Security adaptive event-triggered control method and system for multi-agent system

Abstract

The application provides a security adaptive event-triggered control method and system for a multi-agent system, and belongs to the technical field of multi-agent system cooperative control and information security. The application fuses a reference signal to be transmitted and a mask signal to obtain an encrypted signal and broadcasts the encrypted signal, and restores the reference signal; error variables are constructed based on the restored reference signal, an adaptive control law is designed to generate a control instruction; an optimization model is constructed to minimize the number of communication triggers and meet the tracking error and control input constraints, an optimization algorithm is used to solve the optimal threshold parameter of the event-triggered mechanism; and the event-triggered condition is judged. The application can realize high-security communication without explicit key distribution, effectively resist phase space reconstruction attacks, and adaptively adjust the event-triggered threshold through Bayesian optimization, thereby significantly reducing the communication load while ensuring tracking accuracy.

Description

Technical Field

[0001] This invention relates to the field of collaborative control and information security technology for multi-agent systems, and particularly to a secure adaptive event-triggered control method and system for multi-agent systems. Background Technology

[0002] Multi-Agent Systems (MASs) achieve global goals through distributed collaboration, demonstrating significant application potential in scenarios such as drone swarms, autonomous driving formations, and smart grids. Their core relies on continuous information exchange between agents to achieve consistency or trajectory tracking tasks. However, in open network environments, plaintext communication is highly susceptible to eavesdropping or reconstructing sensitive data such as state information and control commands, thereby exposing system intentions and even triggering malicious attacks. Simultaneously, continuous communication incurs high bandwidth and energy consumption, making it difficult to meet the deployment requirements of resource-constrained platforms. Therefore, how to ensure collaborative performance while simultaneously ensuring communication security and resource efficiency has become a key challenge for MASs to achieve practical engineering applications.

[0003] 1. In the paper "Event-triggered privacy-preserving bipartite consensus for multi-agent systems based on encryption" published in *Neurocomputing* (Neurocomputing 503, 162–172, 2022), Zewei Yang et al. proposed a privacy-preserving consensus protocol based on Paillier homomorphic encryption. This method allows agents to aggregate states in the ciphertext domain, avoiding direct disclosure of the original state, and reduces communication frequency by incorporating an event-triggered mechanism. However, this scheme only provides semantic security and cannot resist privacy inference attacks based on the aggregation results. Furthermore, homomorphic operations have high computational overhead, making it difficult to apply to highly dynamic systems.

[0004] 2. In the paper "Privacy-preserving secure consensus of multiagent systems: An event-responsive chaotic encryption mechanism" (J. Franklin Inst. 362(18), 108170,2025) published in the Journal of the Franklin Institute by Bing Hu et al., an event-responsive chaotic encryption method (ERCEM) was proposed. This method uses a chaotic sequence to dynamically mask the transmitted signal at each event trigger and updates the initial chaotic value to achieve "one-time pad", which significantly improves the anti-eavesdropping ability. However, this scheme relies on the precise pre-sharing of the initial conditions between the transmitter and receiver to maintain chaotic synchronization. Once the key is leaked or there is a slight deviation, decryption will fail. At the same time, a single chaotic system is vulnerable to phase space reconstruction attacks, and its security still has hidden dangers.

[0005] 3. In the paper "Prescribed performance distributed event-triggered control" (Automatica 182, 112551, 2025) published in *Automatica*, Tao Xu et al. designed a distributed event-triggered control scheme with specified performance. This method simultaneously constrains the transient and steady-state behavior of tracking errors through a performance function and introduces edge adaptive gain to eliminate dependence on global topology information, effectively reducing the number of communications while ensuring high precision consistency. However, its event triggering threshold and performance boundary are determined by preset rules, lacking explicit modeling and systematic optimization of the trade-off between "communication overhead" and "control performance," making it difficult to flexibly adjust the strategy according to specific task requirements.

[0006] 1. Although the existing technology 1 (Yang et al., 2022) combines encryption and event triggering, the homomorphic encryption mechanism it uses has limited security, is susceptible to advanced inference attacks, and has high computational complexity, sacrificing system real-time performance and making it difficult to deploy efficiently on resource-constrained multi-agent platforms.

[0007] 2. Although the chaotic encryption proposed in existing technology 2 (Hu et al., 2025) has the characteristic of "one-time pad", its security is highly dependent on the fragile initial condition synchronization mechanism and lacks robustness to key leakage or channel disturbance. At the same time, the structure of a single chaotic source is simple and easily cracked by modern cryptanalysis methods, which cannot meet the requirements of high security level.

[0008] 3. Existing technology 3 (Xu et al., 2025) achieves high-performance tracking and low communication load in event-triggered control, but its parameter design is static or experience-driven, and it fails to incorporate communication frequency as an optimizable target into a unified framework. It lacks intelligent parameter tuning capabilities, which limits its adaptability and deployment flexibility in diverse task scenarios. Summary of the Invention

[0009] The present invention aims to at least partially solve one of the technical problems in the related art.

[0010] To address the limitations of existing technologies that can only handle communication security or efficiency issues individually and lack support for synergistic optimization of security and efficiency, this invention aims to provide a secure adaptive event-triggered control method for multi-agent systems. It simultaneously solves multiple challenges that existing technologies cannot simultaneously address, such as high-security communication (e.g., resisting key leakage and phase space reconstruction attacks), adaptive fuzzy control (coping with unknown nonlinearities and disturbances), and intelligent scheduling of communication resources. Furthermore, it eliminates the need to redesign encryption mechanisms or manually adjust event trigger thresholds for different task scenarios and performance requirements, enabling automatic trade-off optimization between communication overhead and control performance. This method is applicable to multi-agent collaborative scenarios of varying scales and dynamic characteristics, ranging from drone swarms to smart grids.

[0011] Another objective of this invention is to propose a safe adaptive event-triggered control system for multi-agent systems.

[0012] To achieve the above objectives, a first aspect of the present invention proposes a safety adaptive event-triggered control method for multi-agent systems, comprising: The sending agent encrypts the reference signal using a locally generated dynamic mask signal, obtains the encrypted signal, and broadcasts it to the network; the receiving agent receives the encrypted signal and restores the reference signal using a dynamic mechanism synchronized with the sending agent. Error variables are constructed based on the restored reference signal and the current system state. An adaptive approximator is used to estimate the unknown nonlinear dynamic characteristics of the system online, and adaptive control commands are generated by combining the backstepping design idea. An optimization model is constructed with the goal of minimizing the number of communication triggers and the conditions of satisfying tracking performance and input constraints. The optimal threshold parameters for event triggering are obtained by solving the problem through an iterative search strategy. The system monitors in real time whether the error variable exceeds the optimal threshold parameter; if it does, the current adaptive control command is immediately applied to the controlled object and the dynamic mask signal is updated; if it does not exceed the threshold, the control command from the previous moment remains unchanged.

[0013] In one embodiment of the present invention, the encryption of the reference signal using a locally generated dynamic mask signal includes: A dynamic encryption model containing multiple chaotic subsystems is constructed at the sending end, and a specific state component in the model is selected as the dynamic mask signal. The reference signal and the dynamic mask signal are superimposed and fused to generate the encrypted signal.

[0014] In one embodiment of the present invention, the step of reconstructing the reference signal using a dynamic mechanism synchronized with the transmitting agent includes: A dynamic encryption model with the same structure as the sending end is synchronously run at the receiving end; Based on the received encrypted signal, the local dynamic encryption model is integrated to reconstruct a restored mask signal that is consistent with the dynamic mask signal. Subtracting the restoration mask signal from the encrypted signal yields a lossless restoration reference signal.

[0015] In one embodiment of the present invention, the step of generating adaptive control instructions by combining backstepping design ideas includes: Virtual error variables are introduced for coordinate transformation, where the virtual error at each step is obtained by subtracting the virtual controller designed in the previous step from the current state variable; Construct a stability function that includes the squared term of the error variable and the parameter estimation error term; By using a fuzzy logic system to approximate an unknown nonlinear function, and designing virtual control laws and parameter adaptive laws layer by layer, the actual control input is finally synthesized.

[0016] In one embodiment of the present invention, the approximation of an unknown nonlinear function using a fuzzy logic system includes: The unknown nonlinear function is represented as the product of the ideal parameter vector and the basis function vector plus the approximation error; An adaptive law for design parameters is used to update the parameter estimates of the fuzzy logic system online, thereby eliminating the influence of unknown nonlinear dynamics.

[0017] In one embodiment of the present invention, the step of obtaining the optimal threshold parameter for event triggering through an iterative search strategy includes: The event trigger condition is defined as the absolute value of the tracking error exceeding the threshold to be optimized; Construct a nonlinear programming model with constraints including an upper limit for the squared integral error, a limit for the maximum instantaneous error, a limit for the amplitude of the control input, and a lower limit for the threshold. A Bayesian optimization algorithm is used to model the objective function using a Gaussian process, and the optimal threshold is selected iteratively by acquiring a lower confidence bound function.

[0018] In one embodiment of the present invention, the use of the Bayesian optimization algorithm includes: The Gaussian process surrogate model is used to probabilistically model the objective function and constraints of the nonlinear programming model, and to predict the distribution of communication trigger counts under different threshold parameters. Based on the strategy of balancing the exploration of unknown regions and the development of known superior regions using the lower confidence bound acquisition function, the next threshold parameter to be evaluated is iteratively selected for system simulation until the optimal threshold that satisfies all constraints and has the fewest triggering times is found.

[0019] In one embodiment of the present invention, keeping the control command from the previous moment unchanged includes: Between two adjacent event triggering times, a zero-order hold operation is performed to keep the control quantity output by the actuator constant at the adaptive control command calculated at the most recent triggering time; When the error variable is detected to exceed the optimal threshold parameter again, the complete closed-loop update process from generating the dynamic mask signal to generating the adaptive control command is re-executed.

[0020] This invention also proposes a safety adaptive event-triggered control system for multi-agent systems, comprising: The signal restoration module is used by the transmitting agent to encrypt the reference signal using a locally generated dynamic mask signal, obtain an encrypted signal, and broadcast it to the network; the receiving agent receives the encrypted signal and restores the reference signal using a dynamic mechanism synchronized with the transmitting agent. The control command generation module is used to construct error variables based on the restored reference signal and the current system state, use an adaptive approximator to estimate the unknown nonlinear dynamic characteristics in the system online, and generate adaptive control commands by combining the backstepping design idea. The parameter optimization module is used to construct an optimization model with the goal of minimizing the number of communication triggers and the conditions of satisfying tracking performance and input constraints, and to obtain the optimal threshold parameters for event triggering through an iterative search strategy. The control trigger module is used to monitor in real time whether the error variable exceeds the optimal threshold parameter; if it does, the current adaptive control command is immediately applied to the controlled object and the dynamic mask signal is updated; if it does not exceed, the control command of the previous moment remains unchanged.

[0021] The security adaptive event-triggered control system for multi-agent systems in this invention can resist advanced attacks such as phase space reconstruction without explicit key distribution, ensuring communication security in open environments; and through Bayesian optimization, it automatically balances communication overhead and control performance, significantly reducing network load while maintaining high-precision tracking.

[0022] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0023] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 This is a flowchart of a safety adaptive event triggering control method for multi-agent systems according to an embodiment of the present invention; Figure 2 This is a detailed logic flowchart of a safety adaptive event triggering control method for multi-agent systems according to an embodiment of the present invention; Figure 3 This is a performance comparison chart based on an embodiment of the present invention; Figure 4 This is a structural diagram of a safety adaptive event-triggered control system for multi-agent systems according to an embodiment of the present invention. Detailed Implementation

[0024] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0025] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0026] The following description, with reference to the accompanying drawings, describes a safe adaptive event-triggered control method and system for multi-agent systems according to an embodiment of the present invention.

[0027] Figure 1 This is a flowchart of a safety adaptive event triggering control method for multi-agent systems according to an embodiment of the present invention.

[0028] like Figure 1 As shown, a safety adaptive event-triggered control method for multi-agent systems includes the following steps: S101, the transmitting agent encrypts the reference signal using a locally generated dynamic mask signal, obtains an encrypted signal, and broadcasts it to the network; the receiving agent receives the encrypted signal and restores the reference signal using a dynamic mechanism synchronized with the transmitting agent. S102 constructs error variables based on the restored reference signal and the current system state, uses an adaptive approximator to estimate the unknown nonlinear dynamic characteristics in the system online, and generates adaptive control commands by combining the backstepping design idea. S103, construct an optimization model with the goal of minimizing the number of communication triggers and the conditions of satisfying tracking performance and input constraints, and solve for the optimal threshold parameters for event triggering through an iterative search strategy; S104, monitor in real time whether the error variable exceeds the optimal threshold parameter; if it does, immediately apply the current adaptive control command to the controlled object and update the dynamic mask signal; if it does not exceed, keep the control command from the previous moment unchanged.

[0029] Specifically, such as Figure 2 As shown, the safety adaptive event-triggered control method for multi-agent systems of the present invention may include the following steps: S1, encryption and transmission of security signals; S2, Design of an adaptive fuzzy controller; S3, Bayesian optimization-driven event triggering mechanism; S4, the generation and execution of control instructions; S5 ensures secure updates and closed-loop operation of system status.

[0030] Furthermore, step S1 specifically includes the following steps: The agent locally constructs a multi-chaotic encryption system with the following state equation:

[0031] In the formula, , , Constitutes the Lorenz subsystem, As a mask signal. The original signal to be transmitted (such as the leader reference signal) is used as a mask signal. The signal is superimposed on the mask signal to form an encrypted signal:

[0032] And broadcast to the network. The receiving agent performs local integration calculations. Accurately recover the mask, and from Subtract the mask from the middle to restore the lossless image. The entire process requires no additional key distribution.

[0033] Furthermore, step S2 specifically includes the following steps: S21. Introduce dummy error variables Perform coordinate transformation:

[0034] In the formula, For the first A virtual controller designed step by step.

[0035] S22. Construct Lyapunov functions:

[0036] In the formula, This refers to the parameter estimation error of the fuzzy system.

[0037] S23. Using fuzzy logic systems to approximate unknown nonlinear functions in a system. And by combining the backstepping method to design virtual control laws layer by layer. And adaptive law Ultimately, the actual control input is obtained. .

[0038] Furthermore, step S3 specifically includes the following steps: S31. Define the event triggering condition as follows:

[0039] In the formula, To track errors, The threshold to be optimized.

[0040] S32. Construct a nonlinear programming model: minimizing the time interval Number of events triggered within The objective is to define the upper limit of the integral squared error (ISE) and the maximum instantaneous error. , Control input amplitude limit and lower threshold The established nonlinear programming model is shown below:

[0041]

[0042] S33. Solve the model using a Bayesian optimization algorithm: Model the objective function using a Gaussian process (GP), and iteratively select the optimal threshold using a lower confidence bound (LCB) acquisition function. Until it converges.

[0043] Furthermore, step S4 specifically includes the following steps: The adaptive fuzzy control law designed in step S2 As an ideal control command, at the moment the event is triggered The actuator applies force to the controlled object, driving its state to converge toward the desired trajectory.

[0044] Furthermore, step S5 specifically includes the following steps: Before the next event is triggered, the control input remains at the value of the previous moment (zero-order hold). When the trigger condition is met, the agent executes S1–S4 again to complete a safe and efficient closed-loop update, thereby significantly reducing the communication load while ensuring high-precision tracking.

[0045] Furthermore, such as Figure 3 As shown, Figure 3 This is a performance comparison chart of the present invention (top left 1 is the original control effect; top right 2 is the optimized control effect; bottom left is the tracking error e(t) of the original control and the optimized control; bottom right is a comparison of the number of updates of the original control and the optimized control).

[0046] In summary, compared with the prior art, the safe and efficient multi-agent cooperative control method of the present invention has the following beneficial effects: 1. No explicit key distribution or manual threshold tuning required: This method does not rely on additional secure channels for key transmission, nor does it require manual adjustment of event triggering thresholds for different task scenarios. It achieves self-synchronous decryption through fuzzy multi-chaotic encryption (FMCE), establishes a nonlinear optimization model for the event triggering mechanism, and automatically solves for the optimal triggering parameters using Bayesian optimization. This allows for deployment in various multi-agent systems, significantly reducing the implementation complexity and operational costs of secure collaborative control.

[0047] 2. High security and strong resistance to attacks: The FMCE algorithm proposed in this invention deeply integrates the key with multiple chaotic state variables. , , and its derived masks In the dynamic evolution, even if key-related signals are intercepted or initial conditions have slight deviations, the security of the original information can be ensured. Compared with existing schemes that rely on single chaotic systems or static mapping rules, this method can effectively resist advanced attacks such as phase space reconstruction and key inference, significantly improving communication confidentiality and system robustness in open environments.

[0048] 3. Explicit Co-optimization of Communication Efficiency and Control Performance: Compared to event-triggered mechanisms that rely solely on static or empirical thresholds, this invention constructs a nonlinear programming model with the objective of minimizing update frequency and constraints on tracking error, instantaneous performance, and control input. This model is then solved using Bayesian optimization, achieving an explicit trade-off and automatic optimization between communication resources and control accuracy. Therefore, while ensuring high tracking accuracy, it significantly reduces network load, making it particularly suitable for bandwidth-constrained or energy-sensitive applications such as UAV swarms and micro-robots.

[0049] 4. Automated and Efficient End-to-End Architecture: From secure signal generation and adaptive control law calculation to event-triggered decision-making, the method of this invention is completed autonomously by the system without human intervention. By organically integrating FMCE secure communication, adaptive fuzzy control, and a Bayesian optimization-driven event-triggered mechanism, a closed-loop, efficient collaborative architecture is formed. This architecture not only ensures the confidential transmission of the leader's reference signal but also maintains excellent tracking performance, demonstrating good scalability and engineering applicability for large-scale, highly dynamic multi-agent systems. In summary, this invention significantly improves the security, communication efficiency, and collaborative accuracy of multi-agent systems in open environments.

[0050] In summary, this invention proposes a secure communication scheme that does not require explicit key transmission, by deeply integrating the encryption key and mask signal into multiple chaotic state variables, i.e., the Lorenz system. , , and its derived masks During the dynamic evolution process, this mechanism maintains key concealment during the numerical calculation phase. Even if key-related signals are intercepted or initial conditions are deviated, it ensures the security of original information (such as the leader reference signal), significantly improving resistance to eavesdropping and reconstruction attacks. This invention addresses the key threshold parameters in the event-triggered mechanism. Treating these variables as optimizable variables, a nonlinear programming model was constructed with the objective of minimizing the number of controller updates, while incorporating integral tracking error, maximum instantaneous error, and control input amplitude as hard constraints. This model, for the first time, explicitly models the trade-off between communication overhead and control performance, providing a systematic optimization framework for the design of event-triggered mechanisms. This invention combines a Gaussian process (GP) surrogate model with a lower confidence bound (LCB) acquisition function for efficient solution of the aforementioned nonlinear programming model. This architecture can automatically search for the optimal trigger threshold with minimal system simulation evaluations. It can dynamically adjust the communication frequency according to specific task requirements (such as allowable error range and actuator limitations) to significantly reduce network load while ensuring basic control performance.

[0051] To implement the method of the above embodiments, such as Figure 4 As shown, this invention proposes a safety adaptive event-triggered control 10 for multi-agent systems, comprising: The signal restoration module 100 is used for the transmitting end intelligent agent to encrypt the reference signal using a locally generated dynamic mask signal, obtain an encrypted signal, and broadcast it to the network; the receiving end intelligent agent receives the encrypted signal and restores the reference signal using a dynamic mechanism synchronized with the transmitting end intelligent agent. The control command generation module 200 is used to construct error variables based on the restored reference signal and the current system state, use an adaptive approximator to estimate the unknown nonlinear dynamic characteristics in the system online, and generate adaptive control commands by combining the backstepping design idea. The parameter optimization module 300 is used to construct an optimization model with the goal of minimizing the number of communication triggers and the conditions of satisfying tracking performance and input constraints, and to obtain the optimal threshold parameters for event triggering through an iterative search strategy. The control trigger module 400 is used to monitor in real time whether the error variable exceeds the optimal threshold parameter; if it exceeds, the current adaptive control command is immediately applied to the controlled object and the dynamic mask signal is updated; if it does not exceed, the control command of the previous moment remains unchanged.

[0052] The system of this invention can resist advanced attacks such as phase space reconstruction without explicit key distribution, ensuring communication security in open environments; and through Bayesian optimization, it automatically balances communication overhead and control performance, significantly reducing network load while maintaining high-precision tracking.

[0053] In the description of this specification, the references to terms such as "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 this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0054] 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 technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

Claims

1. A safety adaptive event-triggered control method for multi-agent systems, characterized in that, include: The transmitting agent uses a locally generated dynamic mask signal to encrypt the reference signal, obtains the encrypted signal, and broadcasts it to the network. The receiving agent receives the encrypted signal and uses a dynamic mechanism synchronized with the sending agent to reconstruct the reference signal; Error variables are constructed based on the restored reference signal and the current system state. An adaptive approximator is used to estimate the unknown nonlinear dynamic characteristics of the system online, and adaptive control commands are generated by combining the backstepping design idea. Specifically, the generation of adaptive control commands by combining the backstepping design idea includes: introducing virtual error variables for coordinate transformation, where the virtual error at each step is obtained by subtracting the virtual controller designed in the previous step from the current state variable; constructing a stability function containing the squared term of the error variable and the parameter estimation error term; approximating the unknown nonlinear function using a fuzzy logic system, and designing virtual control laws and parameter adaptive laws layer by layer, and finally synthesizing the actual control input. An optimization model is constructed with the objective of minimizing the number of communication triggers and the conditions of satisfying tracking performance and input constraints. The optimal threshold parameters for event triggering are obtained through an iterative search strategy. Specifically, a Bayesian optimization algorithm is used for iterative search, which includes: using a Gaussian process surrogate model to probabilistically model the objective function and constraints of the nonlinear programming model to predict the distribution of the number of communication triggers under different threshold parameters; and using a strategy of balancing the exploration of unknown regions and the development of known good regions based on the lower confidence bound acquisition function to iteratively select the next threshold parameter to be evaluated for system simulation until the optimal threshold that satisfies all constraints and minimizes the number of triggers is found. The system monitors in real time whether the error variable exceeds the optimal threshold parameter; if it does, the current adaptive control command is immediately applied to the controlled object and the dynamic mask signal is updated; if it does not exceed the threshold, the control command from the previous moment remains unchanged.

2. The method according to claim 1, characterized in that, The encryption process of the reference signal using a locally generated dynamic mask signal includes: A dynamic encryption model containing multiple chaotic subsystems is constructed at the sending end, and a specific state component in the model is selected as the dynamic mask signal. The reference signal and the dynamic mask signal are superimposed and fused to generate the encrypted signal.

3. The method according to claim 2, characterized in that, The process of reconstructing the reference signal using a dynamic mechanism synchronized with the transmitting agent includes: A dynamic encryption model with the same structure as the sender is run synchronously at the receiving end; Based on the received encrypted signal, the local dynamic encryption model is integrated to reconstruct a restored mask signal that is consistent with the dynamic mask signal. Subtracting the restoration mask signal from the encrypted signal yields a lossless restoration reference signal.

4. The method according to claim 1, characterized in that, The method of approximating an unknown nonlinear function using a fuzzy logic system includes: The unknown nonlinear function is represented as the product of the ideal parameter vector and the basis function vector plus the approximation error; An adaptive law for design parameters is used to update the parameter estimates of the fuzzy logic system online, thereby eliminating the influence of unknown nonlinear dynamics.

5. The method according to claim 1, characterized in that, The process of obtaining the optimal threshold parameters for event triggering through an iterative search strategy includes: The event trigger condition is defined as the absolute value of the tracking error exceeding the threshold to be optimized; Construct a nonlinear programming model with constraints including an upper limit for the squared integral error, a limit for the maximum instantaneous error, a limit for the amplitude of the control input, and a lower limit for the threshold. A Bayesian optimization algorithm is used to model the objective function using a Gaussian process, and the optimal threshold is selected iteratively by acquiring a lower confidence bound function.

6. The method according to claim 1, characterized in that, Maintaining the control command from the previous moment unchanged includes: Between two adjacent event triggering times, a zero-order hold operation is performed to keep the control quantity output by the actuator constant at the adaptive control command calculated at the most recent triggering time; When the error variable is detected to exceed the optimal threshold parameter again, the complete closed-loop update process from generating the dynamic mask signal to generating the adaptive control command is re-executed.

7. A safety adaptive event-triggered control system for multi-agent systems, characterized in that, include: The signal restoration module is used by the transmitting agent to encrypt the reference signal using a locally generated dynamic mask signal, obtain the encrypted signal, and broadcast it to the network. The receiving agent receives the encrypted signal and uses a dynamic mechanism synchronized with the sending agent to reconstruct the reference signal; The control command generation module is used to construct error variables based on the restored reference signal and the current system state, perform online estimation of unknown nonlinear dynamic characteristics in the system using an adaptive approximator, and generate adaptive control commands by combining the backstepping design concept. Specifically, the generation of adaptive control commands by combining the backstepping design concept includes: introducing virtual error variables for coordinate transformation, where the virtual error at each step is obtained by subtracting the virtual controller designed in the previous step from the current state variable; constructing a stability function containing the squared term of the error variable and the parameter estimation error term; approximating the unknown nonlinear function using a fuzzy logic system, and designing virtual control laws and parameter adaptive laws layer by layer, and finally synthesizing the actual control input. The parameter optimization module is used to construct an optimization model with the goal of minimizing the number of communication triggers and satisfying tracking performance and input constraints. It then uses an iterative search strategy to find the optimal threshold parameters for event triggering. Specifically, the iterative search employs a Bayesian optimization algorithm, which includes: using a Gaussian process surrogate model to probabilistically model the objective function and constraints of the nonlinear programming model, predicting the distribution of communication trigger counts under different threshold parameters; and iteratively selecting the next threshold parameter to be evaluated based on a lower confidence bound acquisition function, balancing the exploration of unknown regions with the development of known superior regions, and performing system simulations until the optimal threshold that satisfies all constraints and minimizes the number of triggers is found. The control trigger module is used to monitor in real time whether the error variable exceeds the optimal threshold parameter; if it does, the current adaptive control command is immediately applied to the controlled object and the dynamic mask signal is updated; if it does not exceed, the control command of the previous moment remains unchanged.

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