Two-stage event triggering finite time control method for complex dynamic network

Abstract

The invention relates to a two-stage event triggering finite time control method for a complex dynamic network, which comprises the following steps of: S1, constructing a system model, constructing a complex dynamic network CDN (Content Delivery Network) consisting of Q mutually coupled nodes, modeling each node, and setting a synchronization target of the complex dynamic network CDN; s2, an event-triggered intermittent traction pulse controller is designed, a novel time-triggered intermittent control strategy is designed, and the starting moment and the ending moment of a control window are determined with the help of a special auxiliary function by means of a two-stage event triggering mechanism; and S3, the complex dynamic network CDN carries out finite time synchronization by utilizing two-stage event trigger time control. According to the invention, a two-stage event triggering mechanism is designed for driving the start and end moments of a control window in intermittent control, and a controller is allowed to realize finite time synchronization in an intermittent operation mode.

Description

Technical Field

[0001] This invention relates to the field of automatic control technology, and in particular to a two-stage event-triggered finite-time control method for complex dynamic networks. Background Technology

[0002] Complex dynamic networks (CDNs) are systems composed of a large number of interacting nodes, which can represent individuals or units within physical, biological, social, or technological systems. Each node follows its own dynamic laws while interconnecting and interacting with other nodes through edges. CDN research involves multiple disciplines, including mathematics, physics, biology, computer science, and social sciences. In recent years, CDNs have been widely used in fields such as communication and information dissemination, power systems, transportation and logistics, ecosystems and disease transmission, and neuroscience, attracting widespread attention. Synchronization is an important and widespread phenomenon in CDNs, referring to the ability of nodes in the network to reach the same state or behavioral pattern under certain conditions. As a collective behavior, CDN synchronization has received extensive research in recent years due to its wide application in many fields such as information processing, image encryption, and secure communication. In existing technologies, some pioneering work has been done on CDN synchronization, and various control strategies have been applied to CDN synchronization, such as adaptive control, traction control, and event-triggered control.

[0003] Finite-time synchronization refers to the use of appropriate control strategies in a network to ensure that the states of all nodes reach a precise consistency within a finite time. This means that the state error between all nodes becomes zero after a specific point in time and remains constant throughout the synchronization process. Therefore, compared to exponential synchronization, finite-time synchronization not only focuses on the final synchronization result but also emphasizes the speed and efficiency of reaching the synchronized state.

[0004] Compared with continuous control strategies, discontinuous control strategies have several unique advantages when dealing with complex dynamic systems, especially in terms of achieving finite-time synchronization, enhancing system robustness, and coping with uncertainty and external disturbances.

[0005] Intermittent control is a non-continuous control strategy that regulates the dynamic behavior of a system by applying control inputs at specific time intervals. Unlike traditional continuous control, intermittent control does not require continuous adjustment of the control signal throughout the entire operation. Instead, it activates or deactivates the controller for certain time periods based on pre-set rules or conditions. This control method is particularly suitable for applications that are sensitive to energy consumption or have limited control resources.

[0006] Event-triggered control (ETC) is an intelligent control strategy designed to reduce control resource usage by updating control inputs only when specific conditions are met, such as system state or error. Unlike traditional methods based on time-periodic sampling and control updates, ETC determines when to perform control actions based on actual needs, effectively reducing computational, communication, and energy consumption. In an ETC system, the controller does not operate at fixed time intervals but only performs control updates when predefined "events" occur. These events are typically based on changes in system state or whether other performance indicators exceed predetermined thresholds. For example, in a networked control system, a new control signal is only sent to the actuator when the state detected by the sensor deviates from the expected trajectory by more than a certain limit.

[0007] Both intermittent control and event-triggered control are discontinuous control methods, offering advantages such as energy savings. However, for intermittent control, the start time and width of the control interval are preset, posing a risk of redundant control actions. Meanwhile, event-triggered control still employs a continuous control strategy between two event trigger times, making its implementation relatively difficult in practical engineering.

[0008] Therefore, there is an urgent need to design a two-level event triggering mechanism to drive the start and end times of the control window in intermittent control, allowing the controller to achieve finite-time synchronization in an intermittent manner. Summary of the Invention

[0009] To address the technical problems existing in the prior art, this invention provides a two-level event-triggered finite-time control method for complex dynamic networks. By designing a two-level event-triggered mechanism to drive the start and end times of the control window in intermittent control, the controller can achieve finite-time synchronization in an intermittent operation manner.

[0010] The method of this invention is implemented using the following technical solution: a two-level event-triggered finite-time control method for complex dynamic networks, comprising the following steps:

[0011] S1. Construct a system model, build a complex dynamic network CDN consisting of Q mutually coupled nodes, model each node, and set the synchronization target of the complex dynamic network CDN.

[0012] S2. Design an event-triggered intermittent traction pulse controller. Design a novel time-triggered intermittent control strategy. Utilize a two-level event triggering mechanism and, with the help of a special auxiliary function, determine the start and end times of the control window.

[0013] S3, Complex Dynamic Network CDN, uses two-level event-triggered time control for limited-time synchronization.

[0014] The present invention is implemented using the following technical solution: a two-stage event-triggered finite-time control system for complex dynamic networks, comprising:

[0015] System Model Building Module: Used to build the system model, construct a complex dynamic network CDN consisting of Q mutually coupled nodes, model each node, and set the synchronization target of the complex dynamic network CDN;

[0016] Two-level time-triggered module: used for the design of event-triggered intermittent traction pulse controller. A new time-triggered intermittent control strategy is designed. With the help of a special auxiliary function, the start and end times of the control window are determined by a two-level event-triggered mechanism.

[0017] Finite-time synchronization module: Complex dynamic network CDNs perform finite-time synchronization by utilizing two-level event-triggered time control.

[0018] The present invention also proposes a storage medium on which a computer program is stored, wherein when the computer program is executed by a processor, the steps of the two-level event-triggered finite-time control method of the present invention are implemented.

[0019] The present invention also proposes a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, it implements the two-level event-triggered finite-time control method of the present invention.

[0020] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0021] 1. This invention designs a two-level event-triggered intermittent finite-time control strategy, which can ensure finite-time synchronization of complex dynamic network CDNs. Unlike existing control schemes, this invention constructs a special auxiliary function to design a two-level event-triggered scheme that can be used for intermittent control, effectively reducing control costs and communication load.

[0022] 2. The controller designed in this invention not only adopts an intermittent control framework, but also determines the start and end times of the control window by the designed event mechanism. This greatly reduces the implementation difficulty of the controller, while also effectively reducing control costs and avoiding redundant control actions. Attached Figure Description

[0023] Figure 1 This is a flowchart of the method of the present invention;

[0024] Figure 2 This is a flowchart illustrating the process of the controller implementing CDN limited event synchronization in this embodiment.

[0025] Figure 3 This is a structural diagram of the system of the present invention. Detailed Implementation

[0026] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0027] Example

[0028] like Figure 1 , Figure 2 As shown in the figure, this embodiment of a two-level event-triggered finite-time control method for complex dynamic networks includes the following steps:

[0029] S1. Construct a system model, build a complex dynamic network CDN consisting of Q mutually coupled nodes, model each node, and set the synchronization target of the complex dynamic network CDN.

[0030] S2. Design an event-triggered intermittent traction pulse controller. Design a novel time-triggered intermittent control strategy. Utilize a two-level event triggering mechanism and, with the help of a special auxiliary function, determine the start and end times of the control window.

[0031] S3, Complex Dynamic Network CDN, uses two-level event-triggered time control for limited-time synchronization.

[0032] Specifically, in this embodiment, the specific process of step S1 is as follows:

[0033] S11. Construct a complex dynamic network CDN consisting of Q mutually coupled nodes, and model each node as follows:

[0034]

[0035] in, It is a constant matrix; This represents the state vector of the i-th node; This represents the state vector of the j-th node; It is a nonlinear function; Represents the control input; Λ represents the internal coupling matrix of a complex dynamic network CDN; l ij This represents an element in the external coupling matrix, used to characterize the strength of external coupling; Let l represent the external coupling matrix, which reflects the neighbor matrix of the network topology; if there is a link between the i-th node and the j-th node, then l ij >0; otherwise, l ij =0; for j=i,

[0036] S12. Set the synchronization goals for complex dynamic network CDN as follows:

[0037]

[0038] in, Represents a state vector, defined This is the synchronization error;

[0039] If nonlinear function The Lipschitz condition is satisfied, meaning there exists a positive constant β such that:

[0040]

[0041] For any Both are valid.

[0042] Specifically, in this embodiment, the specific process of step S2 is as follows:

[0043] S21, Order and Let m represent the m-th control interval and the m-th non-control interval, respectively. t m Let τ be the starting time of the m-th control interval. m This represents the width of the m-th control interval. To achieve finite-time synchronization in complex dynamic network CDNs, a novel event-triggered intermittent control strategy is designed:

[0044]

[0045] Where r1 represents the control gain, used to eliminate the effects of nonlinearity, r1 > 0; r2 represents another control gain, used to achieve finite-time control, r2 > 0; sign(·) is the sign function, t represents time, that is, the state value at time t, and T represents the transpose.

[0046] S22. Use event triggering conditions to determine the start time t of the control window. m and the end time t m +τ m The two-level event triggering mechanism is designed as follows:

[0047]

[0048] in, express The transpose of is used to construct a large column vector. Let f be a positive definite and differentiable function that satisfies:

[0049]

[0050] Where C represents a parameter that adjusts the settlement time; the larger C is, the shorter the settlement time, and vice versa. Θ represents the initial value, and Θ represents a freely adjustable value. The coefficients of the initial value are Θ = diag{θ1, θ2}, where diag{·} represents a diagonal matrix.

[0051] Specifically, in this embodiment, in the two-level event triggering mechanism, in a special type of auxiliary function With the help of [the system], the start and end times of the control window can be determined. This type of special function is only effective for intermittent finite-time control and cannot be applied to other control schemes. It is specifically designed for intermittent finite-time control.

[0052] Under the action of the event-triggered intermittent control strategy of the present invention, the following synchronization error system can be obtained according to formulas (1) and (2):

[0053]

[0054] in,

[0055] The error system can also be represented as follows:

[0056]

[0057] in, Represents the Kronecker product; A represents the system matrix. The large matrix after Kronecker product I Q Let Q represent the identity matrix.

[0058] Specifically, in this embodiment, the specific process of step S3 is as follows:

[0059] S31. If the nonlinear function The Lipschitz condition is satisfied, and the control parameters r1 and r2 satisfy:

[0060]

[0061] Where, λ max (·) and λ min (·) represent the maximum and minimum eigenvalues ​​of the matrix, respectively, and β represents... The coefficient in, A T This represents the transpose of matrix A.

[0062] S32. Under the control of the designed controller, complex dynamic network CDN can achieve finite-time synchronization, and the settling time satisfies:

[0063]

[0064] The specific implementation process is as follows:

[0065] Using Lyapunov functions:

[0066]

[0067] for The controller is in the working state; according to step S31, we can obtain:

[0068]

[0069] make because According to formula (8), we can obtain the following for in, Describing auxiliary functions The upper realm, Describing auxiliary functions The upper bound; according to The definition can be used to prove that for and Therefore, there exists a moment Make

[0070] for The controller is in sleep mode; it can be obtained

[0071]

[0072] Where ξ is a notation,

[0073] Based on the two-level event triggering mechanism, we can further conclude that: for Therefore, we can obtain: for any t ≥ t0, because It is stable over a finite period of time, therefore It will also converge to zero within a finite time. Therefore, complex dynamic network CDNs can achieve finite-time stability through the designed two-stage event-triggered intermittent control, and the settling time T satisfies... Therefore, complex dynamic network CDNs can achieve finite-time synchronization under the controller designed in this invention.

[0074] Specifically, in this embodiment, step S32 further includes the following steps:

[0075] When t = tm At that time, according to formula (4), we can obtain: when Control input Therefore, from formula (8), we can obtain:

[0076]

[0077] when At that time, control input We can obtain:

[0078]

[0079] according to and The definition of is as follows: Therefore, it can be obtained

[0080] but

[0081] when When the control input is zero, the controller is not working; this can be obtained from the event triggering mechanism. If the system dynamics are divergent when there is no control input, i.e., ξ>0, then we have Then according to as well as It can be further obtained This means that in the designed event triggering mechanism, there is a minimum interval between the start and end times of the control interval, as well as between the end time of the control interval and the start time of the next control interval.

[0082] Compared with similar existing controllers, such as intermittent controllers and event-triggered controllers, the two-stage event-triggered intermittent control designed in this invention has certain advantages, as shown in Table 1:

[0083] Table 1 Comparison of the controller designed in this patent with similar existing controllers

[0084]

[0085] The specific advantages are as follows: The controller designed in this invention not only adopts an intermittent control framework, but also determines the start and end times of the control window by the designed event mechanism. This greatly reduces the implementation difficulty of the controller, while also effectively reducing control costs and avoiding redundant control actions.

[0086] like Figure 3 As shown, based on the same inventive concept, the present invention also provides a two-stage event-triggered finite-time control system for complex dynamic networks, comprising:

[0087] System Model Building Module: Used to build the system model, construct a complex dynamic network CDN consisting of Q mutually coupled nodes, model each node, and set the synchronization target of the complex dynamic network CDN;

[0088] Two-level time-triggered module: used for the design of event-triggered intermittent traction pulse controller. A new time-triggered intermittent control strategy is designed. With the help of a special auxiliary function, the start and end times of the control window are determined by a two-level event-triggered mechanism.

[0089] Finite-time synchronization module: Complex dynamic network CDNs perform finite-time synchronization by utilizing two-level event-triggered time control.

[0090] Furthermore, this invention also proposes a storage medium and a computer device. The storage medium stores a computer program, which, when executed by a processor, implements steps S1-S3 of the two-level event-triggered finite-time control method of this invention. The computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the two-level event-triggered finite-time control method of this invention, i.e., the process including the aforementioned steps S1-S3.

[0091] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A two-stage event-triggered finite-time control method for complex dynamic networks, characterized in that, Includes the following steps: S1. Construct a system model, build a complex dynamic network CDN consisting of Q mutually coupled nodes, model each node, and set the synchronization target of the complex dynamic network CDN. S2. Design an event-triggered intermittent traction pulse controller. Design a novel time-triggered intermittent control strategy. Utilize a two-level event triggering mechanism and, with the help of a special auxiliary function, determine the start and end times of the control window. S3, Complex Dynamic Network CDN, uses two-level event-triggered time control for limited-time synchronization.

2. The two-stage event-triggered finite-time control method for complex dynamic networks according to claim 1, characterized in that, The specific process of step S1 is as follows: S11. Construct a complex dynamic network CDN consisting of Q mutually coupled nodes, and model each node as follows: in, It is a constant matrix; This represents the state vector of the i-th node; This represents the state vector of the j-th node; It is a nonlinear function; Represents the control input; Λ represents the internal coupling matrix of a complex dynamic network CDN; l ij This represents an element in the external coupling matrix, used to characterize the strength of external coupling; Let l represent the external coupling matrix, which reflects the neighbor matrix of the network topology; if there is a link between the i-th node and the j-th node, then l ij >0; otherwise, l ij =0; for j=i, S12. Set the synchronization goals for complex dynamic network CDN as follows: in, Represents a state vector, defined This is the synchronization error; If nonlinear function The Lipschitz condition is satisfied, meaning there exists a positive constant β such that: For any Both are valid.

3. The two-stage event-triggered finite-time control method for complex dynamic networks according to claim 1, characterized in that, The specific process of step S2 is as follows: S21, Order and Let m represent the m-th control interval and the m-th non-control interval, respectively. t m Let τ be the starting time of the m-th control interval. m Let m represent the width of the m-th control interval; design a novel event-triggered intermittent control strategy: Where r1 represents the control gain, used to eliminate the effects of nonlinearity, r1 > 0; r2 represents another control gain, used to achieve finite-time control, r2 > 0; sign(·) is the sign function, t represents time, that is, the state value at time t, and T represents the transpose. S22. Use event triggering conditions to determine the start time t of the control window. m and the end time t m +τ m The two-level event triggering mechanism is designed as follows: in, express The transpose of is used to construct a large column vector. Let f be a positive definite and differentiable function that satisfies: Where C represents the parameter for adjusting the settling time, Θ represents the initial value, and Θ represents a freely adjustable value. The coefficients of the initial value are Θ = diag{θ1, θ2}, where diag{·} represents a diagonal matrix.

4. The two-stage event-triggered finite-time control method for complex dynamic networks according to claim 3, characterized in that, The specific process of step S2 also includes: Under the action of the event-triggered intermittent control strategy, the following synchronization error system can be obtained according to formulas (1) and (2): in, The error system is also represented as follows: in, Represents the Kronecker product; A represents the system matrix. The large matrix after Kronecker product I Q Let Q represent the identity matrix.

5. The two-stage event-triggered finite-time control method for complex dynamic networks according to claim 4, characterized in that, The specific process of step S3 is as follows: S31. If the nonlinear function The Lipschitz condition is satisfied, and the control parameters r1 and r2 satisfy: Where, λ max (·) and λ min (·) represent the maximum and minimum eigenvalues ​​of the matrix, respectively, and β represents... The coefficient in, A T This represents the transpose of matrix A. S32. Complex dynamic network CDN achieves finite-time synchronization under the action of the designed controller, and the settling time satisfies: The specific implementation process is as follows: Using Lyapunov functions: for The controller is in the working state; according to step S31, we get: make because According to formula (8), for in, Describing auxiliary functions The upper realm, Describing auxiliary functions The upper bound; according to The definition leads to the conclusion that for and There exists a moment Make for The controller is in sleep mode; Where ξ is a notation, Based on the two-level event triggering mechanism, we get: For We obtain: For any t ≥ t0, It is stable for a limited time. If the settlement time T converges to zero in a finite time, then the settlement time T satisfies the following condition.

6. The two-stage event-triggered finite-time control method for complex dynamic networks according to claim 5, characterized in that, The specific process of step S32 also includes: When t = t m At that time, according to formula (4), we get: when Control input From formula (8): when At that time, control input get: according to and The definition of is as follows: get but when When the control input is zero, the controller is not working; this is determined by the event triggering mechanism. If the system dynamics are divergent when there is no control input, i.e., ξ > 0, then we have Then according to as well as get 7. A two-stage event-triggered finite-time control system for complex dynamic networks, characterized in that, include: System Model Building Module: Used to build the system model, construct a complex dynamic network CDN consisting of Q mutually coupled nodes, model each node, and set the synchronization target of the complex dynamic network CDN; Two-level time-triggered module: used for the design of event-triggered intermittent traction pulse controller. A new time-triggered intermittent control strategy is designed. With the help of a special auxiliary function, the start and end times of the control window are determined by a two-level event-triggered mechanism. Finite-time synchronization module: Complex dynamic network CDNs perform finite-time synchronization by utilizing two-level event-triggered time control.

8. A storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the two-level event-triggered finite-time control method according to any one of claims 1-6.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the two-level event-triggered finite-time control method as described in any one of claims 1-6.

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