Fixed-time synchronization coupled chua circuit adaptive pinning control method and system

Abstract

This disclosure provides an adaptive restraint control method and system for fixed-time synchronization of coupled Chua's circuits, relating to the field of network adaptive control technology. The method includes: establishing a nonlinear complex network model of the coupled Chua's circuit; constructing a topology graph of the coupled Chua's circuit and converting it into a strongly connected graph, while simultaneously dividing all Chua's circuit nodes into restraint points and non-restraint points; constructing a system error model of the coupled Chua's circuit, analyzing the synchronization error of the coupled Chua's circuit system, and designing control methods for the restraint points and coupling strength formulas between the non-restraint points and their connected nodes based on Lyapunov stability principles and fixed-time synchronization principles; constructing a Lyapunov function, and solving for the synchronization time of the coupled Chua's circuit based on the controller input of the restraint points and the coupling strength formulas for the non-restraint points. The circuit system disclosed herein can achieve synchronization within a fixed time in various environments.

Description

Technical Field

[0001] This disclosure relates to the field of network adaptive control technology, specifically to an adaptive restraint control method and system for a fixed-time synchronized coupled Chua's circuit. Background Technology

[0002] The statements in this section are merely background information relating to this disclosure and do not necessarily constitute prior art.

[0003] A typical networked complex system consists of many nodes and edges connecting them. Nodes represent different individuals in the real system, while edges represent relationships between them. Typically, an edge is connected between two nodes if they have a specific relationship, and not otherwise. Two nodes connected by an edge are considered adjacent in the network. The complexity of networked complex systems manifests in the following ways: 1. Structural complexity is mainly reflected in the diverse characteristics of the network structure. 2. Network evolution is mainly reflected in the creation and disappearance of nodes or connections. 3. Connection weights between nodes differ and may have directionality. 4. The node set may belong to a nonlinear dynamic system, for example, the node state changes complexly over time. 5. Nodes in a networked complex system can represent anything. 6. These multiple complexities interact, leading to more unpredictable results.

[0004] Due to the rapid development of the internet and the arrival of the network age, various network-related concepts have sprung up like mushrooms after rain. Society's understanding of "networking" has evolved from the original network of tools, power grids, and transportation networks to the abstract concepts of the internet and the neural networks of the human brain. It can be said that networking is ubiquitous. Therefore, through in-depth research on complex networked systems, we can discover and reveal the commonalities and laws governing complex networked systems in nature and human society, and understand and grasp their macroscopic characteristics. Furthermore, through this understanding and mastery, we can regulate complex networked systems to control beneficial synchronization and avoid harmful synchronization, thus achieving beneficial impacts on nature and human life. Beneficial synchronization, such as synchronization in communication networks, can be used for signal identification; harmful synchronization, such as the synchronization phenomenon caused by multiple routers publishing information, leads to network congestion and reduced network speed.

[0005] However, even in the presence of disturbances, synchronization in networked complex systems heavily depends on topology and coupling strength. A key aspect of achieving synchronization in networked complex systems based on spanning trees or strongly connected topologies is the need for sufficiently strong coupling to overcome the effects of node disturbances.

[0006] Finite-time synchronization has garnered significant attention due to its proven ability to achieve faster synchronization. Furthermore, finite-time controllers can enhance system robustness and are better able to counteract disturbances. However, a drawback of finite-time control is that the synchronization time depends on the system's initial conditions, which are not always known for complex networked systems. To address this issue, the concept of fixed-time control theory has been introduced, where synchronization time is independent of initial conditions. Moreover, the synchronization time of a fixed-time control system is a bounded constant that can be predicted based on the controller parameters. Many previous studies have assumed that the coupling strength is constant and known, and the impact of coupling strength on fixed-time synchronization has not been fully investigated. Clearly, coupling strength can be further used to achieve fixed-time synchronization of unconstrained nodes and enhance disturbance resistance. Therefore, research should focus on improving fixed-time constrained control strategies and coupling adjustment algorithms to address persistent disturbance problems.

[0007] The inventors found that research has focused on disturbance suppression and synchronization for various types of disturbances, but has not considered that control strategies need to be designed at each node, which is impractical for complex networked systems. At the same time, the monotonically increasing coupling strength may limit the applicability of the proposed method. Existing methods cannot solve the problem that synchronization time is affected by the initial state of the system under finite-time synchronization, and the initial state of the system is not always known, making it difficult to predict the system synchronization time. In addition, for coupled Chua's circuits, there are many nodes in a system, and controlling all nodes to achieve synchronous stability requires a lot of resources. Summary of the Invention

[0008] To address the aforementioned issues, this disclosure proposes an adaptive restraint control method and system for coupled Chua's circuits with fixed-time synchronization. It proposes a fixed-time adaptive restraint control strategy and coupling adjustment scheme to suppress the negative impact of interference on nodes and resolve the influence of coupling strength on synchronization time under fixed-time synchronization.

[0009] According to some embodiments, the present disclosure adopts the following technical solutions:

[0010] An adaptive restraint control method for a fixed-time synchronized coupled Chua's circuit includes:

[0011] A nonlinear complex network model of coupled Chua's circuit is established, the Chua's circuit nodes in the complex network are obtained, and the dynamic behavior relationship between each Chua's circuit node is expressed by equations.

[0012] Construct a topology diagram of the coupled Chua's circuit, number each Chua's circuit node, convert the topology diagram into a strongly connected graph, and divide all Chua's circuit nodes into two parts: tethered nodes and non-tethered nodes.

[0013] An error model of a coupled Chua's circuit system is constructed. By analyzing the synchronization error of the coupled Chua's circuit system, and based on the Lyapunov stability principle and the fixed-time synchronization principle, a control method for the restraint point and a formula for the coupling strength between the non-restraint point and its connection node are designed.

[0014] Construct a Lyapunov function and, based on the controller input at the restraint point and the coupling strength formula at the non-restraint point, solve for the time required for the coupled Chua's circuit to achieve synchronization.

[0015] According to some embodiments, the present disclosure adopts the following technical solutions:

[0016] A fixed-time synchronized coupled Chua's circuit adaptive restraint control system includes:

[0017] The model building module is used to build a nonlinear complex network model of coupled Chua's circuit, obtain the Chua's circuit nodes in the complex network and express the dynamic behavior relationship between each Chua's circuit node using equations.

[0018] Construct a topology diagram of the coupled Chua's circuit, number each Chua's circuit node, convert the topology diagram into a strongly connected graph, and divide all Chua's circuit nodes into two parts: tethered nodes and non-tethered nodes.

[0019] The controller construction module is used to build an error model of the coupled Chua's circuit system. By analyzing the synchronization error of the coupled Chua's circuit system, and based on the Lyapunov stability principle and the fixed-time synchronization principle, the control method of the restraint point and the coupling strength formula between the non-restraint point and its connection node are designed.

[0020] The control output module is used to construct the Lyapunov function and, based on the controller input at the restraint point and the coupling strength formula at the non-restraint point, solve for the time when the coupled Chua's circuit reaches synchronization.

[0021] According to some embodiments, the present disclosure adopts the following technical solutions:

[0022] A computer-readable storage medium comprising a stored program, wherein the program executes the fixed-time synchronized coupled Chua's circuit adaptive restraint control method.

[0023] According to some embodiments, the present disclosure adopts the following technical solutions:

[0024] An electronic device includes: one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs including an adaptive restraint control method for performing the fixed-time synchronization coupled Chua's circuit.

[0025] Compared with the prior art, the beneficial effects of this disclosure are as follows:

[0026] Compared to finite-time synchronization, the fixed-time synchronization method disclosed herein allows the synchronization time of the coupled Chua's circuit system to be unaffected by the initial system values, making it easier to predict the synchronization time. Using an adaptive restraint control method, unlike previous methods that controlled all nodes in the coupled Chua's circuit system, only a subset of nodes need to be controlled to achieve the same effect, significantly reducing resource consumption. Furthermore, by employing an adaptive coupling adjustment method, the coupling strength changes with environmental variations, enabling the coupled Chua's circuit system in this patent to achieve synchronization within a fixed timeframe in various environments. Attached Figure Description

[0027] The accompanying drawings, which form part of this disclosure, are used to provide a further understanding of this disclosure. The illustrative embodiments of this disclosure and their descriptions are used to explain this disclosure and do not constitute an undue limitation of this disclosure.

[0028] Figure 1 This is a flowchart of the method disclosed herein.

[0029] Figure 2 This is a topology diagram of the coupled Chua's circuit system disclosed herein.

[0030] Figure 3 This is a coupling diagram of the two Chua's circuit systems disclosed herein.

[0031] Figure 4 This is a node state diagram of the coupled Chua's circuit system under fixed-time synchronization.

[0032] Figure 5 This is a system error diagram for the fixed-time synchronization of the coupled Chua's circuit system disclosed herein.

[0033] Figure 6 This is a diagram showing the input of the pinning control under fixed-time synchronization of the coupled Chua's circuit system disclosed herein.

[0034] Figure 7 This is a diagram showing the indirect coupling strength at the non-restraint point under fixed-time synchronization of the coupled Chua's circuit system of this disclosure.

[0035] Figure 8 This is an estimate of the fixed-time synchronization of the coupled Chua's circuit system disclosed herein. Detailed Implementation

[0036] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0037] It should be noted that the following detailed descriptions are illustrative and intended to provide further explanation of this disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure pertains.

[0038] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this disclosure. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms “comprising” and / or “including” are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0039] Example 1

[0040] One embodiment of this disclosure provides an adaptive restraint control method for a coupled Chua's circuit with fixed-time synchronization. This disclosure aims to explore the robustness of fixed-time synchronization and anti-interference performance of coupled Chua's circuits. To achieve these goals, a fixed-time adaptive restraint control strategy and coupling adjustment scheme are proposed, aiming to suppress the negative impact of interference on nodes and address the issue that synchronization time is affected by the initial state of the system under finite-time synchronization, which is not always known, making it difficult to predict the system synchronization time. This solves the problem that for coupled Chua's circuits, controlling all nodes to achieve synchronous stability in a system with many nodes requires significant resources. Adaptive coupling adjustment enables this patent to be effective in various environments. The specific steps are as follows:

[0041] Step 1: Establish a nonlinear complex network system model of the coupled Chua's circuit system: Consider a system consisting of N Chua's circuit nodes and subject to continuous disturbances and control inputs. Based on graph theory, use equations to express the dynamic behavior of each Chua's circuit node.

[0042] Step Two: Construct the topology of the coupled Chua's circuit system, numbering each Chua's circuit node. Using graph theory and the synchronization principle of complex networks, design the topology of the coupled Chua's circuit system as a strongly connected graph to ensure synchronization. This disclosure uses one of the topologies for illustration, such as... Figure 2 The structure shown has each Chua's circuit node directly or indirectly coupled to the other Chua's circuit nodes in the system, and at the same time divides all Chua's circuit nodes into two parts: restraint points and non-restraint points.

[0043] The requirement for this division is that the number of restraint points does not exceed 20% of the total number of nodes in the entire coupled Chua's circuit system.

[0044] Step 3: Construct an error model of the coupled Chua's circuit system by summing the state errors of each connected Chua's circuit node in the coupled Chua's circuit system, and output the system synchronization error.

[0045] Step 4: Based on the effects of continuous interference and nonlinear dynamics in the coupled Chua's circuit system, and in order to reduce the system synchronization error, the synchronization error system of the coupled Chua's circuit system is analyzed according to the Lyapunov stability principle and the fixed-time synchronization principle, and a controller for the restraint point is designed.

[0046] Step 5: In the coupled Chua's circuit system model designed in Step 1, there is a coupling relationship between the two connected Chua's circuits, which is represented by the coupling strength. In order to reduce the synchronization error of the coupled Chua's circuit system, the synchronization error system of the coupled Chua's circuit system is analyzed according to the Lyapunov stability principle and the fixed time synchronization principle, and the coupling strength formula between the non-restraint point and its connection node is designed.

[0047] Step Six: Construct the Lyapunov function based on Lyapunov's second method. Using the control input and coupling strength formulas from Steps Four and Five, conduct theoretical verification based on the Lyapunov stability principle and the fixed-time synchronization principle. Then, perform practical testing using the computer simulation software MATLAB.

[0048] As one embodiment, the adaptive restraint and coupling control method for fixed-time synchronization of Chua's circuit system is implemented as follows:

[0049] S1: By considering the nonlinear dynamic system in the coupled Chua's circuit system, the effects of continuous state-dependent disturbances, coupling regulation, and restraint control input, a model of the coupled Chua's circuit system is established, with the following equations:

[0050]

[0051] in, , It is the first in the system The status and control inputs of each node; a system with 30 nodes. Represented as time. The connectivity between nodes is determined by... Decision, among which Indicates the first Node and the There are links between the nodes. This indicates that there is no link between the two nodes. The coupling strength between a node and its connected nodes is determined by a scalar parameter. Represented. The nonlinear dynamics and time-varying disturbances in the system are represented by functions. and This indicates that, respectively, the Lipschtsky conditions are satisfied. Conditions related to the state ,in , and It is an unknown constant.

[0052] Where is the nonlinear term of the coupled Chua's circuit, it can be expressed as:

[0053]

[0054] in, It is the voltage of the Chua's circuit. It is electric current. Represents capacitor, It's an inductor. It is a resistor. .at the same time The disturbance is .

[0055] S2. Constructing the topology graph and dividing the nodes.

[0056] Each node of the Chua's circuit is numbered, and using graph theory and the synchronization principle of complex networks, the topology of the coupled Chua's circuit system is designed as a strongly connected graph. Figure 2 (This is only one scenario in this disclosure), and the nodes in the system are divided into restraining nodes. Non-controllable nodes The node distribution is as follows:

[0057]

[0058] S3. Establish a systematic error model

[0059] A system error model is established by coupling the sum of the state errors of all two connected nodes in the Chua's circuit system. for:

[0060]

[0061] S4. Control methods for designing restraint points

[0062] The control input of the restraint point changes the state of the restraint point, that is, it changes the voltage and current in a single Chua's circuit, thereby counteracting the negative effects of nonlinear dynamic systems and state-dependent disturbances. The control method of the restraint point is constructed as follows:

[0063]

[0064] in, The constant is The estimated value, Indicates whether two nodes are connected, where Indicates the first Node and the The nodes are connected. This indicates that the two nodes are not connected. Represented as the first Node error. For the first The state of the node, For the first The state of the node.

[0065] It is an adaptive method designed based on the system error of the coupled Chua's circuit system, which is used to adjust the restraint control and coupling strength so that the error of the whole system is gradually reduced.

[0066]

[0067] in,

[0068]

[0069] It is an adaptive control term designed for the restraint controller based on the Lyapunov stability principle and the fixed-time synchronization principle.

[0070]

[0071] For a very small scalar, Let be a constant between (0, 1). A constant greater than 1 The constant is The estimated value, and:

[0072]

[0073]

[0074]

[0075] in, It is a constant greater than 0.

[0076] S5. Control methods for designing restraint points

[0077] To achieve system synchronization within a fixed time, the coupling strength between nodes in the non-restrained points and their connected nodes is indirectly controlled. This is achieved by adjusting the coupling voltage between two coupled Chua's circuits, as shown in the formula:

[0078]

[0079] It is also based on the Lyapunov stability principle and the fixed-time synchronization principle, and is a coupling term designed for coupling regulation.

[0080]

[0081] in It is a constant.

[0082] S6. Theoretical Verification and Simulation

[0083] The controller involved is theoretically verified using Lyapunov's second method and a formula for fixed-time synchronization. The Lyapunov function using Lyapunov's second method in this disclosure is:

[0084]

[0085] The formula for fixed-time synchronization is: And needs to meet and , By applying the designed control strategy to the Lyapunov function and finally transforming it into a formula for fixed-time synchronization, it can be demonstrated that the control strategy enables the system to achieve synchronization within a fixed time. The results are then verified using the computer software MATLAB.

[0086] In this disclosure, the values ​​of the necessary parameters for experimental verification are:

[0087]

[0088] Based on the principle of fixed-time synchronization and The coupled Chua's circuit system in this invention will achieve synchronization within 6 seconds.

[0089] Example 2

[0090] One embodiment of this disclosure provides a fixed-time synchronized coupled Chua's circuit adaptive restraint control system, comprising:

[0091] The model building module is used to build a nonlinear complex network model of coupled Chua's circuit, obtain the Chua's circuit nodes in the complex network and express the dynamic behavior relationship between each Chua's circuit node using equations.

[0092] Construct a topology diagram of the coupled Chua's circuit, number each Chua's circuit node, convert the topology diagram into a strongly connected graph, and divide all Chua's circuit nodes into two parts: tethered nodes and non-tethered nodes.

[0093] The controller construction module is used to build an error model of the coupled Chua's circuit system. By analyzing the synchronization error of the coupled Chua's circuit system, and based on the Lyapunov stability principle and the fixed-time synchronization principle, the control method of the restraint point and the coupling strength formula between the non-restraint point and its connection node are designed.

[0094] The control output module is used to construct the Lyapunov function and, based on the controller input at the restraint point and the coupling strength formula at the non-restraint point, solve for the time when the coupled Chua's circuit reaches synchronization.

[0095] Specifically, the system in Embodiment 2 performs all the method steps as described in Embodiment 1.

[0096] Example 3

[0097] One embodiment of this disclosure provides a computer-readable storage medium including a stored program, wherein the program executes the described fixed-time synchronized coupled Chua's circuit adaptive restraint control method.

[0098] Example 4

[0099] One embodiment of this disclosure provides an electronic device including: one or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs including an adaptive restraint control method for performing the fixed-time synchronization coupled Chua's circuit.

[0100] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0101] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1The steps of the function specified in one or more boxes.

[0102] While the specific embodiments of this disclosure have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this disclosure. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this disclosure are still within the scope of protection of this disclosure.

Claims

1. A method for adaptive restraint control of a fixed-time synchronized coupled Chua's circuit, characterized in that, include: A nonlinear complex network model of coupled Chua's circuit is established, the Chua's circuit nodes in the complex network are obtained, and the dynamic behavior relationship between each Chua's circuit node is expressed by equations. Construct a topology diagram of the coupled Chua's circuit, number each Chua's circuit node, convert the topology diagram into a strongly connected graph, and divide all Chua's circuit nodes into two parts: tethered nodes and non-tethered nodes. An error model of a coupled Chua's circuit system is constructed. By analyzing the synchronization error of the coupled Chua's circuit system, and based on the Lyapunov stability principle and the fixed-time synchronization principle, a control method for the restraint point and a formula for the coupling strength between the non-restraint point and its connection node are designed. Construct a Lyapunov function and, based on the controller input at the restraint point and the coupling strength formula at the non-restraint point, solve for the time required for the coupled Chua's circuit to achieve synchronization.

2. The adaptive restraint control method for fixed-time synchronized coupled Chua's circuit as described in claim 1, characterized in that, By considering the nonlinear dynamic system in the coupled Chua's circuit system, the effects of continuous state-dependent disturbances, coupling regulation, and restraint control inputs, a model of the coupled Chua's circuit system is established.

3. The adaptive restraint control method for fixed-time synchronized coupled Chua's circuit as described in claim 1, characterized in that, Obtain the Chua's circuit nodes in the complex network, and use corresponding functions to describe the dynamic behavior relationship and time-varying perturbation between each Chua's circuit node, and ensure that the dynamic behavior relationship and time-varying perturbation function between each Chua's circuit node satisfy the Lipschtsky condition and the state-dependent condition, respectively.

4. The adaptive restraint control method for fixed-time synchronized coupled Chua's circuit as described in claim 1, characterized in that, Construct a topology graph of the coupled Chua's circuit, number each Chua's circuit node, and use graph theory and the principle of synchronization of complex networks to design the topology graph of the coupled Chua's circuit system as a strongly connected graph. Divide the nodes into tethered nodes and non-tethered nodes, and give the distribution of the corresponding tethered nodes and non-tethered nodes.

5. The adaptive restraint control method for fixed-time synchronized coupled Chua's circuit as described in claim 1, characterized in that, The control method for the designed restraint point is that the control input of the restraint point changes the state of the restraint point by changing the voltage and current in a single Chua's circuit to counteract the effects of nonlinear dynamic systems and state-related disturbances.

6. The adaptive restraint control method for fixed-time synchronized coupled Chua's circuit as described in claim 1, characterized in that, The coupling strength between nodes in the non-restraint point and their connected nodes is indirectly controlled, that is, the system achieves synchronization within a fixed time by adjusting the coupling voltage between two coupled Chua's circuits.

7. A fixed-time synchronized coupled Chua's circuit adaptive restraint control system, characterized in that, include: The model building module is used to build a nonlinear complex network model of coupled Chua's circuit, obtain the Chua's circuit nodes in the complex network and express the dynamic behavior relationship between each Chua's circuit node using equations. Construct a topology diagram of the coupled Chua's circuit, number each Chua's circuit node, convert the topology diagram into a strongly connected graph, and divide all Chua's circuit nodes into two parts: tethered nodes and non-tethered nodes. The controller construction module is used to build an error model of the coupled Chua's circuit system. By analyzing the synchronization error of the coupled Chua's circuit system, and based on the Lyapunov stability principle and the fixed-time synchronization principle, the control method of the restraint point and the coupling strength formula between the non-restraint point and its connection node are designed. The control output module is used to construct the Lyapunov function and, based on the controller input at the restraint point and the coupling strength formula at the non-restraint point, solve for the time when the coupled Chua's circuit reaches synchronization.

8. The fixed-time synchronized coupled Chua's circuit adaptive restraint control system as described in claim 7, characterized in that, By considering the nonlinear dynamic system in the coupled Chua's circuit system, the effects of continuous state-dependent disturbances, coupling regulation, and restraint control inputs, a model of the coupled Chua's circuit system is established.

9. A computer-readable storage medium, characterized in that, The storage medium includes a stored program, wherein the program executes the fixed-time synchronized coupled Chua's circuit adaptive restraint control method as described in any one of claims 1-6.

10. An electronic device, characterized in that, include: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs including an adaptive restraint control method for a coupled Chua's circuit with fixed-time synchronization as described in any one of claims 1-6.

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