A nonlinear multi-agent system dynamic event-triggered consensus control method based on topological information

Abstract

This invention discloses a dynamic event-triggered consensus control method for nonlinear multi-agent systems based on topology information. The method includes: describing the communication topology using a time-varying directed graph; introducing dynamic auxiliary variables and performance adaptive variables to design topology-dependent time-varying controller gains and distributed dynamic event triggering functions; defining state estimates and various errors; deriving a compact form of system-level error dynamics; integrating the effects of topology switching, control inputs, and nonlinear terms; setting triggering rules, with events triggered by triggering function conditions or topology switching, updating the controller, and broadcasting the state; analyzing system stability using topology-dependent Lyapunov functions; and avoiding Zeno-related abnormal triggering behavior through threshold adaptive constraints. This method fully utilizes local topological information, reduces control conservatism, minimizes resource consumption, achieves exponential convergence tracking of the leader's state by followers, and adapts to dynamic topology switching and nonlinear environments.

Description

Technical Field

[0001] This invention relates to the field of event-triggered control technology for multi-agent systems, and in particular to a dynamic event-triggered consistency control method for nonlinear multi-agent systems based on topology information. Background Technology

[0002] Cooperative control of multi-agent systems, as an important branch of distributed control theory, has wide applications in scenarios such as UAV cooperative search, multi-robot platooning transportation, and distributed scheduling of smart grids. Leader-follower consensus is one of its core research directions. This architecture generates the globally desired trajectory through a leader, while followers track the state by relying on local neighbor information, effectively reducing the system's communication and computational burden. However, real-world systems often face problems such as limited communication bandwidth and energy supply constraints. The periodic information exchange of traditional time-triggered control can easily lead to resource waste, prompting the development of event-triggered control mechanisms. Furthermore, the communication topology between agents in real-world systems is easily affected by factors such as distance, occlusion, and node movement, resulting in dynamic switching. Additionally, agents often exhibit non-ideal dynamic characteristics, making consensus control of multi-agent systems with nonlinear terms under directed switching topologies a pressing technical challenge.

[0003] Existing technologies have two significant drawbacks: First, the controller and triggering mechanism designs do not fully integrate topology characteristics. Most methods use uniform parameter designs for all topologies, failing to utilize local information from different topologies. This results in a conservative control strategy that is difficult to adapt to changes in system characteristics caused by dynamic topology switching. Second, resource utilization efficiency is insufficient. Static event triggering mechanisms tend to trigger too frequently as the system approaches a steady state. While some dynamic event triggering methods have made improvements, they do not introduce performance adaptive adjustment mechanisms, cannot flexibly optimize triggering thresholds based on the real-time state of the system, and do not fully consider the impact of nonlinear dynamics on control performance. This makes it difficult to effectively reduce communication and computing resource consumption while ensuring control accuracy. Summary of the Invention

[0004] To overcome the shortcomings and deficiencies of existing technologies, this invention provides a dynamic event-triggered consistency control method for nonlinear multi-agent systems based on topological information.

[0005] The technical solution adopted in this invention is a dynamic event-triggered consistency control method for a nonlinear multi-agent system based on topological information, comprising the following steps: S1. Construct a multi-agent system with one leader and N followers. Describe the communication topology using a time-varying directed graph. Introduce dynamic auxiliary variables and performance adaptive variables to design the topology-dependent time-varying controller gain and distributed dynamic event triggering function. Define the adjacency matrix, Laplace matrix, and matrix H containing the leader's communication state. Clarify the dynamic model of the followers and the leader and the Lipschitz nonlinear constraints. S2, based on the matrix pair stabilization property and the topological connectivity assumption, designs a time-varying controller gain that depends on the currently active topology. This gain is determined by solving the topology-related Riccati inequality, which is associated with the system matrix, the input matrix, and the positive definite matrix. S3 introduces topology-dependent dynamic auxiliary variables and performance adaptive variables through a distributed dynamic event triggering function, and correlates estimation error and state tracking-related variables by adjusting the triggering threshold in real time. S4 defines the follower state estimate, estimation error, and tracking error, derives a compact expression for error dynamics, and integrates the effects of topology switching, control input, and nonlinear terms. S5, set event triggering rules. The triggering time is triggered when the triggering function meets the conditions or when the topology is switched. The controller is updated and the status information is broadcast at the triggering time. S6 uses topologically dependent Lyapunov functions to analyze system stability and avoids Zeno abnormal triggering behavior through threshold adaptive constraints.

[0006] Furthermore, the dynamic models for followers and leaders are as follows: , in, For the i-th follower state, For the follower to control the input, For the leader state, A, B, and C are constant matrices of appropriate dimensions. For a continuously differentiable nonlinear function that satisfies the Lipschitz condition, Let n be a real vector space. It is a time variable.

[0007] Furthermore, the Riccati inequality for topological dependence is: , The controller gain is: ; in, It is a positive definite matrix of topological dependence. This is a topology switching signal. It is a positive definite diagonal matrix. For a matrix containing Laplace Communication Matrix with Leaders The combination matrix, These are the minimum and maximum eigenvalues ​​of the matrix, respectively. This is the Lipschitz constant. To adjust the parameters, It is an n-order identity matrix.

[0008] Furthermore, the distributed dynamic event triggering function is as follows: , Dynamic auxiliary variables satisfy: , Performance adaptive variables satisfy: , in, These are topology-related combined parameters. To estimate the error, This is the state estimate. For topologically dependent state combinations, As a dynamic variable, To adjust the parameters, This is for tracking error.

[0009] Furthermore, the compact form of the error dynamics is: ; in, To track the error vector, To estimate the error vector, It is an N-order identity matrix. For Kronecker product, This is a nonlinear error vector.

[0010] Furthermore, topology-related parameters They are respectively: , , , in, To adjust the matrix, They are respectively The inverse matrix and its inverse transpose.

[0011] Furthermore, the average length of stay meets the following requirements: ;in, , , topological sets, Topology The corresponding positive definite matrix, For decomposition parameters, For topology The corresponding adjustment parameters.

[0012] Further, S3 includes the following sub-steps: S31, determining the currently active topology, and extracting the adjacency matrix, Laplacian matrix, and combination matrix corresponding to the topology. S32, Obtain matrix eigenvalue related parameters; S33, Calculate based on topological parameters and Configure according to system performance requirements Adjust the range of parameter values; S33, initialize dynamic auxiliary variables. With performance adaptive variables S34. Clarify the initial value constraints and parameter relationships in the dynamic update equation; S35. Integrate parameters and variables to construct a complete distributed dynamic event triggering function, and determine the topological dependencies and computational logic of each component in the function.

[0013] Furthermore, S4 includes the following sub-steps: S41, defining each follower in the trigger interval. Internal state estimates ,in, S42, define the estimation error based on the state estimate, the actual state, and the leader's state. With tracking error Construct the error vector and S43, Combining the dynamics model of followers and leaders, and substituting the controller gain expression, the time derivative equation of the tracking error is derived; S44, The individual error dynamics are integrated into a system-level compact form through Kronecker product operation, incorporating the combined effects of topology switching, control input, and nonlinear error terms.

[0014] Furthermore, S5 includes the following sub-steps: S51, setting the trigger time determination criteria, and clarifying when the trigger function... Or topology switching caused , The event is triggered when a set of intelligent agents is formed; S52, at the triggering time Update the state estimates of the followers. The current actual state Reset estimation error S53, based on the updated state estimate and topology information, recalculate the controller input. S54 ensures that the control signal matches the current topology and system state; S55 broadcasts the updated state estimate to the neighboring agent of the follower, completes the local information interaction update, and provides the basis for the control logic of the next trigger interval.

[0015] Beneficial Effects: This invention proposes a dynamic event-triggered consistency control method for nonlinear multi-agent systems based on topology information. By designing a time-varying controller gain dependent on the currently active topology and constructing a distributed dynamic event triggering function in conjunction with topology-related parameters, it fully utilizes local information from different topologies, adapts to system characteristic changes brought about by dynamic topology switching, and significantly reduces the conservatism of the control strategy. Addressing the problem of insufficient resource utilization efficiency, topology-dependent dynamic auxiliary variables and performance adaptive variables are introduced to flexibly adjust the triggering threshold in real time, avoiding the drawbacks of excessively frequent triggering in static triggering mechanisms. This significantly reduces communication and computing resource consumption while ensuring control accuracy. Simultaneously, by defining state estimates and various errors, a compact form of system-level error dynamics is derived, integrating the effects of topology switching, control input, and nonlinear terms to ensure the stability of control performance under nonlinear dynamics. The system stability is analyzed using a topology-dependent Lyapunov function, and Zeno's abnormal triggering behavior is avoided through threshold adaptive constraints, enabling followers to quickly converge and track the leader's state. This demonstrates strong adaptability and high efficiency in nonlinear multi-agent systems with limited communication resources and dynamic topology switching. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0017] Figure 1 This is a flowchart of the method steps of the present invention. Detailed Implementation

[0018] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. The application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0019] like Figure 1As shown, a dynamic event-triggered consensus control method for a nonlinear multi-agent system based on topology information is proposed, comprising the following steps: 1. A dynamic event-triggered consensus control method for a nonlinear multi-agent system based on topology information, characterized by comprising the following steps: S1, constructing a multi-agent system containing one leader and N followers, describing the communication topology through a time-varying directed graph, introducing dynamic auxiliary variables and performance adaptive variables to design a topology-dependent time-varying controller gain and a distributed dynamic event triggering function, defining the adjacency matrix, the Laplace matrix, and the matrix H containing the leader's communication state, and clarifying the dynamic model of the followers and the leader and the Lipschitz nonlinear constraints; S2, based on the matrix pair stabilization property and the topology connectivity assumption, designing a time-varying controller gain dependent on the currently active topology. The gain is determined by solving the topology-dependent Riccati inequality, relating the system matrix, input matrix, and positive definite matrix; S3 introduces topology-dependent dynamic auxiliary variables and performance adaptive variables through a distributed dynamic event triggering function, and correlates estimation error and state tracking-related variables by adjusting the triggering threshold in real time; S4 defines the follower state estimate, estimation error, and tracking error, derives a compact expression of error dynamics, and integrates the effects of topology switching, control input, and nonlinear terms; S5 sets event triggering rules, with the triggering time determined by the fulfillment of the triggering function conditions or by topology switching, updating the controller and broadcasting state information at the triggering time; S6 uses a topology-dependent Lyapunov function to analyze system stability and avoids Zeno abnormal triggering behavior through threshold adaptive constraints.

[0020] Step S1 completes the basic construction and parameter definition of the multi-agent system, providing model support for subsequent control strategy design. In specific implementation, the system composition is first clarified, defining an overall architecture including one leader agent and N follower agents. The value of N can be adjusted according to the actual application scenario; a typical value is six followers to adapt to small to medium-sized collaborative task requirements. Next, a time-varying directed graph is used to describe the communication topology between agents. This graph characterizes individual agents and their directed communication connections through node sets and edge sets. Based on this, an adjacency matrix, a Laplace matrix, and a combination matrix H are defined. Elements in the adjacency matrix use 0 or 1 to indicate whether a direct communication link exists between corresponding agents. The Laplace matrix is ​​constructed using the rule that diagonal elements are the sum of adjacent elements in the corresponding row, and off-diagonal elements are the negative values ​​of adjacent elements. The combination matrix H integrates the Laplace matrix and the leader communication state matrix; the latter uses diagonal elements of 0 or 1 to indicate whether each follower can receive information from the leader. Subsequently, the dynamics models of followers and leaders are defined. These models must include state variables, control inputs, and nonlinear terms, while strictly adhering to the Lipschitz nonlinear constraint. This constraint requires that the difference in the nonlinear functions be bounded, and the Lipschitz constant must be determined based on the agent's dynamic characteristics, typically taking a value of 0.33 to suit most nonlinear scenarios. The entire implementation process must ensure that all matrix dimensions match, the topology accurately reflects the communication relationships between agents, and the dynamics model is consistent with the actual agent characteristics, laying a solid foundation for subsequent control gain design, trigger mechanism construction, and stability analysis.

[0021] Step S2 involves designing the topology-dependent time-varying controller gain to improve control adaptability by fully utilizing topology information. During implementation, two key preconditions are first verified: first, the stabilizing properties of matrix pairs, ensuring suitable control inputs for system stability, which is the foundation of controller design; and second, the topology connectivity assumption, requiring a fixed and connected joint communication graph within each time interval, including a directed spanning tree rooted at the leader, ensuring information can be transmitted from the leader to all followers. Based on these two assumptions, the controller gain design process is initiated. The core is solving the Riccati inequality related to the currently active topology. This inequality integrates the system matrix, input matrix, positive definite matrix, nonlinear term correlation matrix, and topology characteristic parameters. The positive definite matrix must meet strict positive definiteness requirements, and its dimension must be consistent with the system state dimension. During the solution process, the eigenvalue information of the adjacency matrix, Laplace matrix, and combination matrix H of the current topology must be considered. The eigenvalue calculation uses the standard matrix eigenvalue solving method to ensure accurate results. The obtained time-varying controller gain is deeply bound to the currently active topology. When the topology changes, the Riccati inequality is immediately resolved based on the parameters of the new topology to update the controller gain, ensuring that the gain always matches the characteristics of the current topology. The gain design needs to balance stability and dynamic response performance. By adjusting the adjustment parameter in the inequality (typically 0.3), the gain characteristics are optimized so that the controller can both suppress nonlinear interference and adapt to the system structure changes brought about by topology switching, providing core control support for subsequent high-precision consistent tracking.

[0022] Step S3 involves constructing a distributed dynamic event triggering function, achieving intelligent adjustment of the trigger threshold through multi-variable collaboration. First, the currently active topology is determined, and key parameters such as the eigenvalues, inverse matrix, and inverse transpose matrix of the corresponding adjacency matrix, Laplacian matrix, and combination matrix are extracted. Standard matrix operation methods are used to calculate the topology-related combination parameters, which directly determine the topology adaptability of the triggering function. Next, a series of adjustment parameters are set based on system performance requirements, including weight parameters in the dynamic triggering function (range 0 to 1), decay coefficients of dynamic auxiliary variables (greater than 0, typical range 0.5 to 0.7), decay coefficients of performance adaptive variables (greater than 0, typical range 1 to 1.5), and proportional parameters (greater than 0). All parameters need to be optimized through multiple trials to ensure the flexibility and stability of the triggering mechanism. Subsequently, the dynamic auxiliary variables and performance adaptive variables are initialized. The initial values ​​of the dynamic auxiliary variables are set to non-negative values ​​(typical range 1.2 to 2.8), and the initial value of the performance adaptive variables is set to 0. The dynamic update equations for both are defined, and these equations are correlated with estimation errors, state tracking-related variables, and adjustment parameters. Finally, by integrating the above parameters and variables, a complete distributed dynamic event triggering function is constructed. The function takes the square of the estimation error and the square of the state tracking related variables as core inputs. Through the real-time updating of dynamic auxiliary variables and performance adaptive variables, the triggering threshold is adjusted online, ensuring that the triggering function can not only respond to changes in system state but also adapt to dynamic topology switching, providing a basis for judgment for the execution of subsequent event triggering rules.

[0023] Step S4 defines the error and models the dynamics, comprehensively integrating the influence of multiple factors to accurately characterize the system dynamics. During implementation, three key variables are first defined: 1) the follower state estimate, which is the actual state of the follower at the most recent trigger moment, used to replace the real-time state for control calculations and information interaction, reducing communication overhead; 2) the estimation error, the difference between the state estimate and the actual state, directly reflecting the accuracy of the state estimate; and 3) the tracking error, the difference between the follower's actual state and the leader's state, a core indicator for measuring consistency performance. Based on these three variables, combined with the controller gain designed in step S2, the dynamic model defined in step S1, and the current topology characteristics, the time derivative equation of the tracking error is derived. The derivation process strictly follows the rules of calculus and matrix operations to ensure the accuracy of the equation. Subsequently, the error dynamics equations of individual followers are integrated into a system-level compact form through Kronecker product operations. This form clearly presents the error evolution law of the overall system, integrating the structural changes brought about by topology switching, the adjustment effect of control input, and the interference effect of nonlinear terms. The influence of nonlinear terms is reflected by the nonlinear error vector, which is the set of differences between the nonlinear functions of each follower and the nonlinear function of the leader. The entire modeling process requires repeated verification of the correctness of the equation derivation to ensure that the compact form can accurately reflect the combined effect of various factors on error evolution, providing precise dynamic model support for subsequent trigger rule setting and stability analysis.

[0024] Step S5 achieves efficient scheduling of control updates and information interaction by clarifying event triggering rules and execution procedures. During implementation, triggering time determination criteria are first set, including two types of triggering conditions: first, the dynamic event triggering function value is greater than or equal to 0, indicating that the estimation error has exceeded the acceptable range and control updates need to be initiated; second, topology switching causes changes in the adjacency matrix elements, indicating a change in the system communication structure, requiring resynchronization of information and control updates. After the triggering time arrives, four core operations are executed according to a fixed procedure: First, the follower's state estimate is updated, resetting it to the current actual state to ensure subsequent control calculations are based on the latest state information; second, the estimation error is reset to zero at the triggering time, laying the foundation for error accumulation calculation in the next trigger interval; third, the controller input is recalculated, combining the updated state estimate, current topology information, and the time-varying controller gain designed in step S2, using a preset control input calculation method to obtain a new control signal, ensuring that the control input matches the current system state and topology; fourth, information is broadcast, sending the updated state estimate to all neighboring agents of the follower via the communication link, and the neighboring agents update their own neighbor state caches based on the received information. The entire process must strictly adhere to real-time requirements. The detection cycle at the trigger moment must be set according to the dynamic characteristics of the system (the typical cycle is much shorter than the system convergence time) to ensure timely response to state changes and topology switching. While ensuring control accuracy, the number of triggers should be minimized to reduce communication and computing resource consumption.

[0025] Step S6 involves system stability analysis and anomaly elimination to ensure the reliable achievement of the consistency control objective. First, a topology-dependent Lyapunov function is constructed. This function integrates a positive definite matrix, a tracking error vector, dynamic auxiliary variables, and performance adaptive variables. The positive definite matrix is ​​consistent with that in step S2. The function form must meet the basic requirements of Lyapunov stability analysis, i.e., the function value is non-negative and its derivative reflects the system's stability trend. Next, stability is analyzed using the average residence time condition. The average residence time must satisfy strict inequality constraints, and its value must be greater than the threshold related to the gain change caused by topology switching (a typical range is set according to the topology switching frequency). By analyzing the derivative of the Lyapunov function and combining it with the topology switching number constraint, it is proven that the system satisfies global exponential consistency, and the convergence rate expression is clarified. The convergence rate must meet the preset performance requirements (ensuring that followers can quickly track the leader's state). Then, the Zeno behavior exclusion process is initiated. Based on the sequence superposition lemma, the event triggering time sequence is decomposed into two subsequences: one triggered by a dynamic triggering function and the other by a topology switch. It is then proven that no Zeno behavior exists in each subsequence: for the dynamic triggering subsequence, the minimum interval between adjacent triggering times (strictly greater than 0) is derived by analyzing the upper bound of the derivative of the estimation error and combining it with the triggering function constraint; for the topology switch subsequence, the average dwell time condition is used to ensure that the number of switches is finite within a finite time.

[0026] Preferably, the dynamic models for followers and leaders are as follows: , in, For the i-th follower state, For the follower to control the input, For the leader state, A, B, and C are constant matrices of appropriate dimensions. For a continuously differentiable nonlinear function that satisfies the Lipschitz condition, Let n be a real vector space. It is a time variable.

[0027] Specifically, the dynamics model is based on the actual operational characteristics of multi-agent systems, fully considering the dynamic differences and commonalities between followers and leaders. First, the core motion laws of the agents are clarified. Followers need to receive control input to achieve state adjustment; therefore, a control input term is introduced into the model. The leader, as the global guide, requires no external control input and generates the desired trajectory solely through its own dynamic evolution; therefore, the model does not include a control input term. Both include state evolution terms dominated by the system matrix and nonlinear terms. The introduction of nonlinear terms is to characterize the actual non-ideal dynamic characteristics of the agents, and by constraining the nonlinear function to satisfy continuous differentiability and the Lipschitz condition, the analyzability and stability of the model are ensured. The state vector dimension is determined based on the actual degrees of freedom of the agent's motion. The system matrix, input matrix, and nonlinear term-related matrices need to be obtained through actual measurement or identification of the agent's dynamic parameters. The Lipschitz constant is determined through gradient boundary analysis of the nonlinear function, and the time variable covers the entire operating cycle of the system. The model is established following the principle of "commonality + individuality". It ensures the consistency of the dynamic models of followers and leaders, and distinguishes the functional positioning of the two by controlling the presence or absence of input items. When implementing it, it is necessary to first determine the matrix parameters and nonlinear function forms through experiments or simulations, and then substitute them into the model for subsequent control strategy design, so as to provide a precise dynamic basis for the entire consistency control method.

[0028] Preferably, the topologically dependent Riccati inequality is: , The controller gain is: ; in, It is a positive definite matrix of topological dependence. This is a topology switching signal. It is a positive definite diagonal matrix. For a matrix containing Laplace Communication Matrix with Leaders The combination matrix, These are the minimum and maximum eigenvalues ​​of the matrix, respectively. This is the Lipschitz constant. To adjust the parameters, It is an n-order identity matrix.

[0029] Specifically, Riccati inequalities and controller gain formulas are used to implement topology-dependent stable control design. First, based on system stability requirements and Lyapunov stability theory, a basic inequality framework is constructed, including the system matrix, input matrix, and positive definite matrix. To adapt to dynamic topology switching, positive definite matrices and combination matrices bound to the current topology are introduced. Through eigenvalue analysis of the combination matrix, a minimum-to-maximum eigenvalue ratio term is introduced to balance control performance under different topologies. Adjustment parameters are added to enhance the flexibility of the inequalities and ensure the existence of feasible solutions. The controller gain formula is derived through optimal solution analysis of the Riccati inequality, directly linking the positive definite matrix to the input matrix to ensure the gain maximizes the control effect. The topology-dependent positive definite matrix is ​​obtained by solving the corresponding Riccati inequality for each possible topology. The combination matrix is ​​generated by superimposing the Laplace matrix of the current topology and the leader communication matrix. The Lipschitz constant is determined based on the characteristics of the nonlinear term. Adjustment parameters, while ensuring the positive definiteness of the inequalities, are selected through multiple simulations and adjustments to achieve optimal values ​​(typical values ​​must satisfy stability constraints). During implementation, it is necessary to first obtain the correlation matrix of the currently active topology, calculate the eigenvalue parameters, substitute them into the Riccati inequality to solve for the positive definite matrix, and then calculate the time-varying controller gain through the gain formula. When switching topologies, the above process is repeated to update the gain, ensuring that the control action matches the topology characteristics in real time.

[0030] Preferably, the distributed dynamic event triggering function is: , Dynamic auxiliary variables satisfy: , Performance adaptive variables satisfy: , in, These are topology-related combined parameters. To estimate the error, This is the state estimate. For topologically dependent state combinations, As a dynamic variable, To adjust the parameters, This is for tracking error.

[0031] Specifically, the distributed dynamic event trigger function and related variable update equations achieve a balance between efficient resource utilization and topology adaptability. During the trigger function derivation, estimation error and state tracking-related variables are used as core inputs. A threshold adjustment mechanism is constructed by introducing topology-dependent parameters. The update equations for dynamic auxiliary variables and performance adaptive variables are designed based on the system state change rate to ensure that the variables reflect system dynamics in real time. In the dynamic auxiliary variable update equation, the decay coefficient is used to control the variable convergence speed, and the proportional parameter is used to balance the influence of the error term. The performance adaptive variable update equation achieves adaptive threshold adjustment through tracking error feedback. The weight parameters must be selected between 0 and 1 to balance the influence of estimation error and state tracking terms. The decay coefficient of the dynamic auxiliary variable is greater than 0 (typically 0.5 to 0.7), and the decay coefficient of the performance adaptive variable is greater than 0 (typically 1 to 1.5). Initial values ​​must meet non-negativity constraints and zero initial value requirements. Topology-related combination parameters are calculated from the matrix eigenvalues ​​of the current topology. The rationale behind this design is that dynamic auxiliary variables can suppress frequent fluctuations in trigger signals, and performance adaptive variables can adjust trigger sensitivity according to the magnitude of tracking error. During implementation, two types of variables need to be initialized first, and estimation error and tracking error need to be collected in real time. The variable values ​​are then substituted into the update equation to calculate the variable values. Finally, all parameters are integrated to construct the trigger function. The function value is used to determine whether an event is triggered, thus achieving a balance between resource consumption and control accuracy.

[0032] Preferably, the compact form of the error dynamics is: ; in, To track the error vector, To estimate the error vector, It is an N-order identity matrix. For Kronecker product, This is a nonlinear error vector.

[0033] Specifically, the compact form of error dynamics integrates the influence of multiple factors to achieve system-level dynamic analysis. First, based on the tracking error and estimation error defined in step S4, and combined with the dynamic models of followers and leaders, the original dynamic equations of the error are obtained by eliminating state variables. To adapt to the distributed characteristics and the impact of topology switching, the Kronecker product is introduced to integrate the individual error equations into a system-level vector form. The topology-related combination matrix and controller gain matrix are incorporated into the equations, and a nonlinear error vector is constructed to centrally reflect the nonlinear differences of all followers and leaders. This derivation strictly follows the rules of matrix operations and the principle of error propagation, ensuring that the equations accurately reflect the combined effects of topology switching, control input, and nonlinear terms on error evolution. The dimension of the error vector is determined by the number of followers and the state dimension; the dimension of the identity matrix matches the dimension of the error vector; and the nonlinear error vector is directly composed of the difference between the nonlinear functions of each follower and the nonlinear function of the leader. During implementation, the state information of all followers and leaders needs to be collected in real time, the tracking error and estimation error calculated, and the error vector and nonlinear error vector constructed. Combined with the combination matrix of the current topology and the controller gain, and substituted into the compact form equations, the system-level error evolution law can be obtained, providing a foundation for subsequent stability analysis.

[0034] Preferably, topology-related parameters They are respectively: , , , in, To adjust the matrix, They are respectively The inverse matrix and its inverse transpose.

[0035] Specifically, topology-related parameters provide quantitative support for trigger functions and stability analysis. Based on the current topology's combination matrix, positive definite matrix, and adjustment matrix, parameter expressions are constructed through matrix inversion, transpose, and Kronecker product operations. The minimum eigenvalue term ensures the positive definiteness of the parameters, while the maximum eigenvalue term determines the upper bound of the parameters. The introduction of the adjustment matrix enhances the flexibility of the parameters, adapting to performance requirements under different topologies. The adjustment matrix is ​​selected as a positive definite matrix, determined through simulation debugging based on system stability requirements. The inverse and inverse transpose matrices of the combination matrix are obtained through matrix inversion operations, with the identity matrix dimension consistent with the state dimension. The remaining parameters utilize the topology-related matrices and eigenvalues ​​already determined in the preceding claims. The physical significance of these parameters lies in their quantification of the impact of topology characteristics on trigger thresholds and stability, providing crucial quantitative basis for the rational construction of trigger functions and the derivation of stability criteria. During implementation, it is necessary to first obtain the core parameters such as the combination matrix and positive definite matrix of the current topology, calculate the inverse matrix, transpose matrix and eigenvalues, substitute them into the parameter expression to obtain three topology-related parameters, and use them as intermediate variables for trigger function construction and stability analysis to ensure the topology adaptability and quantification rigor of the entire control method.

[0036] Preferably, the average dwell time meets the following requirements: ;in, , , topological sets, Topology The corresponding positive definite matrix, For decomposition parameters, For topology The corresponding adjustment parameters.

[0037] Specifically, the average residence time constraint formula provides a quantitative criterion for system stability under dynamic topology switching. Based on the jump characteristics of the Lyapunov function at the time of topology switching, and combined with the eigenvalue relationship between the positive definite matrices corresponding to each topology, a parameter is constructed by introducing the maximum eigenvalue ratio term. This parameter quantifies the maximum possible jump amplitude of the Lyapunov function under different topology switching. At the same time, by integrating the attenuation coefficient, adjustment parameter, and topology-related variables obtained from stability analysis, the minimum attenuation-related parameter is obtained. This parameter reflects the system's stable attenuation capability under a single topology. Substituting these two parameters into the core constraint logic of average residence time, that is, limiting the topology switching frequency by residence time to ensure that the system can maintain overall stability during the switching process, the constraint formula for average residence time is derived. The set of all possible topologies needs to be determined based on the communication characteristics of the agents in the actual application scenario. The positive definite matrix corresponding to each topology is obtained by solving the Riccati inequality under that topology. The decomposition parameters need to be selected with positive values ​​to ensure the effectiveness of the attenuation term. Other adjustment parameters follow the topology-related values ​​determined in the preceding claims. The maximum eigenvalue ratio term is calculated by traversing all topology combinations, and the minimum attenuation-related parameter is determined by taking the minimum value of the corresponding parameter under each topology. The formula is based on the theory of switching system stability. By limiting the minimum average interval of topology switching, the system fluctuations brought about by switching are balanced with the stable attenuation effect under a single topology. In implementation, the maximum eigenvalue ratio corresponding to all topology combinations and the attenuation-related parameters under each topology need to be calculated first to determine the threshold of the average dwell time. During system operation, the topology switching frequency is monitored in real time to ensure that it meets the average dwell time constraint, providing a key guarantee for the global exponential stability of the entire system in a dynamic topology environment.

[0038] Preferably, step S3 includes the following sub-steps: S31, determining the currently active topology and extracting the adjacency matrix, Laplacian matrix, and combination matrix corresponding to the topology. S32, Obtain matrix eigenvalue related parameters; S33, Calculate based on topological parameters and Configure according to system performance requirements Adjust the range of parameter values; S33, initialize dynamic auxiliary variables. With performance adaptive variables S34. Clarify the initial value constraints and parameter relationships in the dynamic update equation; S35. Integrate parameters and variables to construct a complete distributed dynamic event triggering function, and determine the topological dependencies and computational logic of each component in the function.

[0039] Specifically, step S3 consists of four sub-steps for constructing distributed dynamic event trigger functions. Each sub-step is progressive and closely related to topology characteristics and system parameters. In step S31, the currently active communication topology is first determined through the topology detection module. The adjacency matrix, Laplace matrix, and combination matrix corresponding to this topology are extracted from the preset topology database. A matrix eigenvalue solving algorithm is used to calculate key parameters such as the minimum and maximum eigenvalues ​​of these matrices, ensuring that the obtained topology parameters accurately reflect the communication connection relationships and information flow characteristics between agents. In step S32, based on the topology parameters obtained in S31, three topology-related intermediate parameters and two threshold adjustment parameters are calculated using a preset combination operation formula. Based on the system's preset control accuracy and resource consumption targets, the value ranges of adjustment parameters such as weight parameters and proportional parameters in the trigger function are determined. The weight parameters must be limited to a specific range to balance the influence of error terms and tracking terms, and the proportional parameters must be greater than a specific threshold to ensure the effectiveness of the trigger function. S33 assigns non-negative initial values ​​to dynamic auxiliary variables and sets zero initial values ​​for performance adaptive variables according to parameter initial value constraints. It clarifies the relationship logic between each parameter in the dynamic update equations of the two types of variables and the topology parameters and error variables, ensuring that variable updates can respond in real time to system state and topology changes. S34 integrates the topology parameters, calculation parameters, adjustment parameters, and initialization variables obtained from the previous three steps. It integrates the components according to preset function construction rules, clarifying the operational relationships and logical order of topology-dependent parameters, dynamic variables, and error variables in the function, forming a complete distributed dynamic event triggering function. This ensures that the function accurately reflects topology characteristics and system state, providing a reliable basis for subsequent trigger rule execution.

[0040] Preferably, S4 includes the following sub-steps: S41, defining each follower in the trigger interval Internal state estimates ,in, S42, define the estimation error based on the state estimate, the actual state, and the leader's state. With tracking error Construct the error vector and S43, Combining the dynamics model of followers and leaders, and substituting the controller gain expression, the time derivative equation of the tracking error is derived; S44, The individual error dynamics are integrated into a system-level compact form through Kronecker product operation, incorporating the combined effects of topology switching, control input, and nonlinear error terms.

[0041] Specifically, step S4 consists of four sub-steps: defining the error and constructing a system-level dynamic model. Each sub-step revolves around the error variable and gradually integrates the model. In S41, an independent trigger interval identifier is first set for each follower. The trigger times of each follower are recorded using timestamps, clarifying that within the current trigger interval, the follower's state estimate is the actual state at the most recent trigger time. This design avoids real-time state transmission and reduces communication overhead through a state caching mechanism. The boundary of the trigger interval is defined by the previous trigger time and the current potential trigger time. In S42, based on the state estimates defined in S41, the estimation error and tracking error for each follower are calculated. The estimation error is the difference between the state estimate and the real-time actual state, and the tracking error is the difference between the real-time actual state and the leader's real-time state. Subsequently, system-level tracking error vectors and estimation error vectors are constructed in the order of follower numbers. The vector dimensions are jointly determined by the number of followers and the state dimension of a single agent. S43 calls upon the follower and leader dynamics model determined in step S1, substitutes the topology-dependent controller gain designed in step S2 into the follower dynamics equation, and derives the time derivative equation of each follower's tracking error through calculus operations and error variable substitution. The derivation process strictly follows the operational rules of dynamics equations to ensure that the equations accurately reflect the evolution of errors. S44 uses Kronecker product operations to integrate the individual error dynamics equations obtained in S43. The structural changes brought about by topology switching are incorporated into the system-level model through a combination matrix, the influence of control input is reflected through the controller gain matrix, and the disturbance of nonlinear terms is represented by a nonlinear error vector. Finally, a compact form of system-level error dynamics is formed, ensuring that the model can comprehensively integrate the influence of multiple factors and provide an accurate mathematical foundation for subsequent stability analysis.

[0042] Preferably, step S5 includes the following sub-steps: S51, setting trigger time determination criteria, and clarifying when the trigger function... Or topology switching caused , The event is triggered when a set of intelligent agents is formed; S52, at the triggering time Update the state estimates of the followers. The current actual state Reset estimation error S53, based on the updated state estimate and topology information, recalculate the controller input. S54 ensures that the control signal matches the current topology and system state; S55 broadcasts the updated state estimate to the neighboring agent of the follower, completes the local information interaction update, and provides the basis for the control logic of the next trigger interval.

[0043] Specifically, step S5 consists of four sub-steps that determine the rules for triggering events and the execution process. Each sub-step is executed sequentially according to time and logical relationships. In S51, two types of triggering criteria are first established. The first criterion calculates the distributed dynamic event trigger function value in real time; when the function value meets preset conditions, the event is triggered. The second criterion uses a topology monitoring module to detect changes in the adjacency matrix elements in real time; when any element changes, it is determined as a topology switch and an event is triggered. The intelligent agent set clearly defines the scope of communication objects to be monitored, ensuring that the triggering criteria cover both system state changes and topology changes. In S52, after the triggering time arrives, the state update process is immediately initiated. Sensors collect the current actual state of the follower, update the state estimate to this actual state, and simultaneously reset the estimation error to zero, completing the synchronous update of state and error. This provides initial conditions for error accumulation and state estimation in the next trigger interval. Based on the updated state estimate from S52, and combining the latest information of the currently active topology with the time-varying controller gain designed in step S2, S53 calls a preset control input calculation algorithm to recalculate the controller input signal adapted to the current state and topology, ensuring that the control signal can accurately respond to the current dynamic characteristics of the system. S54 broadcasts the updated state estimate to all neighboring agents of the follower through the agent's communication module. Upon receiving the signal, the neighboring agents update their locally stored follower state information, completing local information exchange and providing the latest neighbor state data for subsequent control calculations and trigger determinations, ensuring the consistency of distributed cooperative control.

[0044] A dynamic event-triggered consistency control method for nonlinear multi-agent systems based on topology information addresses the conservatism of existing methods due to insufficient integration of topology characteristics. Its core advantage lies in constructing a topology-dependent full-process design system. The controller gain is adjusted in real-time according to the currently activated topology, and the triggering function and related parameters are deeply bound to topology characteristics. This fully leverages the local information of different topologies, accurately adapting to system characteristic changes brought about by dynamic topology switching, significantly reducing the conservatism of the control strategy and improving adaptability to dynamic topology environments. To address the issue of insufficient resource utilization efficiency, dynamic auxiliary variables and performance adaptive variables are innovatively introduced to achieve real-time flexible adjustment of the trigger threshold, avoiding the drawback of frequent triggering as the system approaches steady state in static triggering mechanisms. Simultaneously, through state estimation and error integration design, unnecessary communication interactions and computational overhead are significantly reduced while ensuring control accuracy, greatly improving resource utilization efficiency.

[0045] Furthermore, this method enhances its ability to overcome both advantages and disadvantages through systematic technical design. By defining multiple error variables and deriving a system-level compact dynamic model, it comprehensively integrates the combined effects of topology switching, control input, and nonlinear terms, effectively addressing the interference of nonlinear dynamics on control performance and ensuring control stability under complex characteristics. Through topology-related stability analysis tools and a dedicated anomaly elimination mechanism, it ensures that the system achieves fast and stable exponential convergence tracking in dynamic topology and nonlinear environments. This not only solves the problem of existing methods' inability to guarantee stability under multiple constraints but also further optimizes dynamic response performance, making the method more practical and reliable in nonlinear multi-agent systems with limited communication resources and dynamic topology switching.

[0046] It should be understood that the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. A and B can be singular or plural. Additionally, the character " / " in this article generally indicates an "or" relationship between the preceding and following related objects, but it can also represent an "and / or" relationship. Please refer to the context for a more accurate understanding.

[0047] In this invention, "at least one" means one or more, and "more than one" means two or more. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of a single item or a plurality of items. For example, at least one of a, b, or c can represent: a, b, c, ab, ac, bc, or abc, where a, b, and c can be a single item or multiple items.

[0048] It should be understood that, in various embodiments of the present invention, the order of the above-mentioned processes does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0049] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0050] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the devices, apparatuses, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0051] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A dynamic event-triggered consistency control method for a nonlinear multi-agent system based on topological information, characterized in that, Includes the following steps: S1. Construct a multi-agent system with one leader and N followers. Describe the communication topology using a time-varying directed graph. Introduce dynamic auxiliary variables and performance adaptive variables to design the topology-dependent time-varying controller gain and distributed dynamic event triggering function. Define the adjacency matrix, Laplace matrix, and matrix H containing the leader's communication state. Clarify the dynamic model of the followers and the leader and the Lipschitz nonlinear constraints. S2, based on the matrix pair stabilization property and the topological connectivity assumption, designs a time-varying controller gain that depends on the currently active topology. This gain is determined by solving the topology-related Riccati inequality, which is associated with the system matrix, the input matrix, and the positive definite matrix. S3 introduces topology-dependent dynamic auxiliary variables and performance adaptive variables through a distributed dynamic event triggering function, and correlates estimation error and state tracking-related variables by adjusting the triggering threshold in real time. S4 defines the follower state estimate, estimation error, and tracking error, derives a compact expression for error dynamics, and integrates the effects of topology switching, control input, and nonlinear terms. S5, set event triggering rules. The triggering time is triggered when the triggering function meets the conditions or when the topology is switched. The controller is updated and the status information is broadcast at the triggering time. S6 uses topologically dependent Lyapunov functions to analyze system stability and avoids Zeno abnormal triggering behavior through threshold adaptive constraints.

2. The dynamic event-triggered consistency control method for a nonlinear multi-agent system based on topological information according to claim 1, characterized in that, The dynamic models for followers and leaders are as follows: ， in, For the i-th follower state, For the follower to control the input, For the leader state, A, B, and C are constant matrices of appropriate dimensions. , For a continuously differentiable nonlinear function that satisfies the Lipschitz condition, Let n be a real vector space. It is a time variable.

3. The dynamic event-triggered consistency control method for a nonlinear multi-agent system based on topological information according to claim 2, characterized in that, The Riccati inequality for topological dependence is: ， The controller gain is: ,in, It is a positive definite matrix of topological dependence. This is a topology switching signal. It is a positive definite diagonal matrix. For a matrix containing Laplace Communication Matrix with Leaders The combination matrix, , These are the minimum and maximum eigenvalues ​​of the matrix, respectively. This is the Lipschitz constant. To adjust the parameters, It is an n-order identity matrix.

4. The dynamic event-triggered consistency control method for a nonlinear multi-agent system based on topological information according to claim 3, characterized in that, The distributed dynamic event triggering function is: ， Dynamic auxiliary variables satisfy: ， Performance adaptive variables satisfy: ， in, These are topology-related combined parameters. To estimate the error, This is the state estimate. For topologically dependent state combinations, , As a dynamic variable, To adjust the parameters, This is for tracking error.

5. The dynamic event-triggered consistency control method for a nonlinear multi-agent system based on topological information according to claim 4, characterized in that, The compact form of error dynamics is: ； in, To track the error vector, To estimate the error vector, It is an N-order identity matrix. For Kronecker product, This is a nonlinear error vector.

6. The dynamic event-triggered consistency control method for a nonlinear multi-agent system based on topological information according to claim 5, characterized in that, Topology-related parameters They are respectively: ， ， ， in, To adjust the matrix, They are respectively The inverse matrix and its inverse transpose.

7. The dynamic event-triggered consistency control method for a nonlinear multi-agent system based on topological information according to claim 6, characterized in that, The average length of stay meets the following requirements: ;in, ， ， topological sets, Topology The corresponding positive definite matrix, For decomposition parameters, For topology The corresponding adjustment parameters.

8. The dynamic event-triggered consistency control method for a nonlinear multi-agent system based on topological information according to claim 7, characterized in that, S3 includes the following sub-steps: S31, determine the currently active topology, and extract the adjacency matrix, Laplacian matrix, and combination matrix corresponding to the topology. S32, Obtain matrix eigenvalue related parameters; S33, Calculate based on topological parameters and Configure according to system performance requirements Adjust the range of parameter values; S33, initialize dynamic auxiliary variables. With performance adaptive variables S34. Clarify the initial value constraints and parameter relationships in the dynamic update equation; S35. Integrate parameters and variables to construct a complete distributed dynamic event triggering function, and determine the topological dependencies and computational logic of each component in the function.

9. A dynamic event-triggered consistency control method for a nonlinear multi-agent system based on topological information according to claim 8, characterized in that, S4 includes the following sub-steps: S41, defining each follower in the trigger interval. Internal state estimates ,in, S42, define the estimation error based on the state estimate, the actual state, and the leader's state. With tracking error Construct the error vector and S43, Combining the dynamics model of followers and leaders, and substituting the controller gain expression, the time derivative equation of the tracking error is derived; S44, The individual error dynamics are integrated into a system-level compact form through Kronecker product operation, incorporating the combined effects of topology switching, control input, and nonlinear error terms.

10. A dynamic event-triggered consistency control method for a nonlinear multi-agent system based on topological information, as described in claim 9, is characterized in that... S5 includes the following sub-steps: S51, setting trigger time determination criteria, and clarifying when the trigger function... Or topology switching caused , , The event is triggered when a set of intelligent agents is formed; S52, at the triggering time Update the state estimates of the followers. The current actual state Reset estimation error S53, based on the updated state estimate and topology information, recalculate the controller input. S54 ensures that the control signal matches the current topology and system state; S55 broadcasts the updated state estimate to the neighboring agent of the follower, completes the local information interaction update, and provides the basis for the control logic of the next trigger interval.

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