then applied to the follower.

2. The method according to claim 1, characterized in that, The leader and followers in the multi-agent system are configured in the following dynamic model: in, The leader's state at time t. for The first derivative, , It is an m-dimensional vector space; —The state of follower i at time t. for The first derivative, , Let i be an m-dimensional vector space; i is the follower label; —A given nonlinear vector function; —A given nonlinear vector function; constant This refers to system time delay; The control input for the followers; the set of followers is denoted as . .

3. The method according to claim 1, characterized in that, The dual-channel attack handling model for the follower-follower and leader-follower systems in the multi-agent system includes: In the multi-agent system, interactive information is received from the leader-follower communication channel and the follower-follower communication channel; The influence of injecting false data into the interactive information is modeled as a two-channel deception attack model. The influence of injecting false data in the follower-follower communication channel is used to characterize the situation where the relative information received by the follower from neighboring followers is contaminated, and the influence of injecting false data in the leader-follower communication channel is used to characterize the situation where the leader information received by the follower is contaminated.

4. The method according to claim 1, characterized in that, The use of Bernoulli random variables to describe the random occurrence of spoofing in the dual-channel attack processing model includes: For follower-follower communication channels Indicates injection into the follower False data in the received relative neighbor information; Based on Bernoulli random variables Describe whether an attack has occurred in the follower-follower communication channel; when When, it indicates from the follower To followers Communication information is affected by false data pollute; when When the time is specified, it indicates that the channel is not under attack at the current moment; The above The probability distribution is as follows: in, For probability labeling, This indicates the probability of an attack occurring in a follower-follower channel. For leader-follower communication channels Indicates injection into the follower The received leader information contained false data, based on Bernoulli random variables. Describe whether an attack occurred in the leader-follower communication channel; when , indicating followers The obtained leader information was Pollution; when This indicates that the leader's information transmission has not been attacked; wherein the... The probability distribution is as follows: in The probability of an attack occurring in the leader-follower channel.

5. The method according to claim 1, characterized in that, Based on the distributed event triggering mechanism, during the process of updating the information triggered by pre-condition judgment of the tracking error and sampling tracking error of the data in the multi-agent system at the first pulse moment: For any follower Its state tracking error relative to the leader is: Its stacking error vector is: ,in For followers The most recent sampling status, The sampling tracking error for the leader's most recent sampled state is: ,and The set of followers is denoted as , This is a transpose operation; At the pulse moment The event triggering condition for the distributed event triggering mechanism is as follows: in For vector norm, For preset trigger parameters, if the conditions are not met, the current sampled information will not support subsequent control updates, and... Triggering new information transmission, For pulse timing: .

6. The method according to claim 1, characterized in that, In the step of performing symmetrical input saturation constraint processing on the distributed pulse control signal to obtain the control input: When a new information transmission is triggered by an event based on the aforementioned distributed event triggering mechanism, the distributed pulse control signal u under the distributed control protocol in the multi-agent system... i (t) is: in; For the members in the weighted adjacency matrix of the followers, Connect the members in the leader connection matrix; Pulse control input after symmetrical input saturation constraint for: in For the Dirac impulse function, Let be a symmetric saturating function, where the set of followers is denoted as . , This refers to the pulse moment.

7. The method according to claim 1, characterized in that, Further includes: Based on the system time delay, follower-follower communication channel attack probability, leader-follower communication channel attack probability, input saturation limit, and event triggering parameters of the multi-agent system, determine the control gain and event triggering parameters that satisfy the sufficient condition of mean-square bounded consistency. The distributed pulse control signal is generated based on the control gain and event triggering parameters to enable the multi-agent system to achieve leader-follower mean-square bounded consistency under dual-channel spoofing attacks and input saturation constraints.

8. A multi-agent system, characterized in that, include: The system includes a leader module, at least two follower modules, wherein the leader module and the follower modules construct follower-follower communication channels and leader-follower communication channels, a dual-channel attack processing module, an event triggering condition evaluation module, a pulse controller module, and an input saturation execution module. The dual-channel attack processing module is configured to describe the random occurrence of attacks using Bernoulli random variables for the fake data injected in the follower-follower channel and the fake data injected in the leader-follower channel, respectively. The event triggering condition evaluation module is configured to, based on a distributed event triggering mechanism, perform a preset condition judgment and trigger information update on the tracking error and sampling tracking error of the data described in the dual-channel attack processing module at the first pulse moment; The pulse controller module is configured to generate a distributed pulse control signal based on the trigger information update instruction. The input saturation execution module is configured to perform symmetrical input saturation constraint processing on the pulse control signal and output control input to the follower module.

9. An electronic device, characterized in that, include: At least one processor; And at least one memory communicatively connected to the processor, wherein: the memory stores program instructions executable by the processor, and the processor invokes the program instructions to execute the control method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that cause the computer to perform the control method as described in any one of claims 1 to 7.

Images