An event-triggered random complex network finite-time synchronization control method based on sampling data

Abstract

The application relates to a random complex network finite time synchronization control method based on sampling data under event triggering, and specifically comprises the following steps: a complex network dynamic differential equation model with random disturbance is established, a controller for realizing finite time synchronization is established, a control signal of the controller is updated when a synchronization error exceeds a preset threshold at a discrete sampling moment, finite time synchronization performance analysis is carried out through a Lyapunov function, a multi-objective optimization function considering the synchronization error, a control cost and a convergence time is constructed by adopting a raccoon optimization algorithm, controller parameters are optimized, an optimal parameter combination is output, and an optimal control scheme is obtained. Compared with the prior art, the application has the advantages of low power consumption, high real-time performance and strong robustness.

Description

Technical Field

[0001] This invention relates to the field of synchronization control of complex networks, and in particular to a finite-time synchronization control method for stochastic complex networks based on sampled data under event triggering. Background Technology

[0002] Complex networks are widely used in fields such as energy, transportation, communication, and biological systems, and their synchronization capability directly affects the stability and performance of the system. Finite-time synchronization control has become one of the core research directions in recent years. This method enables the system to achieve state synchronization within a finite time, and has advantages such as fast convergence speed and strong anti-interference ability.

[0003] To reduce communication overhead, event-triggered control mechanisms are widely used. Under this mechanism, control signals are only updated or sent when the system state meets a certain trigger condition, thereby greatly reducing unnecessary information transmission.

[0004] Random disturbances are ubiquitous factors in real-world systems, such as sensor noise, external random shocks, and parameter uncertainties. Therefore, studying finite-time synchronization of stochastic complex networks has significant practical implications.

[0005] Traditional finite-time synchronization methods for complex networks typically employ continuous feedback control, requiring real-time updates to control signals. While this technique achieves finite-time synchronization, it results in a significant waste of communication bandwidth and computational resources, making it difficult to apply in resource-constrained practical engineering scenarios.

[0006] Existing technologies attempt to combine event-triggered mechanisms with finite-time control, but they still struggle to integrate with sampling mechanisms and fail to achieve finite-time synchronization within a discrete sampling framework. Continuous communication leads to significant computational and data transmission, increasing system energy consumption.

[0007] Existing research on controller parameters mostly relies on empirical adjustments and lacks systematic optimization methods, making it difficult to balance convergence speed and control cost under finite time conditions.

[0008] In real industrial systems, noise and uncertainty are common, and traditional control methods do not perform well in random environments.

[0009] Chinese invention patent CN113759979B discloses an event-driven online trajectory planning method for a UAV sling system. This method transforms the dynamic equation of the sling system's load swing angle into the form of a nonlinear affine system, introduces a reduced valence function and reinforcement learning mechanism, and solves the optimal control problem for suppressing the load swing angle through neural network approximation. This invention reduces the computational burden on the UAV's onboard processor for handling both neural network learning and adaptive optimal control processes through online trajectory planning, resulting in better swing reduction and improved positioning performance. However, it still suffers from problems such as high continuous control communication costs making precise finite-time synchronization difficult, difficulty adapting control parameters to dynamic conditions in complex network environments, lack of systematic manual parameter tuning, and difficulty in dynamically balancing communication, computation, and control.

[0010] In summary, there is currently a lack of a finite-time synchronization control method for random complex networks based on sampled data under event-triggered conditions to solve or partially solve the above problems. Summary of the Invention

[0011] The purpose of this invention is to overcome the shortcomings of the prior art by providing a finite-time synchronization control method for random complex networks based on sampled data under event triggering, so as to solve or partially solve the problems of high continuous control communication costs making it difficult to achieve accurate finite-time synchronization, difficulty in adapting control parameters to dynamic operating conditions in complex network environments, lack of systematic manual parameter tuning, and difficulty in dynamically balancing communication-computation-control.

[0012] The objective of this invention can be achieved through the following technical solutions: This invention provides a finite-time synchronization control method for random complex networks based on sampled data under event triggering, the method specifically comprising: S1. Establish a differential equation model of the dynamics of a complex network with random perturbations; S2. Based on the differential equation model, a controller for achieving finite-time synchronization is constructed, a synchronization error is defined, and the control signal of the controller is updated when the synchronization error exceeds a preset threshold at discrete sampling times. The trigger function of the controller is determined according to the set fixed sampling period. S3. Perform finite-time synchronization performance analysis using the Lyapunov function, and substitute the expected value of the corresponding Lyapunov function into the controller to obtain the parameter constraints of the controller; S4. The Raccoon Optimization Algorithm is used to construct a multi-objective optimization function that comprehensively considers synchronization error, control cost and convergence time. The controller parameters are tuned, the optimal parameter combination is output, and the optimal control scheme is obtained, so as to realize the finite-time synchronization control of a random complex network based on sampled data under event triggering.

[0013] As a preferred technical solution, the differential equation model is expressed as follows: In the formula, , For the number of nodes, the first Node status , For the nonlinear function of the node, positive constant For the coupling strength of complex networks, and Given a constant matrix, For external coupling matrix, For internal coupling matrix, For the first The state of each node For the control input to be designed, For diffusion coupling function, Indicates the first The state of each node Let Wiener process be used to represent random perturbation. To represent the differential, Let be the node dimension.

[0014] As a preferred technical solution, the random disturbance is modeled as follows: In the formula, For random perturbation, Let be an unknown but bounded constant vector. Given a bounded matrix, This is the standard Wiener process.

[0015] As a preferred technical solution, the controller is represented as follows: In the formula, positive numbers and To control the gain, , representing the coefficients that guarantee the system convergence in a finite time. For the first The node of the first Next trigger time Represents a symbolic function. Indicates synchronization error. This indicates taking the absolute value. This indicates a control input.

[0016] As a preferred technical solution, the synchronization error is defined as follows: The error dynamics system is represented as: In the formula, the target synchronization trajectory Dynamics of isolated nodes generate, For the nonlinear function of the node, positive constant For the coupling strength of complex networks, and Given a constant matrix, For external coupling matrix, For internal coupling matrix, For diffusion coupling function, Let be an unknown but bounded constant vector. , indicating the first The random disturbance term experienced by each node, and To control the gain, This indicates taking the absolute value. Represents a symbolic function. For the first The node of the first Next trigger time Denotes the coefficients that guarantee the system convergence in a finite time. Given a bounded matrix, This is the standard Wiener process.

[0017] As a preferred technical solution, the trigger function is expressed as follows: In the formula, For the first Measurement error at each node, For trigger parameters, For the first The node of the first Next trigger time Indicates synchronization error. Indicates taking the absolute value; The triggering time of the triggering function is: In the formula, The infimum represents the earliest time that satisfies the condition. A positive integer, representing the number of sampling periods that have elapsed since the last trigger. The sampling period.

[0018] As a preferred technical solution, the Lyapunov function is derived by substituting its mathematical expectation into the controller: In the formula, For mathematical expectation, Let be the Lipschitz constant of the nonlinear function, satisfying the inequality , , represented as a Lyapunov function, For the number of nodes, This indicates taking the largest eigenvalue. , is a symmetric matrix. Given a constant matrix, Given the transpose of a constant matrix, , is a symmetric matrix. Indicates synchronization error. This represents the transpose of the synchronization error. For the coupling strength of complex networks, For external coupling matrix, For internal coupling matrix, for, and To control the gain, For the first The node of the first Next trigger time Represents a symbolic function. Denotes the coefficients that guarantee the system convergence in a finite time. Let be an unknown but bounded constant vector. These are elements of the noise correlation matrix. Indicates taking the absolute value; The upper bound of the controller is represented as: In the formula, , representing the attenuation coefficient, For triggering parameters.

[0019] As a preferred technical solution, stability analysis is performed based on the upper bound of the controller, resulting in the following inequality: In the formula, , indicating taking The largest eigenvalue, For external coupling matrix, It is a symmetric matrix. Let be the Lipschitz constant of the nonlinear function. The noise correlation matrix is... This represents the fractional power of the Lyapunov function. The coefficients that guarantee the system convergence within a finite time. This indicates taking the absolute value.

[0020] As a preferred technical solution, the finite time is manifested as follows: In the formula, and To control the gain, The attenuation coefficient is... For the coupling strength of complex networks, for The largest eigenvalue, To obtain the largest eigenvalue, , , , Let be the Lipschitz constant of the nonlinear function. The noise correlation matrix is... For mathematical expectation, For trigger parameters, and This represents the fractional power of the Lyapunov function. Denotes the coefficients that guarantee the system convergence in a finite time. For a limited time.

[0021] As a preferred technical solution, the multi-objective optimization function is expressed as: In the formula, These are the weighting coefficients. As a penalty item, Let be the error function. For controller, For a limited time, This indicates taking the absolute value.

[0022] Compared with the prior art, the present invention has at least one of the following beneficial effects: (1) This invention combines the event triggering mechanism of periodic sampling with finite time control, and updates the control signal only when the discrete sampling time and the synchronization error exceeds the preset threshold. It designs finite time synchronization for discrete triggering times, ensuring that the system can accurately predict and reach the synchronization state within a finite time even when the information is discontinuous. This solves the problem that traditional discrete control is difficult to achieve accurate finite time synchronization due to information loss, while continuous control has high communication costs. It achieves finite time synchronization while reducing communication resource consumption.

[0023] (2) This invention introduces the Raccoon optimization algorithm and deeply integrates it with the event triggering mechanism-finite time control framework to construct a multi-objective optimization function that comprehensively considers synchronization error, control cost and convergence time to optimize the controller parameters and obtain the optimal parameter combination that satisfies multiple constraints. This solves the problem that the control parameters are difficult to adapt to dynamic working conditions in complex network environments and that manual parameter tuning leads to the system performance not reaching the theoretical optimal level. It achieves the balance between optimizing system performance and cost while ensuring finite time synchronization accuracy.

[0024] (3) This invention works in a closed loop by using a periodic sampling event triggering mechanism, a finite-time synchronous control based on discrete sampling data and a multi-objective optimization function. Periodic event triggering provides the system with an energy-saving underlying architecture, finite-time control ensures the determinism of the system response, and the raccoon optimization algorithm provides the optimal parameters for dynamic adaptation. This solves the problem of the difficulty in dynamically balancing communication, computing and control in complex industrial control scenarios, and enables the system to simultaneously meet the requirements of low power consumption, high real-time performance and strong robustness in resource-constrained practical engineering. Attached Figure Description

[0025] Figure 1 This is a system flowchart of the present invention; Figure 2 This is a distribution diagram of the event triggering times at each node in the experiment. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0027] To address the problems existing in the prior art, this embodiment provides a finite-time synchronization control method for random complex networks based on sampled data under event triggering. This method achieves finite-time synchronization of the random network system by acquiring information and triggering control signals at discrete sampling times. Specifically, it includes: S1. Establish a dynamic model of a complex network with random perturbations.

[0028] Assume the network includes The node, its first Node status It satisfies the following stochastic differential equation: In the formula, For the nonlinear function of the node, positive constant For the coupling strength of complex networks, and Given a constant matrix, Let be an external coupling matrix that satisfies the condition that the row sum is zero and the diagonal elements are negative. For internal coupling matrix, For the first The state of each node For the control input to be designed, This is a diffusion coupling function that describes the random coupling between nodes. Indicates the first The state of each node Let Wiener process be used to represent random perturbation. To represent the differential, Let be the node dimension.

[0029] The random disturbance term is further modeled as follows: In the formula, For random perturbation, Let be an unknown but bounded constant vector. Given a bounded matrix, This is the standard Wiener process.

[0030] S2. To achieve finite-time synchronization, design a controller of the following form: In the formula, positive numbers and To control the gain, , representing the coefficients that guarantee the system convergence in a finite time. For the first The node of the first Next trigger time Represents a symbolic function. Indicates synchronization error. This indicates taking the absolute value. This indicates a control input.

[0031] S3. Assume the target's synchronous trajectory Dynamics of isolated nodes Generate, and define the synchronization error of each node as: Then the error dynamics system can be written as: In the formula, For the nonlinear function of the node, positive constant For the coupling strength of complex networks, and Given a constant matrix, For external coupling matrix, For internal coupling matrix, For diffusion coupling function, Let be an unknown but bounded constant vector. , indicating the first The random disturbance term experienced by each node, and To control the gain, This indicates taking the absolute value. Represents a symbolic function. For the first The node of the first Next trigger time Denotes the coefficients that guarantee the system convergence in a finite time. Given a bounded matrix, This is the standard Wiener process.

[0032] like Figure 1 As shown, the method of the present invention achieves finite-time synchronization of a random network system by acquiring information and triggering control signals at discrete sampling moments. Based on the event triggering mechanism, at each sampling moment, the system collects the real-time status of each node in the network, calculates the current synchronization error and measurement error based on the obtained status, determines whether the current error meets the preset triggering conditions, updates the control signal if the conditions are met, and maintains the original control signal if the conditions are not met. The finally determined control signal is sent to the network node and waits for the next sampling moment.

[0033] S4. Assume the fixed sampling period is a positive number. The set of sampling times is The measurement error is... , If the trigger parameter is specified, then the trigger function is defined as follows: In the formula, For the first Measurement error at each node, For trigger parameters, For the first The node of the first Next trigger time Indicates synchronization error. This indicates taking the absolute value.

[0034] The trigger time is determined as follows: In the formula, The infimum represents the earliest time that satisfies the condition. A positive integer, representing the number of sampling periods that have elapsed since the last trigger. The sampling period.

[0035] S5. To analyze the finite-time synchronization performance of the system, select... Let Lyapunov be the function. Taking the expected value of this Lyapunov function and substituting it into the controller design, we obtain the following through derivation: In the formula, For mathematical expectation, Let be the Lipschitz constant of the nonlinear function, satisfying the inequality , , represented as a Lyapunov function, For the number of nodes, This indicates taking the largest eigenvalue. It is a symmetric matrix. Given a constant matrix, Given the transpose of a constant matrix, It is a symmetric matrix. Indicates synchronization error. This represents the transpose of the synchronization error. For the coupling strength of complex networks, For external coupling matrix, For internal coupling matrix, For the first The state of each node and To control the gain, For the first The node of the first Next trigger time Represents a symbolic function. Denotes the coefficients that guarantee the system convergence in a finite time. Let be an unknown but bounded constant vector. These are elements of the noise correlation matrix. Indicates taking the absolute value; The constant represents the upper bound of the system's nonlinear strength and is used in stability analysis to constrain the growth rate of the nonlinear term. The upper bound of the control term is further derived based on the event triggering conditions: in .

[0036] The inequality can be derived as follows: Combining the upper bound conditions of all terms, we obtain: In the formula, For trigger parameters, , indicating taking The largest eigenvalue, For external coupling matrix, It is a symmetric matrix. Let be the Lipschitz constant of the nonlinear function. The noise correlation matrix is... This represents the fractional power of the Lyapunov function. The coefficients used to ensure the system converges within a finite time. Noise correlation matrix. It is a diagonal matrix, where each element ,parameter Determined by the boundary conditions of random perturbation: In the formula, This represents the error difference form of the diffusion coupling function. The intensity matrix represents the random perturbation. Represents the trace of a matrix. Indicates the first The synchronization error of each node.

[0037] matrix It characterizes the cumulative intensity of random disturbances experienced by each node in the network, under finite-time synchronization conditions. As a negative term, the stronger the surface random disturbance, the lower the control gain required to achieve synchronization. and The matrix is ​​also correspondingly larger. ,in satisfy , It is a coupling function The Lipschitz constant. The introduction of these disturbances enhances the practicality and robustness of the control method, enabling it to adapt to real-world complex network environments.

[0038] S6. If control parameters exist Makes the following matrix inequalities hold: The inequality is then derived as follows: In the formula, and To control the gain, The attenuation coefficient is... For the coupling strength of complex networks, for The largest eigenvalue, To obtain the largest eigenvalue, , , , Let be the Lipschitz constant of the nonlinear function. The noise correlation matrix is... For mathematical expectation, For trigger parameters, and This represents the fractional power of the Lyapunov function. This represents the coefficient that guarantees the system convergence within a finite time.

[0039] According to the finite-time stability theory, the system will [result in] a finite-time stability event. Internal synchronization is achieved, and satisfy: S7. To optimize control performance, the Raccoon Optimization Algorithm is used to optimize the control parameters. Perform automatic tuning. The objective function for optimization is: In the formula, These are the weighting coefficients. This is a penalty term used to ensure that synchronization conditions are met. Let be the error function. For controller, For a limited time.

[0040] The raccoon optimization algorithm performs global search and local optimization by simulating raccoon predation behavior, and finally outputs a result that makes... The optimal control scheme is obtained by minimizing the optimal parameter combination, thereby achieving finite-time synchronization control of a stochastic complex network based on sampled data under event triggering.

[0041] Experiments were conducted based on the method of this invention. A stochastic complex network with 6 nodes, each with a dimension of 3, was designed. A vehicle lateral dynamics model based on sliding mode control was used as the system. Each node in the network was affected by random perturbations, and the coupling strength was 0.1. The experimental results are shown in Table 1. The event trigger times are sparsely distributed and aperiodic, and the control signal is updated only at the trigger time, significantly reducing the execution frequency. The average trigger rate of the system is only 26.4%, compared to the 100% trigger rate of the traditional continuous control method, reducing the system communication load by 73.6%. The event trigger times of each node are as follows: Figure 2 As shown, the experimental results fully demonstrate that the design can significantly reduce the consumption of communication and computing resources and improve resource utilization efficiency.

[0042] Table 1 Event Trigger Statistics for Each Node In summary, the method of this invention, through a novel control strategy and the introduction of an optimization algorithm, successfully achieves finite-time synchronization of random complex networks while significantly reducing resource consumption, and has broad practical application value.

[0043] 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 person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered 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 finite-time synchronization control method for a stochastic complex network based on sampled data under event-triggered conditions, characterized in that, The method specifically includes: S1. Establish a differential equation model of the dynamics of a complex network with random perturbations; S2. Based on the differential equation model, a controller for achieving finite-time synchronization is constructed, a synchronization error is defined, and the control signal of the controller is updated when the synchronization error exceeds a preset threshold at discrete sampling times. The trigger function of the controller is determined according to the set fixed sampling period. S3. Perform finite-time synchronization performance analysis using the Lyapunov function, and substitute the expected value of the corresponding Lyapunov function into the controller to obtain the parameter constraints of the controller; S4. The Raccoon Optimization Algorithm is used to construct a multi-objective optimization function that comprehensively considers synchronization error, control cost and convergence time. The controller parameters are tuned, the optimal parameter combination is output, and the optimal control scheme is obtained, so as to realize the finite-time synchronization control of a random complex network based on sampled data under event triggering.

2. The event-triggered, sampled data-based finite-time synchronization control method for stochastic complex networks according to claim 1, characterized in that, The differential equation model is expressed as: In the formula, , For the number of nodes, the first Node status , For the nonlinear function of the node, positive constant For the coupling strength of complex networks, and Given a constant matrix, For external coupling matrix, For internal coupling matrix, For the first The state of each node For the control input to be designed, For diffusion coupling function, Indicates the first The state of each node Let Wiener process be used to represent random perturbation. To represent the differential, Let be the node dimension.

3. The event-triggered, sampled data-based finite-time synchronization control method for stochastic complex networks according to claim 2, characterized in that, The random perturbation is modeled as follows: In the formula, For random perturbation, Let be an unknown but bounded constant vector. Given a bounded matrix, This is the standard Wiener process.

4. The event-triggered, sampled data-based finite-time synchronization control method for stochastic complex networks according to claim 1, characterized in that, The controller is represented as: In the formula, positive numbers and To control the gain, , representing the coefficients that guarantee the system convergence in a finite time. For the first The node of the first Next trigger time Represents a symbolic function. Indicates synchronization error. This indicates taking the absolute value. This indicates a control input.

5. The event-triggered, sampled data-based finite-time synchronization control method for stochastic complex networks according to claim 1, characterized in that, The synchronization error is defined as The error dynamics system is represented as: In the formula, the target synchronization trajectory Dynamics of isolated nodes generate, For the nonlinear function of the node, positive constant For the coupling strength of complex networks, and Given a constant matrix, For external coupling matrix, For internal coupling matrix, For diffusion coupling function, Let be an unknown but bounded constant vector. , indicating the first The random disturbance term experienced by each node, and To control the gain, This indicates taking the absolute value. Represents a symbolic function. For the first The node of the first Next trigger time Denotes the coefficients that guarantee the system convergence in a finite time. Given a bounded matrix, This is the standard Wiener process.

6. The event-triggered, sampled data-based finite-time synchronization control method for stochastic complex networks according to claim 1, characterized in that, The trigger function is expressed as follows: In the formula, For the first Measurement error at each node, For trigger parameters, For the first The node of the first Next trigger time Indicates synchronization error. Indicates taking the absolute value; The triggering time of the triggering function is: In the formula, The infimum represents the earliest time that satisfies the condition. A positive integer, representing the number of sampling periods that have elapsed since the last trigger. The sampling period.

7. The event-triggered, sampled data-based finite-time synchronization control method for stochastic complex networks according to claim 1, characterized in that, The Lyapunov function is derived by substituting its mathematical expectation into the controller: In the formula, For mathematical expectation, Let be the Lipschitz constant of the nonlinear function, satisfying the inequality , , represented as a Lyapunov function, For the number of nodes, This indicates taking the largest eigenvalue. , is a symmetric matrix. Given a constant matrix, Given the transpose of a constant matrix, , is a symmetric matrix. Indicates synchronization error. This represents the transpose of the synchronization error. For the coupling strength of complex networks, For external coupling matrix, For internal coupling matrix, For the first The state of each node and To control the gain, For the first The node of the first Next trigger time Represents a symbolic function. Denotes the coefficients that guarantee the system convergence in a finite time. Let be an unknown but bounded constant vector. These are elements of the noise correlation matrix. Indicates taking the absolute value; The upper bound of the controller is represented as: In the formula, , representing the attenuation coefficient, For triggering parameters.

8. The event-triggered, sampled data-based finite-time synchronization control method for stochastic complex networks according to claim 7, characterized in that, Based on the upper bound of the controller, stability analysis yields the following inequality: In the formula, , indicating taking The largest eigenvalue, For external coupling matrix, It is a symmetric matrix. Let be the Lipschitz constant of the nonlinear function. The noise correlation matrix is... This represents the fractional power of the Lyapunov function. To ensure the system converges within a finite time, the coefficients, This indicates taking the absolute value.

9. The event-triggered, sampled data-based finite-time synchronization control method for stochastic complex networks according to claim 1, characterized in that, The finite time is represented as follows: In the formula, and To control the gain, The attenuation coefficient is... For the coupling strength of complex networks, for The largest eigenvalue, To obtain the largest eigenvalue, , , , Let be the Lipschitz constant of the nonlinear function. The noise correlation matrix is... For mathematical expectation, For trigger parameters, and This represents the fractional power of the Lyapunov function. Denotes the coefficients that guarantee the system convergence in a finite time. For a limited time.

10. The event-triggered, sampled data-based finite-time synchronization control method for stochastic complex networks according to claim 1, characterized in that, The multi-objective optimization function is expressed as: In the formula, These are the weighting coefficients. As a penalty item, Let be the error function. For controller, For a limited time, This indicates taking the absolute value.

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