A multi-agent distributed adaptive dynamic double-event-triggered consensus control method and system

Abstract

The application discloses a kind of multi-agent distributed adaptive dynamic double-event trigger consistency control method and system, belong to multi-agent system control technical field, including by radial basis function neural network to unknown nonlinear term is approximated on line, and disturbance observer is estimated to estimate compound uncertain term, provide disturbance estimation signal that can be realized for control compensation.And recursive design virtual control and adaptive law under dynamic surface control framework, avoid derivation explosion in backstepping design by first-order filter, while combining constraint potential function realizes the processing to state constraint, guarantee closed loop signal bounded.The control update trigger time and communication reporting trigger time are respectively constructed, and the trigger function is designed based on the error of two branches, to reduce the control update and communication overhead of networked system.

Description

Technical Field

[0001] This application belongs to the field of multi-agent system control technology, specifically relating to a multi-agent distributed adaptive dynamic dual-event triggered consistency control method and system. Background Technology

[0002] Multi-agent systems (MASs) consist of multiple interacting agents that achieve global task objectives through local information exchange and distributed control. Due to their excellent flexibility and scalability in fields such as automation, robotics, and aerospace, the cooperative control problem of MASs has attracted widespread attention in recent years. Especially in the case of nonlinear characteristics and unknown external disturbances, designing efficient and reliable distributed control strategies to achieve consistency / cooperative tracking remains an important research direction in the field of control.

[0003] To address the consensus control objective, existing research has focused on fixed-time consensus control designs based on event-triggered mechanisms. For problems related to input delay and uncertain disturbances, event-triggered control schemes have been proposed (Liu J, Zhang Y, Sun C, et al. Fixed-time consensus of multi-agent systems with input delay and uncertain disturbances via event-triggered Control [J]. Information Sciences, 2019, 480: 261–272.), achieving fixed-time consensus in multi-agent systems. While traditional asymptotic and finite-time consensus algorithms can achieve system state convergence based on the consensus objective, they often suffer from slow convergence speeds or limitations where the upper bound of convergence time depends on the initial state. To overcome these issues, fixed-time consensus and set-time consistency methods have been proposed, characterized by an upper bound of convergence time that does not depend on initial conditions and can be preset. However, these methods typically require continuous controller updates, leading to high communication and computational overhead, which is detrimental to the long-term stable operation of resource-constrained networked systems.

[0004] As an effective means of reducing resource consumption, event-triggered control, through the design of intelligent triggering mechanisms, updates the controller only when necessary, thereby reducing the communication and computational burden. In recent years, for the multi-agent fixed-time consensus problem with unknown bounded disturbances, a dynamic event-triggered fixed-time consensus control method has been proposed. By introducing dynamic variables to adjust the triggering conditions online, it is possible to reduce the number of triggers while ensuring fixed-time convergence performance (Zheng W, Dong Y, Wang H. Dynamic Event-triggered fixed-time consensus control of multi-agent systems with unknown bounded disturbances [J]. International Journal of Control, 2023, 97(5): 1037–1048.). Although dynamic event-triggered control reduces the triggering frequency and suppresses Zeno behavior to some extent by introducing internal dynamic variables, it still has some shortcomings in networked multi-agent consensus scenarios:

[0005] (1) Control updates and communication updates share the same trigger sequence. Many existing methods use a single event trigger sequence for both control input updates and neighbor information broadcast updates. In this case, to ensure the convergence requirement of consistency at fixed or preset times, the trigger conditions often need to be designed more conservatively, which leads to an increase in the communication update frequency as the control performance requirements increase. Conversely, if the trigger conditions are relaxed to reduce the communication update frequency, the sampling and holding error of the neighbor information increases, which in turn causes the neighbor information used in the consistency coupling term to deviate from its current value, affecting the controllability and convergence of the consistency error.

[0006] (2) It is difficult to separately characterize and constrain control update overhead and communication overhead. Under the single-trigger mechanism, the number of control updates and the number of communication broadcasts usually change synchronously. The design parameters of the trigger condition can only act on both types of overhead at the same time, making it difficult to establish independent upper bounds or optimization indicators for control update overhead and communication overhead in theoretical analysis. Therefore, when the system is simultaneously constrained by computing resources and communication bandwidth, the single-trigger mechanism is difficult to provide a resource allocation method with clear adjustability.

[0007] (3) The neighbor information error introduced by sample-and-hold increases the conservatism of the analysis and reduces the convergence performance margin. In event-triggered communication, the neighbor state usually participates in the consistency coupling term in the form of zero-order hold, and the coupling term is actually composed of the current state and the most recent broadcast value of the neighbor. The neighbor information error introduced by this will appear directly in the derivative expression of the consistency error and enter the Lyapunov derivative inequality as an additional term. In order to ensure stability and convergence, the error term needs to be bounded, which usually forces the triggering condition to be more conservative or requires a larger control gain, thereby reducing the saving effect of the triggering mechanism and compressing the design margin of the convergence performance. Summary of the Invention

[0008] Purpose of the invention: This application develops a multi-agent distributed adaptive dynamic dual-event triggered consistency control method and system, aiming to solve the technical problems in the prior art.

[0009] Technical Solution: In a first aspect, this application provides a multi-agent distributed adaptive dynamic dual-event triggered consensus control method, wherein the multi-agent includes a leader agent and follower agents connected by communication, and the method includes:

[0010] The non-strict feedback nonlinear system model of the follower agent is constructed as the first model, which includes unknown nonlinear perturbations and external perturbations;

[0011] A second model is obtained by characterizing the unknown nonlinear perturbation using a radial basis function neural network.

[0012] A disturbance observer for the external disturbance is constructed based on the second model;

[0013] The dynamic relationship of the disturbance estimation error is obtained based on the second model and the disturbance observer, and the multi-agent system is controlled and compensated based on the dynamic relationship of the disturbance estimation error.

[0014] Based on the dynamic surface control framework, the adaptive controller of the second model is recursively derived by backstepping through a first-order filter and a constraint potential function, and the disturbance and error interference to the control input parameters in the second model are suppressed based on the adaptive controller.

[0015] Obtain the time consistency controller of the multi-agent system, and combine the control update trigger time and the communication reporting trigger time to obtain the control update error and the communication reporting error;

[0016] The update time of the control input parameters in the second model is obtained based on the control update error, and the update time of the neighbor cache is obtained based on the communication reporting error.

[0017] In some embodiments, the characterization formula based on the radial basis function neural network for characterizing the unknown nonlinear perturbation includes:

[0018] ;

[0019] in, This refers to the unknown nonlinear perturbation represented by a radial basis function neural network. It is a constant weight vector; For Gaussian functions; To approximate the error, , To approximate the upper bound of the error; For the first The state variables of each agent The compact set it belongs to.

[0020] In some embodiments, the representation formula of the second model includes:

[0021] ;

[0022] in, , Let be the order of the non-strict feedback nonlinear system. The sequence number of the follower agent; and For unknown nonlinear dynamics, ideal weight parameters are used. and For Gaussian functions; and To approximate the error; and External disturbance; It is a state vector; For the follower intelligent agent The output.

[0023] In some embodiments, the characterization formula of the disturbance observer includes:

[0024] ;

[0025] in, , Let be the order of the non-strict feedback nonlinear system. The sequence number of the follower agent; These are real-time observations of external disturbances; The auxiliary system state of the disturbance observer; For design parameters, >0; , is the state vector; , is the state vector; For unknown nonlinear dynamics, ideal weight parameters are used. This is the Gaussian function.

[0026] In some embodiments, the dynamic relationship characterization formula for the perturbation estimation error includes:

[0027] ;

[0028] in, The disturbance estimation error The first derivative; The first derivative of the external disturbance; For design parameters, >0; Weight estimation error Transpose of; For Gaussian functions; To approximate the error, , To approximate the upper bound of the error.

[0029] In some embodiments, the adaptive controller of the second model, based on a dynamic surface control framework, is derived by backstepping through a first-order filter and a constraint potential function:

[0030] Determine the consistency error surface, state errors at each layer, and filtering errors of the follower agent;

[0031] Obtain the initial Lyapunov function containing the constraint potential function and parameter error terms;

[0032] The derivative of the initial Lyapunov function is calculated, and the upper bound of the initial derivative is obtained by combining the perturbation estimation error, the consistency error surface, and the Young's inequality.

[0033] Based on the upper bound of the preliminary derivative, a virtual controller and its weight adaptive law are obtained. The virtual controller and its weight adaptive law make the dominant term of the upper bound of the preliminary derivative negative, and the consistency error surface and parameter estimation error are bounded, and converge to the desired neighborhood.

[0034] The control signal output by the virtual controller is input into a first-order low-pass filter to obtain the recursive filter output.

[0035] The recursive filtering error is characterized by the control signal output by the virtual controller and the recursive filter output, and the dynamics of the recursive filtering error are obtained.

[0036] Based on the recursive filtering error, a recursive Lyapunov function containing the constraint potential function and parameter error term is obtained.

[0037] The upper bound of the recursive derivative is obtained by taking the derivative of the recursive Lyapunov function and combining it with the perturbation observer, the state error of each layer, the dynamics of the recursive filter error, and the Young's inequality.

[0038] The real controller and its adaptive law are obtained based on the upper bound of the recursive derivative.

[0039] After the recursion is completed, the control signal output by the actual controller is input into the first-order low-pass filter to obtain the final filtered output.

[0040] The final filtering error is characterized by the control signal output by the actual controller after the recursion is completed and the final filtered output, and the dynamics of the final filtering error are obtained.

[0041] Based on the final filtering error, obtain the final Lyapunov function, which includes the constraint potential function and the parameter error term;

[0042] The upper bound of the final derivative is obtained by taking the derivative of the recursive Lyapunov function and combining the perturbation estimation error and the state error of the final layer.

[0043] Based on the upper bound of the final derivative, an adaptive control term containing the tanh function is obtained, which serves as the adaptive controller to suppress disturbances and errors from interfering with the control input parameters in the second model.

[0044] In some embodiments, the characterization formula for the consistency error surface includes:

[0045] ;

[0046] in, For follower intelligent agents With the output of the leader agent and neighbor output The overall deviation is used to characterize the consistency error surface; For follower intelligent agents The ID of the neighboring intelligent agent; For follower intelligent agents The number of neighboring intelligent agents; For follower intelligent agents and Neighbor Intelligent Agent Communication weights between them; For follower intelligent agents The communication weights between the leader agent and the leader agent;

[0047] The formulas for characterizing the state error of each layer include:

[0048] ;

[0049] in, For the follower intelligent agent In the Layer state error; For the follower intelligent agent In the The state vector of the layer; Virtual control signal The output after passing through a first-order low-pass filter , Let the order be the non-strict feedback nonlinear system.

[0050] The formula for characterizing the filtering error includes:

[0051] ;

[0052] in, The filtering error is mentioned above. This is the filtered output of the virtual controller.

[0053] In some embodiments, the characterization formula of the time consistency controller includes:

[0054] ;

[0055] in, For control input; For measurement error; ; Let the order be the non-strict feedback nonlinear system. For control parameters; For convergence time; It is a time-varying scaling function; , For follower intelligent agents The number of neighboring intelligent agents, For follower intelligent agents The sorting number of the neighboring intelligent agents. For follower intelligent agents and Neighbor Intelligent Agent Communication weights between them For the follower intelligent agent The state vector, For the follower intelligent agent Neighbor Intelligent Agent The state vector; To smoothly adjust parameters; This is a dynamic compensation variable.

[0056] In some embodiments, the characterization formulas for the control update error and the communication reporting error include:

[0057] ; ;

[0058] in, The control update error; To control the timing of update triggering; The communication reporting error; This is the trigger time for communication reporting;

[0059] ;

[0060] in, It is a consecutive combination of terms;

[0061] The method further includes:

[0062] Obtain internal dynamic variables, and based on these internal dynamic variables, obtain control update trigger functions and communication reporting trigger functions, wherein the characterization formulas for the control update trigger functions and the communication reporting trigger functions include:

[0063] ;

[0064] in, To control the update trigger function; For communication reporting trigger function; For positive design parameters, ; Adjust parameters to trigger the threshold; To control the dynamic variables of the update trigger function; Dynamic variables for the communication reporting trigger function;

[0065] The update time of the input control input parameters is determined based on the control update trigger function, and the update time of the neighbor cache is determined based on the communication reporting trigger function.

[0066] Secondly, embodiments of this application also provide a multi-agent distributed adaptive dynamic dual-event triggered consensus control system, wherein the multi-agent includes a leader agent and follower agents connected in communication, and the system includes:

[0067] The first model acquisition module is used to construct a non-strict feedback nonlinear system model of the follower agent as a first model, the first model including unknown nonlinear perturbation and external perturbation;

[0068] The second model acquisition module is used to acquire a second model based on the radial basis function neural network characterizing the unknown nonlinear disturbance.

[0069] The disturbance observer acquisition module is used to construct a disturbance observer for the external disturbance based on the second model;

[0070] The control compensation module is used to obtain the disturbance estimation error based on the second model and the disturbance observer, and to perform control compensation on the multi-agent system based on the disturbance estimation error.

[0071] The disturbance suppression module is used to backstep the adaptive controller of the second model based on the dynamic surface control framework, through a first-order filter and a constraint potential function, and to suppress the disturbance and error on the control input parameters in the second model based on the adaptive controller.

[0072] The error acquisition module is used to acquire the time consistency controller of the multi-agent system, and to acquire the control update error and communication reporting error by combining the control update trigger time and the communication reporting trigger time.

[0073] The control update acquisition module is used to acquire the update time of the control input parameters in the second model based on the control update error, and to acquire the update time of the neighbor cache based on the communication reporting error.

[0074] Beneficial Effects: Compared with existing technologies, the multi-agent distributed adaptive dynamic dual-event triggered consensus control method provided in this application approximates unknown nonlinear terms online through a radial basis function neural network and constructs a disturbance observer to estimate composite uncertainties, providing an achievable disturbance estimation signal for control compensation. Furthermore, it recursively designs virtual control and adaptive laws within a dynamic surface control framework, avoids derivative explosion in backstep design through a first-order filter, and combines constraint potential functions to handle state constraints, ensuring the boundedness of the closed-loop signal. It separately constructs control update trigger times and communication reporting trigger times, and designs trigger functions based on the errors of the two branches to reduce the control update and communication overhead of the networked system. Attached Figure Description

[0075] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0076] Figure 1 A flowchart illustrating the steps of the multi-agent distributed adaptive dynamic dual-event triggered consistency control method provided in this application embodiment;

[0077] Figure 2 A module connection diagram of the multi-agent distributed adaptive dynamic dual-event triggered consensus control system provided in the embodiments of this application;

[0078] Figure 3 A flowchart illustrating the multi-agent distributed adaptive dynamic dual-event triggered consensus control method provided in this application embodiment;

[0079] Figure 4 This is the communication topology diagram of each agent in the multi-agent distributed adaptive dynamic dual-event triggered consensus control method provided in the embodiments of this application;

[0080] Figure 5 Output graphs for each agent;

[0081] Figure 6 For state constraint error variables picture;

[0082] Figure 7 For state constraint error variables picture;

[0083] Figure 8 This is a trajectory tracking error diagram;

[0084] Figure 9 The timing of the control update for each intelligent agent is determined.

[0085] Figure 10 A diagram showing the trigger times for communication reporting between various intelligent agents;

[0086] Figure reference numerals: 10, First model acquisition module; 20, Second model acquisition module; 30, Disturbance observer acquisition module; 40, Control compensation module; 50, Disturbance suppression module; 60, Error acquisition module; 70, Control update acquisition module. Detailed Implementation

[0087] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0088] Multi-agent systems (MASs) consist of multiple interacting agents that achieve global task objectives through local information exchange and distributed control. Due to their excellent flexibility and scalability in fields such as automation, robotics, and aerospace, the cooperative control problem of MASs has attracted widespread attention in recent years. Especially in the case of nonlinear characteristics and unknown external disturbances, designing efficient and reliable distributed control strategies to achieve consistency / cooperative tracking remains an important research direction in the field of control.

[0089] To address the consensus control objective, existing research has focused on fixed-time consensus control designs based on event-triggered mechanisms. For problems related to input delay and uncertain disturbances, event-triggered control schemes have been proposed (Liu J, Zhang Y, Sun C, et al. Fixed-time consensus of multi-agent systems with input delay and uncertain disturbances via event-triggered Control [J]. Information Sciences, 2019, 480: 261–272.), achieving fixed-time consensus in multi-agent systems. While traditional asymptotic and finite-time consensus algorithms can achieve system state convergence based on the consensus objective, they often suffer from slow convergence speeds or limitations where the upper bound of convergence time depends on the initial state. To overcome these issues, fixed-time consensus and set-time consistency methods have been proposed, characterized by an upper bound of convergence time that does not depend on initial conditions and can be preset. However, these methods typically require continuous controller updates, leading to high communication and computational overhead, which is detrimental to the long-term stable operation of resource-constrained networked systems.

[0090] As an effective means of reducing resource consumption, event-triggered control, through the design of intelligent triggering mechanisms, updates the controller only when necessary, thereby reducing the communication and computational burden. In recent years, for the multi-agent fixed-time consensus problem with unknown bounded disturbances, a dynamic event-triggered fixed-time consensus control method has been proposed. By introducing dynamic variables to adjust the triggering conditions online, it is possible to reduce the number of triggers while ensuring fixed-time convergence performance (Zheng W, Dong Y, Wang H. Dynamic Event-triggered fixed-time consensus control of multi-agent systems with unknown bounded disturbances [J]. International Journal of Control, 2023, 97(5): 1037–1048.). Although dynamic event-triggered control reduces the triggering frequency and suppresses Zeno behavior to some extent by introducing internal dynamic variables, it still has some shortcomings in networked multi-agent consensus scenarios:

[0091] (1) Control updates and communication updates share the same trigger sequence. Many existing methods use a single event trigger sequence for both control input updates and neighbor information broadcast updates. In this case, to ensure the convergence requirement of consistency at fixed or preset times, the trigger conditions often need to be designed more conservatively, which leads to an increase in the communication update frequency as the control performance requirements increase. Conversely, if the trigger conditions are relaxed to reduce the communication update frequency, the sampling and holding error of the neighbor information increases, which in turn causes the neighbor information used in the consistency coupling term to deviate from its current value, affecting the controllability and convergence of the consistency error.

[0092] (2) It is difficult to separately characterize and constrain control update overhead and communication overhead. Under the single-trigger mechanism, the number of control updates and the number of communication broadcasts usually change synchronously. The design parameters of the trigger condition can only act on both types of overhead at the same time, making it difficult to establish independent upper bounds or optimization indicators for control update overhead and communication overhead in theoretical analysis. Therefore, when the system is simultaneously constrained by computing resources and communication bandwidth, the single-trigger mechanism is difficult to provide a resource allocation method with clear adjustability.

[0093] (3) The neighbor information error introduced by sample-and-hold increases the conservatism of the analysis and reduces the convergence performance margin. In event-triggered communication, the neighbor state usually participates in the consistency coupling term in the form of zero-order hold, and the coupling term is actually composed of the current state and the most recent broadcast value of the neighbor. The neighbor information error introduced by this will appear directly in the derivative expression of the consistency error and enter the Lyapunov derivative inequality as an additional term. In order to ensure stability and convergence, the error term needs to be bounded, which usually forces the triggering condition to be more conservative or requires a larger control gain, thereby reducing the saving effect of the triggering mechanism and compressing the design margin of the convergence performance.

[0094] In view of this, the embodiments of this application provide a multi-agent distributed adaptive dynamic dual-event triggered consistency control method. This method uses a radial basis function neural network to approximate unknown nonlinear terms online and constructs a disturbance observer to estimate composite uncertainties, providing an achievable disturbance estimation signal for control compensation. Furthermore, it recursively designs virtual control and adaptive laws within a dynamic surface control framework, avoids derivative explosion in backstep design using a first-order filter, and combines constraint potential functions to handle state constraints, ensuring the boundedness of the closed-loop signal. Control update trigger times and communication reporting trigger times are constructed separately, and trigger functions are designed based on the errors of the two branches to reduce the control update and communication overhead of the networked system. Internal dynamic variables and corresponding update laws are introduced to adjust the trigger threshold, thereby reducing the number of triggers and eliminating Zeno behavior while ensuring consistency performance.

[0095] Specifically, this application uses graph theory to describe the communication relationships between agents. Please refer to [link / reference]. Figure 4 , Figure 4 This is the communication topology of each agent in the multi-agent distributed adaptive dynamic dual-event triggered consensus control method provided in the embodiments of this application. It uses an undirected graph. Let represent the communication topology between all agents, where The set of all vertices. Let be the set of edges. This is an adjacency matrix. In the communication topology graph, vertices represent the position of each follower agent, and edges represent information exchange between agents. , Represents intelligent agents With intelligent agents The communication weights between them, when the communication topology is an undirected graph. .if ,So ,if ,So ,here Represents intelligent agents It can transmit its own state information to the intelligent agent. Then the node The set of neighboring vertices can be represented as Furthermore, the Laplace matrix of an undirected communication topology is defined as follows: , Called a node The in-degree matrix, where Define the connection matrix between leaders and followers as follows: When the follower intelligent agent When able to receive information from the leader agent, ,otherwise, .

[0096] Specifically, the relevant lemmas adopted in this application include:

[0097] Lemma 1 for , , ,and Then there is .

[0098] Lemma 2 Consider the following system, ,in, initial value , It is a nonlinear function, and .

[0099] If there exists a continuous radially unbounded function satisfy, The system has arbitrary solutions satisfy:

[0100] .

[0101] in, , Representation function exist If the upper right derivative at a given point is true, then the system is said to be globally stable in a real fixed time, and the solution set is given by... Convergence time satisfy .in, .

[0102] Lemma 3 Assumption Then there is .

[0103] Lemma 4 A connected undirected graph Laplace matrix abbreviated as is a positive semi-definite symmetric matrix, and its eigenvalues, from smallest to largest, are . , It is the eigenvector corresponding to the eigenvalue 0, if ,but .in .

[0104] Lemma 5 For any real number ,have ,in, , .

[0105] In some embodiments, please refer to Figure 1 and Figure 3 , Figure 1 This is a flowchart illustrating the steps of the multi-agent distributed adaptive dynamic dual-event triggered consistency control method provided in this application embodiment. Figure 3 This is a flowchart of the multi-agent distributed adaptive dynamic dual-event triggered consensus control method provided in this application embodiment. The multi-agent distributed adaptive dynamic dual-event triggered consensus control method provided in this application embodiment is specifically implemented through steps 100 to 700:

[0106] Step 100: Construct a non-strict feedback nonlinear system model of the follower agent as the first model. The first model includes unknown nonlinear perturbations and external perturbations.

[0107] In some embodiments, it is considered that one leader and A multi-agent system consisting of several followers. The agents exchange information through an undirected communication topology. For each follower... The available information includes: its own measurable state and output, the sampled information reported by its neighboring followers at the time of communication, and the leader's output information represented by the connection matrix when the leader connects.

[0108] Each follower agent The dynamics are a class A nonlinear system of order-order nonstrict feedback can be expressed as:

[0109]

[0110] in, . Represents an unknown nonlinear function; External disturbance (unknown but bounded); This is the state vector. It contains positive constants. and This makes it possible to have This constraint requires the controller to ensure consistency and tracking performance while avoiding performance degradation or security risks caused by state out-of-bounds errors.

[0111] Assumption 1: External disturbance and its highest point The derivatives of all orders are bounded.

[0112] Assumption 2: The following inequality is satisfied:

[0113] ,

[0114] in, It is a positive real number and satisfies the corresponding conditions.

[0115] Assumption 3: Assuming and its first The first derivative is continuous and bounded. It is a positive number, and Must meet:

[0116] .

[0117] Theorem 1: First define Then we have:

[0118] .

[0119] in, Representation matrix The smallest eigenvalue.

[0120] Control Objective: Under the aforementioned topology, system uncertainties, and state constraints, the control objective of this paper is to design a distributed adaptive controller for each follower agent. With the corresponding triggering mechanism, the closed-loop system satisfies:

[0121] 1) Preset time consistency: at any given preset time Internally, it causes all followers to output. With Leader Output A consensus is reached, and the upper bound of the convergence time does not depend on the initial state;

[0122] 2) Constraints and Boundedness: Maintain state constraints throughout the control process. It is not destroyed and all closed-loop signals are guaranteed to be consistent and bounded (including state, control input, adaptive parameters and observation errors, etc.).

[0123] 3) Resource saving and feasibility: While ensuring the above performance, the frequency of controller updates and communication reporting is significantly reduced.

[0124] Step 200: Based on the radial basis function neural network, the unknown nonlinear perturbation is represented to obtain the second model.

[0125] In some embodiments, to cope with the system Unknown nonlinear External disturbances Regarding the impact on the performance of consistent control, this application constructs a disturbance observer for each agent to estimate the uncertainties in the system and provide a usable disturbance compensation signal for the subsequent adaptive dynamic surface controller, thereby reducing the adverse effects of unknown disturbances on closed-loop stability and convergence speed.

[0126] Radial basis function neural networks (RBFNNs) are used to approximate functions. Based on the general approximation property of RBFNN, the unknown term can be represented as a linear combination of ideal weights and basis functions plus the approximation error. The representation formulas for unknown nonlinear perturbations based on radial basis function neural networks include:

[0127] (2)

[0128] in, This refers to the unknown nonlinear perturbation represented by a radial basis function neural network. It is a constant weight vector; For Gaussian functions; For the first The state variables of each agent The compact set it belongs to, To approximate the error, To approximate the upper bound of the error, ,satisfy:

[0129]

[0130] In some embodiments, the representation formula of the second model includes:

[0131] (3)

[0132] in, , For non-strict feedback nonlinear systems, The sequence number of the follower agent; and For unknown nonlinear dynamics, ideal weight parameters are used. and For Gaussian functions; and To approximate the error; and External disturbance; It is a state vector; For follower intelligent agents The output of .

[0133] Step 300: Construct a disturbance observer for external disturbances based on the second model.

[0134] In some embodiments, the characterization formula for the perturbation observer in System 3 includes:

[0135] ;

[0136] (4)

[0137] in, , For non-strict feedback nonlinear systems, The sequence number of the follower agent; These are real-time observations of external disturbances; The auxiliary system state of the disturbance observer; For design parameters, >0; , is the state vector; , is the state vector; For unknown nonlinear dynamics, ideal weight parameters are used. This is the Gaussian function.

[0138] Step 400: Obtain the disturbance estimation error based on the second model and the disturbance observer, and perform control compensation on the multi-agent system based on the disturbance estimation error.

[0139] In some embodiments, for analyzing observer performance, the characterization formulas for the weight estimation error and the perturbation estimation error include:

[0140] ;

[0141] in, This refers to the weight estimation error; This represents the error in perturbation estimation. Ideal weight parameters; ; ; These are real-time observations of external disturbances.

[0142] In some embodiments, the formula characterizing the dynamic relationship of the perturbation estimation error includes:

[0143] (5)

[0144] in, For perturbation estimation error The first derivative; The first derivative of the external disturbance; For design parameters, >0; Weight estimation error transpose; For Gaussian functions; To approximate the error, , To approximate the upper bound of the error.

[0145] Step 500: Based on the dynamic surface control framework, the adaptive controller of the second model is recursively derived by backstepping through the first-order filter and the constraint potential function, and the disturbance and error on the control input parameters in the second model are suppressed based on the adaptive controller.

[0146] In some embodiments, the step of backstepping the adaptive controller of the second model based on the dynamic surface control framework using a first-order filter and a constraint potential function is specifically implemented through steps 501 to 514:

[0147] Step 501: Determine the consistency error surface, state errors at each layer, and filtering errors of the follower agent.

[0148] In some embodiments, an adaptive dynamic surface control is constructed for a multi-agent system, and the first... The characterization formulas for the consistency error surface of an agent include:

[0149] (6)

[0150] in, For follower intelligent agents With the output of the leader agent and neighbor output The overall deviation is used to characterize the consistency error surface when When local consistency errors converge, global consistency is promoted. For follower intelligent agents The ID of the neighboring intelligent agent; For follower intelligent agents The number of neighboring intelligent agents; For follower intelligent agents and Neighbor Intelligent Agent Communication weights between them; For follower intelligent agents The communication weights between the leader agent and the leader agent;

[0151] In some embodiments, for each layer of a non-strict feedback structure, the characterization formula for the state error of each layer includes:

[0152] (7)

[0153] in, For follower intelligent agents In the Layer state error; For follower intelligent agents In the The state vector of the layer; Virtual control signal The output after passing through a first-order low-pass filter , For non-strict feedback nonlinear systems, this is the order.

[0154] In some embodiments, virtual control signals After passing through a first-order low-pass filter, the result is... The formulas defining the filtering error include:

[0155] (8)

[0156] in, This is the filtering error; For the filtered output of the virtual controller, it is understandable that the introduction of the filter avoids affecting the output of the virtual controller. Repeated differentiation is used to suppress differentiation explosion.

[0157] In some embodiments, please refer to steps 502 to 504 to construct a constraint potential function ( Preliminary Lyapunov function (type) and parameter error term We then differentiated the inequality to obtain its upper bound. Next, we designed the virtual controller for the first step. With the weight adaptive law, it is possible to The dominant term in the equation is negative, thus ensuring the error... The parameter estimation error is bounded and converges to the desired neighborhood:

[0158] Step 502: Obtain the initial Lyapunov function containing the constraint potential function and parameter error terms.

[0159] In some embodiments, the initial Lyapunov function The characterization formulas include:

[0160]

[0161] in, It is a positive definite symmetric matrix. ,in These are invariants to be defined.

[0162] Step 503: Differentiate the initial Lyapunov function and obtain the upper bound of the initial derivative by combining the perturbation estimation error, the consistency error surface, and the Young's inequality.

[0163] In some embodiments, differentiating both sides of equation (9) and substituting them into equation (9) Japanese style We can then conclude that:

[0164]

[0165] in .

[0166] Using Young's inequality, the following estimate can be obtained:

[0167]

[0168]

[0169]

[0170]

[0171]

[0172]

[0173]

[0174] in, These are normal design parameters.

[0175] Depend on – achievable The upper bound of the preliminary derivative:

[0176]

[0177] Step 504: Obtain the virtual controller and its weight adaptive law based on the upper bound of the preliminary derivative. The virtual controller and its weight adaptive law make the dominant term of the upper bound of the preliminary derivative negative, and the consistency error surface and parameter estimation error are bounded and converge to the desired neighborhood.

[0178] In some embodiments, the following virtual controller and weight adaptive law are constructed:

[0179]

[0180]

[0181] in It is a constant.

[0182] Will , Substitution We can obtain:

[0183]

[0184] In some embodiments, please refer to steps 505 to 510, this application will Obtained through a first-order low-pass filter Write out the dynamics of the filtering error, and then construct the recursive Lyapunov function. Taking its derivative yields an upper bound for the recursive derivative, which in turn provides the form of the real control or the next level of virtual control and the adaptive law, ensuring the continuation of the Lyapunov decreasing structure:

[0185] Step 505: Input the control signal output by the virtual controller into a first-order low-pass filter to obtain the recursive filter output.

[0186] In some embodiments, the virtual signal is made visible by the action of a first-order low-pass filter. This first-order low-pass filter (time constant is...) )get:

[0187]

[0188] Step 506: Characterize the recursive filtering error by using the control signal output by the virtual controller and the recursive filter output, and determine the dynamics of the recursive filtering error.

[0189] In some embodiments, by and The dynamics of the filtering error can be derived:

[0190]

[0191] Step 507: Obtain the recursive Lyapunov function containing the constraint potential function and parameter error term based on the recursive filtering error.

[0192] In some embodiments, let And construct the recursive Lyapunov function:

[0193]

[0194] in, .

[0195] Step 508: Take the derivative of the recursive Lyapunov function and obtain the upper bound of the recursive derivative by combining the perturbation observer, the state error of each layer, the dynamics of the recursive filter error, and the Young's inequality.

[0196] In some embodiments, for Differentiate both sides and then... , , Substitution ,get:

[0197]

[0198] Then, based on Young's inequality, we derive the upper bound of the recurrence derivative:

[0199]

[0200] Step 509: Obtain the real controller and its adaptive law based on the upper bound of the recursive derivative;

[0201] In some embodiments, the real controller and adaptive law are constructed according to Equation 23 as follows:

[0202]

[0203]

[0204] in

[0205] set up ,Will , Substitution We can obtain:

[0206]

[0207]

[0208]

[0209]

[0210]

[0211] In some embodiments, please refer to steps 510 to 514, and the result is also obtained through a first-order low-pass filter. and Construct the final Lyapunov function and give the adaptive control term containing... A robust structure is used to suppress disturbances and errors from affecting the control input.

[0212] Step 510: Input the control signal output by the actual controller after the recursion is completed into a first-order low-pass filter to obtain the final filtered output.

[0213] In some embodiments, the function of a first-order low-pass filter is retained to filter artificial signals. The time constant of this device is ,get:

[0214]

[0215] Step 511: After the recursion is completed, the control signal output by the real controller and the final filter output characterize the final filter error, and obtain the dynamics of the final filter error.

[0216] In some embodiments, by formula With formula We can obtain:

[0217]

[0218] in .

[0219] Step 512: Obtain the final Lyapunov function containing the constraint potential function and parameter error term based on the final filtering error.

[0220] In some embodiments, the final representation of the Lyapunov function includes:

[0221] in .

[0222] Step 513: Take the derivative of the recursive Lyapunov function and combine the perturbation estimation error and the state error of the final layer to obtain the upper bound of the final derivative.

[0223] In some embodiments, for Differentiate both sides and , , Substituting, we obtain the upper bound of the final derivative:

[0224]

[0225] in,

[0226] The final layer's adaptive control term is written as:

[0227]

[0228] in, , It is a positive design constant.

[0229] Step 514: Obtain the adaptive control term containing the tanh function based on the upper bound of the final derivative. This is an adaptive controller used to suppress disturbances and errors from interfering with the control input parameters in the second model.

[0230] Step 600: Obtain the time consistency controller of the multi-agent system, and obtain the control update error and communication reporting error by combining the control update trigger time and the communication reporting trigger time.

[0231] In some embodiments, under the dynamic event dual-trigger mechanism, the preset time consistency controller for the agent is designed as follows: As shown:

[0232] (32)

[0233] in For control parameters, This is the most recent trigger time for the agent; the controller state is maintained until the next trigger time.

[0234] Furthermore, for the controller of Equation 32, the following measurement error is constructed:

[0235] (33)

[0236] Combining Equations 32 and 33, the characterization formula for the final time-consistent controller is determined as follows:

[0237] (34)

[0238] in, For control input; For measurement error; This is the control gain constant; For non-strict feedback nonlinear systems, this is the order. For control parameters, ; For convergence time; It is a time-varying scaling function; , For follower intelligent agents The number of neighboring intelligent agents, For follower intelligent agents The sorting number of the neighboring intelligent agents. For follower intelligent agents and Neighbor Intelligent Agent Communication weights between them For follower intelligent agents The state vector, For follower intelligent agents Neighbor Intelligent Agent The state vector; To smoothly adjust parameters; This is a dynamic compensation variable.

[0239] Step 700: Obtain the update time of the control input parameters in the second model based on the control update error, and obtain the update time of the neighbor cache based on the communication reporting error.

[0240] In some embodiments, to further reduce the communication and computational overhead of networked multi-agent systems and reduce the frequency of control input updates, this application divides the event triggering mechanism into two categories: control update triggering time sets. Set of communication reporting trigger times Among them, the update of control input only occurs when... Occurs, that is, for any In the control law, all quantities that require "trigger hold" are based on the most recent control update time. The sampled values ​​are used to obtain the segmented holding control input. .

[0241] Because communication only Occurrence, intelligent agent Unable to obtain neighbors Real-time status Therefore, in End-to-end definition of neighbor cache state: Accordingly, the consistent coupling quantity is constructed in the form of "ontology real-time - neighbor cache". This definition allows communication reporting to be triggered via a refresh. This will affect This allows the dual-trigger mechanism to be strictly integrated with closed-loop control.

[0242] Set of control update trigger times The control input is updated and remains unchanged between two adjacent control update triggers. Specifically, for any The control input is designed as follows:

[0243]

[0244] To facilitate the construction of triggering conditions, a continuous combination term is defined:

[0245]

[0246] Double event triggering occurs when the same combination item is accessed. Two types of freeze times are employed, including control update error and communication reporting error. The trigger times for these two types of errors do not need to be the same. This allows for the compression of the control update frequency and communication frequency while maintaining performance. The characterization formulas for control update error and communication reporting error include:

[0247] ; (37)

[0248] in, To control update errors and determine when to update. ; To control the timing of update triggering; This is used to report communication errors and determine when to broadcast a refresh of the neighbor's cache; This is the trigger time for communication reporting;

[0249] ;

[0250] in, It is a consecutive combination of terms;

[0251] In some embodiments, to further reduce the number of triggers and avoid Zeno behavior, this application introduces internal dynamic variables and constructs a dynamic threshold trigger function. The multi-agent distributed adaptive dynamic dual-event triggering consistency control method of this application also includes: (The text then goes on to describe the design of control update trigger functions and communication reporting trigger functions.)

[0252] Obtain internal dynamic variables, and based on these variables, obtain the control update trigger function and the communication reporting trigger function. The characterization formulas for the control update trigger function and the communication reporting trigger function include:

[0253] (38)

[0254] in, To control the update trigger function; For communication reporting trigger function; For positive design parameters, ; To trigger threshold adjustment parameters, ; To control the dynamic variables of the update trigger function, ; For the communication reporting trigger function's dynamic variables, ;

[0255] Furthermore, to balance control energy consumption, communication usage, and the magnitude of control input changes, this application introduces a multi-objective cost function:

[0256] ;

[0257] in Indicates the communication reporting indication quantity. .

[0258] Therefore, the internal dynamic variable update law is designed as follows:

[0259]

[0260] The control update trigger time and the communication reporting trigger time are respectively defined as the moment when the trigger function first reaches a non-negative value:

[0261] ;

[0262] Among them, when When it occurs, the intelligent agent Update control input And keep; when When it occurs, the intelligent agent Broadcast to neighbors The neighbors refresh their cache accordingly. .

[0263] As can be seen from the definition of the triggering time, in Inside ,thereby:

[0264] ;

[0265] Similarly, in Inside:

[0266] ;

[0267] Will Substitution ,get:

[0268]

[0269] This is used to prove that the internal dynamic variables are bounded and to further derive the positive lower bound of the trigger interval, thereby avoiding Zeno behavior.

[0270] The update time of the input control parameters is determined based on the control update trigger function, and the update time of the neighbor buffer is determined based on the communication reporting trigger function.

[0271] For example, please refer to Figure 5 , Figure 5 Output graphs for each agent, from Figure 5 As can be seen, under the proposed control strategy, the outputs of each agent can quickly and smoothly approach the desired curve, and the agents maintain a very high degree of consistency.

[0272] Please see Figure 6 , Figure 6 For state constraint error variables picture, Figure 6 The thick black solid line in the middle represents the upper and lower bounds of state constraint 1. Throughout the entire operation, the state error variable of all agents is strictly limited within the safe boundary, which proves that the method of this application can effectively handle the state-constrained problem in complex nonlinear systems.

[0273] Please refer to 7. Figure 7 For state constraint error variables picture, Figure 7 The thick black line in the middle represents the upper and lower bounds of the preset state constraint 2. Even when there are unknown external disturbances and nonlinear dynamics in the system, the agent does not violate any rules.

[0274] Please see Figure 8 , Figure 8 For the trajectory tracking error map, from Figure 8As can be seen, the tracking errors of all agents converge to a very small neighborhood near the origin in a very short time and remain stable in subsequent operation.

[0275] Please see Figure 9 , Figure 9 Update the timing diagram for each intelligent agent's control. Figure 9 The discrete points on the horizontal axis represent the moments when each agent controller actually performs an update action; by Figure 9 It can be seen that during the initial transient adjustment phase of the system, the trigger points are relatively dense to ensure the system's rapid response; however, once the system enters a steady state, the trigger points become extremely sparse. This triggering mechanism can update the control law based on the real-time operating status of the system, reducing the number of calculations by the controller and the frequency of actions by the underlying actuators, thereby reducing the physical wear and energy consumption of the controller.

[0276] Please see Figure 10 , Figure 10 A diagram showing the trigger times for communication reporting between various intelligent agents. Figure 10 This demonstrates discrete-time points in a distributed topological network where an agent broadcasts its state information to neighboring nodes. Figure 10 It can be seen that this triggering mechanism reduces the occupation of communication bandwidth and the consumption of computing resources, thereby improving resource utilization.

[0277] Understandably, the multi-agent distributed adaptive dynamic dual-event triggered consistency control method provided in this application uses a radial basis function neural network to approximate unknown nonlinear terms online and constructs a disturbance observer to estimate composite uncertainties, providing an achievable disturbance estimation signal for control compensation. Furthermore, it recursively designs virtual control and adaptive laws within a dynamic surface control framework, avoids derivative explosion in backstep design using a first-order filter, and combines constraint potential functions to handle state constraints, ensuring the boundedness of the closed-loop signal. It constructs control update trigger times and communication reporting trigger times separately, and designs trigger functions based on the errors of the two branches to reduce the control update and communication overhead of the networked system. It introduces internal dynamic variables and corresponding update laws to adjust the trigger threshold, thereby reducing the number of triggers and eliminating Zeno behavior while ensuring consistency performance.

[0278] Accordingly, embodiments of this application also provide a multi-agent distributed adaptive dynamic dual-event triggered consensus control system. Please refer to [link to relevant documentation]. Figure 2 , Figure 2 This is a module connection diagram of the multi-agent distributed adaptive dynamic dual-event triggered consensus control system provided in this application embodiment. The multi-agent distributed adaptive dynamic dual-event triggered consensus control system provided in this application embodiment includes:

[0279] The first model acquisition module 10 is used to construct a non-strict feedback nonlinear system model of the follower agent as the first model. The first model includes unknown nonlinear perturbations and external perturbations.

[0280] The second model acquisition module 20 is used to acquire the second model based on the radial basis function neural network to characterize the unknown nonlinear disturbance.

[0281] The disturbance observer acquisition module 30 is used to construct a disturbance observer for external disturbances based on the second model;

[0282] The control compensation module 40 is used to obtain the disturbance estimation error based on the second model and the disturbance observer, and to perform control compensation on the multi-agent system based on the disturbance estimation error.

[0283] The disturbance suppression module 50 is used to backstep the adaptive controller of the second model based on the dynamic surface control framework, through a first-order filter and a constraint potential function, and to suppress disturbances and errors on the control input parameters in the second model based on the adaptive controller.

[0284] Error acquisition module 60 is used to acquire the time consistency controller of the multi-agent system, and to acquire the control update error and communication reporting error by combining the control update trigger time and the communication reporting trigger time.

[0285] The control update acquisition module 70 is used to acquire the update time of the control input parameters in the second model based on the control update error, and to acquire the update time of the neighbor cache based on the communication reporting error.

[0286] This application has provided a detailed description of a multi-agent distributed adaptive dynamic dual-event triggered consistency control method and system provided in the embodiments of this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The description of the above embodiments is only for the purpose of helping to understand the method and its core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A multi-agent distributed adaptive dynamic dual-event triggered consensus control method, characterized in that, Applied to a multi-agent system, the multi-agent system comprising a leader agent and follower agents connected in communication, the method includes: The non-strict feedback nonlinear system model of the follower agent is constructed as the first model, which includes unknown nonlinear perturbations and external perturbations; A second model is obtained by characterizing the unknown nonlinear perturbation using a radial basis function neural network. A disturbance observer for the external disturbance is constructed based on the second model; The dynamic relationship of the disturbance estimation error is obtained based on the second model and the disturbance observer, and the multi-agent system is controlled and compensated based on the dynamic relationship of the disturbance estimation error; the dynamic relationship characterization formula of the disturbance estimation error includes: ； in, The disturbance estimation error The first derivative; The first derivative of the external disturbance; For design parameters, >0; Weight estimation error Transpose of; For Gaussian functions; To approximate the error, , To approximate the upper bound of the error; Based on a dynamic surface control framework, an adaptive controller for the second model is recursively derived through backstepping using a first-order filter and a constraint potential function. This adaptive controller is then used to suppress disturbances and errors affecting the control input parameters in the second model. The steps of recursively deriving the adaptive controller for the second model based on a dynamic surface control framework using a first-order filter and a constraint potential function include: The consistency error surface, state errors at each layer, and filtering errors of the follower agent are determined; the characterization formula for the consistency error surface includes: ； in, For follower intelligent agents With the output of the leader agent and neighbor output The overall deviation is used to characterize the consistency error surface; For follower intelligent agents The ID of the neighboring intelligent agent; For follower intelligent agents The number of neighboring intelligent agents; For follower intelligent agents and Neighbor Intelligent Agent Communication weights between them; For follower intelligent agents The communication weights between the leader agent and the leader agent; The characterization formulas for the state errors of each layer include: ； in, For the follower intelligent agent In the Layer state error; For the follower intelligent agent In the The state vector of the layer; Virtual control signal The output after passing through a first-order low-pass filter , Let the order be the non-strict feedback nonlinear system. The formula for characterizing the filtering error includes: ； in, The filtering error is mentioned above. This is the filtered output of the virtual controller; Obtain the initial Lyapunov function containing the constraint potential function and parameter error terms; The derivative of the initial Lyapunov function is calculated, and the upper bound of the initial derivative is obtained by combining the perturbation estimation error, the consistency error surface, and the Young's inequality. Based on the upper bound of the preliminary derivative, a virtual controller and its weight adaptive law are obtained. The virtual controller and its weight adaptive law make the dominant term of the upper bound of the preliminary derivative negative, and the consistency error surface and parameter estimation error are bounded, and converge to the desired neighborhood. The control signal output by the virtual controller is input into a first-order low-pass filter to obtain the recursive filter output. The recursive filtering error is characterized by the control signal output by the virtual controller and the recursive filter output, and the dynamics of the recursive filtering error are obtained. Based on the recursive filtering error, a recursive Lyapunov function containing the constraint potential function and parameter error term is obtained. The upper bound of the recursive derivative is obtained by taking the derivative of the recursive Lyapunov function and combining it with the perturbation observer, the state error of each layer, the dynamics of the recursive filter error, and the Young's inequality. The real controller and its adaptive law are obtained based on the upper bound of the recursive derivative. After the recursion is completed, the control signal output by the actual controller is input into the first-order low-pass filter to obtain the final filtered output. The final filtering error is characterized by the control signal output by the actual controller after the recursion is completed and the final filtered output, and the dynamics of the final filtering error are obtained. Based on the final filtering error, obtain the final Lyapunov function, which includes the constraint potential function and the parameter error term; The upper bound of the final derivative is obtained by taking the derivative of the recursive Lyapunov function and combining the perturbation estimation error and the state error of the final layer. Based on the upper bound of the final derivative, an adaptive control term containing the tanh function is obtained, which is the adaptive controller used to suppress disturbances and errors from interfering with the control input parameters in the second model. Obtain the time consistency controller of the multi-agent system, and combine the control update trigger time and the communication reporting trigger time to obtain the control update error and the communication reporting error; The update time of the control input parameters in the second model is obtained based on the control update error, and the update time of the neighbor cache is obtained based on the communication reporting error.

2. The multi-agent distributed adaptive dynamic dual-event triggered consensus control method according to claim 1, characterized in that, The characterization formula for the unknown nonlinear perturbation based on the radial basis function neural network includes: ； in, This refers to the unknown nonlinear perturbation represented by a radial basis function neural network. It is a constant weight vector; For Gaussian functions; To approximate the error, , To approximate the upper bound of the error; For the first The state variables of each agent The compact set it belongs to.

3. The multi-agent distributed adaptive dynamic dual-event triggered consistency control method according to claim 1, characterized in that, The characterization formulas for the second model include: ; in, , Let be the order of the non-strict feedback nonlinear system. The sequence number of the follower agent; and For unknown nonlinear dynamics, ideal weight parameters are used. and For Gaussian functions; and To approximate the error; and External disturbance; It is a state vector; For the follower intelligent agent The output of .

4. The multi-agent distributed adaptive dynamic dual-event triggered consensus control method according to claim 1, characterized in that, The characterization formula for the disturbance observer includes: ； in, , Let be the order of the non-strict feedback nonlinear system. The sequence number of the follower agent; These are real-time observations of external disturbances; The auxiliary system state of the disturbance observer; For design parameters, >0; , is the state vector; , is the state vector; For unknown nonlinear dynamics, ideal weight parameters are used. This is the Gaussian function.

5. The multi-agent distributed adaptive dynamic dual-event triggered consensus control method according to claim 1, characterized in that, The characterization formula for the time consistency controller includes: ； in, For control input; For measurement error; This is the control gain constant; Let the order be the non-strict feedback nonlinear system. For control parameters; For convergence time; It is a time-varying scaling function; , For follower intelligent agents The number of neighboring intelligent agents, For follower intelligent agents The sorting number of the neighboring intelligent agents. For follower intelligent agents and Neighbor Intelligent Agent Communication weights between them For the follower intelligent agent The state vector, For the follower intelligent agent Neighbor Intelligent Agent The state vector; To smoothly adjust parameters; This is a dynamic compensation variable.

6. The multi-agent distributed adaptive dynamic dual-event triggered consistency control method according to claim 5, characterized in that, The formulas for characterizing the control update error and the communication reporting error include: ； ； in, The control update error; To control the timing of update triggering; The communication reporting error; This is the trigger time for communication reporting; ； in, It is a consecutive combination of terms; The method further includes: Obtain internal dynamic variables, and based on these internal dynamic variables, obtain control update trigger functions and communication reporting trigger functions, wherein the characterization formulas for the control update trigger functions and the communication reporting trigger functions include: ； in, To control the update trigger function; For communication reporting trigger function; To trigger the gain parameter, ; Adjust parameters to trigger the threshold; To control the dynamic variables of the update trigger function; Dynamic variables for the communication reporting trigger function; The update time of the input control input parameters is determined based on the control update trigger function, and the update time of the neighbor cache is determined based on the communication reporting trigger function.

7. A multi-agent distributed adaptive dynamic dual-event triggered consensus control system, characterized in that, Applied to a multi-agent system, the multi-agent system comprising a leader agent and follower agents connected in communication, the control system includes: The first model acquisition module (10) is used to construct a non-strict feedback nonlinear system model of the follower agent as a first model, the first model including unknown nonlinear perturbation and external perturbation; The second model acquisition module (20) is used to acquire the second model based on the radial basis function neural network characterizing the unknown nonlinear disturbance. The disturbance observer acquisition module (30) is used to construct a disturbance observer for the external disturbance based on the second model; The control compensation module (40) is used to obtain the dynamic relationship of the disturbance estimation error based on the second model and the disturbance observer, and to perform control compensation on the multi-agent system based on the dynamic relationship of the disturbance estimation error; the dynamic relationship characterization formula of the disturbance estimation error includes: ； in, The disturbance estimation error The first derivative; The first derivative of the external disturbance; For design parameters, >0; Weight estimation error Transpose of; For Gaussian functions; To approximate the error, , To approximate the upper bound of the error; The disturbance suppression module (50) is used to backstep the adaptive controller of the second model based on the dynamic surface control framework using a first-order filter and a constraint potential function, and to suppress disturbances and errors on the control input parameters of the second model based on the adaptive controller; the step of backstepping the adaptive controller of the second model based on the dynamic surface control framework using a first-order filter and a constraint potential function includes: The consistency error surface, state errors at each layer, and filtering errors of the follower agent are determined; the characterization formula for the consistency error surface includes: ； in, For follower intelligent agents With the output of the leader agent and neighbor output The overall deviation is used to characterize the consistency error surface; For follower intelligent agents The ID of the neighboring intelligent agent; For follower intelligent agents The number of neighboring intelligent agents; For follower intelligent agents and Neighbor Intelligent Agent Communication weights between them; For follower intelligent agents The communication weights between the leader agent and the leader agent; The characterization formulas for the state errors of each layer include: ； in, For the follower intelligent agent In the Layer state error; For the follower intelligent agent In the The state vector of the layer; Virtual control signal The output after passing through a first-order low-pass filter , Let the order be the non-strict feedback nonlinear system. The formula for characterizing the filtering error includes: ； in, The filtering error is mentioned above. This is the filtered output of the virtual controller; Obtain the initial Lyapunov function containing the constraint potential function and parameter error terms; The derivative of the initial Lyapunov function is calculated, and the upper bound of the initial derivative is obtained by combining the perturbation estimation error, the consistency error surface, and the Young's inequality. Based on the upper bound of the preliminary derivative, a virtual controller and its weight adaptive law are obtained. The virtual controller and its weight adaptive law make the dominant term of the upper bound of the preliminary derivative negative, and the consistency error surface and parameter estimation error are bounded, and converge to the desired neighborhood. The control signal output by the virtual controller is input into a first-order low-pass filter to obtain the recursive filter output. The recursive filtering error is characterized by the control signal output by the virtual controller and the recursive filter output, and the dynamics of the recursive filtering error are obtained. Based on the recursive filtering error, a recursive Lyapunov function containing the constraint potential function and parameter error term is obtained. The upper bound of the recursive derivative is obtained by taking the derivative of the recursive Lyapunov function and combining it with the perturbation observer, the state error of each layer, the dynamics of the recursive filter error, and the Young's inequality. The real controller and its adaptive law are obtained based on the upper bound of the recursive derivative. After the recursion is completed, the control signal output by the actual controller is input into the first-order low-pass filter to obtain the final filtered output. The final filtering error is characterized by the control signal output by the actual controller after the recursion is completed and the final filtered output, and the dynamics of the final filtering error are obtained. Based on the final filtering error, obtain the final Lyapunov function, which includes the constraint potential function and the parameter error term; The upper bound of the final derivative is obtained by taking the derivative of the recursive Lyapunov function and combining the perturbation estimation error and the state error of the final layer. Based on the upper bound of the final derivative, an adaptive control term containing the tanh function is obtained, which is the adaptive controller used to suppress disturbances and errors from interfering with the control input parameters in the second model. Error acquisition module (60) is used to acquire the time consistency controller of the multi-agent system, and acquire the control update error and communication reporting error in combination with the control update trigger time and the communication reporting trigger time; The control update acquisition module (70) is used to acquire the update time of the control input parameters in the second model based on the control update error, and to acquire the update time of the neighbor cache based on the communication reporting error.

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