A preset time synchronization control method for time-delay memristive neural networks

Abstract

The application discloses a preset time synchronization control method of a time-delay memristive neural network, comprising the following steps: constructing a driving system and a response system of the time-delay memristive neural network; setting a synchronization error according to the driving system and the response system, and establishing a complete synchronization error system; designing a preset time feedback controller; constructing an energy function to verify the preset time stability of the synchronization error system; determining the conditions for realizing the preset time synchronization of the driving system and the response system, and simulating and verifying. The proposed preset time stability theorem has universality and simplifies the existing preset time stability theorem. The preset time is applied to the Lyapunov functional as a parameter, so that the stable time of the error system can be flexibly regulated according to the change of the preset parameter, and is not affected by the initial conditions of the system. Secondly, the controller designed by the application has a simple form, can reduce unnecessary energy consumption of the system, and can effectively control the error system.

Description

Technical Field

[0001] This application relates to the field of neural network technology, specifically to a preset time synchronization control method for a time-delay memristor neural network. Background Technology

[0002] Research on neural networks has always been a hot topic in artificial intelligence technology. A neural network is a highly complex nonlinear system with rich dynamic behaviors, and its dynamic model can be implemented using a very large-scale integrated circuit. Traditional neural network models have fixed resistance values, which cannot well simulate changes in synaptic strength. The advent of memristors has broken this deadlock. The advantages of memristors, such as their nanoscale structure and non-volatility of information after power failure, make them excellent devices for simulating neural synapses, and memristor neural networks also exhibit more complex dynamic behaviors. In the process of information transmission in the human brain, time delays are unavoidable. Therefore, this invention uses a memristor neural network with time-varying delays as a carrier to study stability and synchronization control. This research can be applied to various practical problems, such as brain science, social networks and power systems, and secure signal transmission.

[0003] There are many existing synchronization methods, such as asymptotic synchronization, finite-time synchronization, and fixed-time synchronization. Chen et al. studied fixed-time synchronization of neural networks and its application in signal transmission; Yu et al. studied finite-time synchronization of complex-valued memristor neural networks; Gunasekaran et al. studied the global asymptotic robust stability of dynamic delay neural networks; and Liu et al. proposed a new pre-set time stability theorem and studied its application in memristor complex-valued BAM neural networks.

[0004] Current synchronization methods have certain drawbacks. For example, the convergence speed of incremental synchronization is difficult to determine, making it impossible to accurately and effectively control the synchronization time; the convergence speed of finite-time synchronization requires prior knowledge of the system's initial values, but some application scenarios cannot obtain the initial conditions; the upper bound of the convergence time of fixed-time synchronization needs to be calculated through controller parameters, which can be cumbersome when there are many parameters. Summary of the Invention

[0005] In order to solve the above-mentioned technical problems, this application proposes the following technical solution:

[0006] In a first aspect, embodiments of this application provide a preset time synchronization control method for a time-delay memristor neural network, characterized in that it includes:

[0007] Constructing the driving and response systems for a time-delay memristor neural network;

[0008] A complete synchronization error system is established by setting the synchronization error based on the drive system and response system.

[0009] Design a preset time feedback controller and a preset time stability theorem;

[0010] Construct an energy function to verify the preset time stability of the synchronization error system;

[0011] Determine the conditions for the drive system and response system to achieve preset time synchronization and verify them through simulation.

[0012] In one possible implementation, the driving system for constructing the time-delay memristor neural network includes:

[0013]

[0014] Where i = 1, 2, ..., n; j = 1, 2, ..., nx i (t) represents the state of the neuron, d i a represents the neuronal self-inhibition rate. ij (·) and b ij (·) represents the connection weight, f j (·) and g j (·) represents an activation function that satisfies the Lipschitz condition, and the Lipschitz constant is set to l. j and p j τ(t) represents the time delay, I i Indicates external input;

[0015] Based on set-valued mapping and differential inclusion theory, system (1) is transformed into the following form:

[0016]

[0017] in,

[0018] a * a ** b * , b** Let Δ be a real number, and let Δ represent the threshold. Indicates by a * and a ** The generated convex closure, Therefore, there exist real numbers. Make:

[0019]

[0020] In one possible implementation, the response system of the time-delay memristor neural network is constructed, including:

[0021] According to set-valued mappings and differential inclusion, there exists achievable

[0022]

[0023] Among them, i=1, 2,..., n; j=1, 2,..., n, u i (t) is the controller to be designed, y i (t) and y j (t) represents the state of the neuron.

[0024] In one possible implementation, a complete synchronization error system is established by setting synchronization errors based on the driving system and the response system, including:

[0025] Let the synchronization error e i (t)=y i (t)-x i (t), the error system is as follows:

[0026]

[0027] Since the drive-response system has different initial values, the purpose of subtraction is to transform the synchronization problem of the drive-response system into the stability problem of the error system.

[0028] In one possible implementation, a preset time feedback controller is designed, including:

[0029]

[0030] Where, Θ i Λ i α i ,β i For feedback gain greater than 0, the exponent is 0 < ξ < 1, η > 1, and T c For the preset time, G c It is a constant greater than zero.

[0031] In one possible implementation, a predefined time stability theorem is designed, including:

[0032] Suppose there exists a regular, positive definite, unbounded function V(e(t)): R→R, and the following two conditions hold:

[0033]

[0034] (2) For any V(e(t))>0, there exist α, β, G c T c >0, η>1, 0<ξ<1 satisfy:

[0035]

[0036] The error system can then reach a preset time stability; among which,

[0037]

[0038] The steady-state time function can be expressed as:

[0039]

[0040] if

[0041]

[0042] Or, if

[0043]

[0044] make It can be obtained When W reaches its minimum value therefore,

[0045]

[0046] In one possible implementation, an energy function is constructed to verify the preset time stability of the synchronization error system, including:

[0047]

[0048] Differentiate the Lyapunov function:

[0049]

[0050] in,

[0051] In one possible implementation, the conditions for the drive system and the response system to achieve preset time synchronization are determined, including:

[0052] The drive system (1) and the response system (4) can achieve preset time synchronization under the action of the controller (6), then

[0053] In one possible implementation, simulation verification includes:

[0054] Assuming the driver-response system is two-dimensional, the relevant parameter settings are as follows:

[0055] Initial conditions: x1(0) = -0.6, x2(0) = 1.2, y1(0) = -0.12, y2(0) = 0.27;

[0056] Neuronal self-inhibition rate: d1 = d2 = 1;

[0057] Activation function: f j (z)=tanh(z), g j (z) = 0.5*(|1+z|-|z-1|);

[0058] External input: I I =0;

[0059] Memristor connection weights:

[0060]

[0061]

[0062]

[0063]

[0064] The system's preset time synchronization is independent of the initial value. Three different initial values ​​are set as follows:

[0065] Group 1: x1(0) = -0.6, x2(0) = 1.2, y1(0) = -0.12, y2(0) = 0.27;

[0066] Group 2: x1(0) = 3, x2(0) = -5, y1(0) = 0.9, y2(0) = 2.3;

[0067] Group 3: x1(0) = 1.5, x2(0) = 2, y1(0) = 0.9, y2(0) = -2.3.

[0068] In this embodiment, the proposed preset time stability theorem is universal and simplifies existing preset time stability theorems. By incorporating the preset time as a parameter in the judgment condition, the settling time of the error system can be flexibly adjusted according to changes in the preset parameter, unaffected by the initial conditions of the system. Furthermore, the controller designed in this invention is simple in form, reducing unnecessary energy consumption while effectively controlling the error system. Attached Figure Description

[0069] Figure 1 A flowchart illustrating a preset time synchronization control method for a time-delay memristor neural network provided in an embodiment of this application;

[0070] Figure 2 This is a state trajectory diagram of an error system without controller operation provided in an embodiment of this application;

[0071] Figure 3 After adding a controller as provided in the embodiments of this application, and Tc Error system state trajectory diagram when = 1;

[0072] Figure 4 After adding a controller as provided in the embodiments of this application, and T c Error system state trajectory diagram when = 0.1;

[0073] Figure 5 After adding the controller and T c When =1, the error system state trajectory diagram under three sets of initial conditions. Detailed Implementation

[0074] The present solution will now be described in conjunction with the accompanying drawings and specific embodiments.

[0075] Figure 1 A flowchart illustrating a preset time synchronization control method for a time-delay memristor neural network provided in this application embodiment is shown below. Figure 1 The preset time synchronization control method of the time-delay memristor neural network in this embodiment includes:

[0076] S101, constructing the driving and response systems for a time-delay memristor neural network.

[0077] The driving system for constructing a time-delay memristor neural network includes:

[0078]

[0079] Where i = 1, 2, ..., n; j = 1, 2, ..., nx i (t) represents the state of the neuron, d i a represents the neuronal self-inhibition rate. ij (·) and b ij (·) represents the connection weight, f j (·) and g j (·) represents an activation function that satisfies the Lipschitz condition, and the Lipschitz constant is set to l. j and p j τ(t) represents the time delay, I i Indicates external input;

[0080] Based on set-valued mapping and differential inclusion theory, system (1) is transformed into the following form:

[0081]

[0082] in,

[0083] Indicates by z * and z ** The generated convex closure, Therefore, there exists Make:

[0084]

[0085] Constructing a response system for a time-delay memristor neural network includes:

[0086] According to set-valued mappings and differential inclusion, there exists achievable

[0087]

[0088] Where i = 1, 2, ..., n; j = 1, 2, ..., nu i (t) is the controller to be designed, and the other parameters are the same as those in (1).

[0089] S102, establish a complete synchronization error system by setting the synchronization error based on the drive system and response system.

[0090] Let e i (t)=y i (t)-x i (t), the error system is as follows:

[0091]

[0092] Since the drive-response system has different initial values, the purpose of subtraction is to transform the synchronization problem of the drive-response system into the stability problem of the error system.

[0093] S103, Design a preset time feedback controller and a preset time stability theorem.

[0094]

[0095] Where, Θ i Λ i α i ,β i >0, 0<ξ<1, η>1, T c For the preset time, G c It is a constant greater than zero.

[0096] Suppose there exists a regular, positive definite, unbounded function V(e(t)): R→R, T c It is a user-defined parameter, and the following two conditions must be met:

[0097] (1)

[0098] (2) For any V(e(t))>0, there exist α, β, Gc T c >0, η>1, 0<ξ<1 satisfy:

[0099]

[0100] The error system can then reach a preset time stability; among which,

[0101]

[0102] The steady-state time function can be expressed as:

[0103]

[0104] if

[0105]

[0106] Or, if

[0107]

[0108] make It can be obtained When W reaches its minimum value therefore,

[0109]

[0110] S104, Construct an energy function to verify the preset time stability of the synchronization error system.

[0111] Constructing an energy function to verify the preset time stability of the synchronization error system includes:

[0112]

[0113] Differentiate the Lyapunov function:

[0114]

[0115] in,

[0116] S105, determine the conditions for the drive system and response system to achieve preset time synchronization and verify them through simulation.

[0117] The drive system (1) and the response system (4) can achieve preset time synchronization under the action of the controller (6), then

[0118] Simulation verification includes:

[0119] Assuming the driver-response system is two-dimensional, the relevant parameter settings are as follows:

[0120] Initial conditions: x1(0) = -0.6, x2(0) = 1.2, y1(0) = -0.12, y2(0) = 0.27;

[0121] Neuronal self-inhibition rate: d1 = d2 = 1;

[0122] Activation function: f j (z)=tanh(z), g j (z) = 0.5*(|1+z|-|z-1|);

[0123] External input: I I =0;

[0124] Memristor connection weights:

[0125]

[0126]

[0127]

[0128]

[0129] The system's preset time synchronization is independent of the initial value. Three different initial values ​​are set as follows:

[0130] Group 1: x1(0) = -0.6, x2(0) = 1.2, y1(0) = -0.12, y2(0) = 0.27;

[0131] Group 2: x1(0) = 3, x2(0) = -5, y1(0) = 0.9, y2(0) = 2.3;

[0132] Group 3: x1(0) = 1.5, x2(0) = 2, y1(0) = 0.9, y2(0) = -2.3.

[0133] See Figures 2-5 As can be seen, the preset time synchronization control involved in this embodiment has strong flexibility. For the error system, its convergence time changes with the preset parameters in the controller, and the convergence time is not affected by the initial value. The proposed preset time stability theorem has universality and simplifies the existing preset time stability theorem. The controller designed in this invention has a simple form, avoids the problem of too many parameters in the controller, can reduce some unnecessary energy consumption of the system, and can effectively control the error system.

[0134] In this application embodiment, "at least one" refers to one or more, and "more than one" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent the existence of A alone, the simultaneous existence of A and B, or the existence of B alone. A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one of the following" and similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one of a, b, and c can represent: a, b, c, ab, ac, bc, or abc, where a, b, and c can be single or multiple.

[0135] The above description is merely a specific embodiment of this application. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the protection scope of this application. The protection scope of this application should be determined by the protection scope of the claims.

Claims

1. A preset time synchronization control method for a time-delay memristor neural network, characterized in that, include: Constructing the driving and response systems for a time-delay memristor neural network; A complete synchronization error system is established by setting the synchronization error based on the drive system and response system. Design a preset time feedback controller and a preset time stability theorem; Design a preset time feedback controller, including: in, , For preset time, It is a constant greater than zero; The design includes a pre-defined time stability theorem, including: Suppose there exists a regular, positive definite, unbounded function. And the following two conditions are true: (1) (2) For any There exist real numbers satisfy: The error system can then reach a preset time stability; among which, The steady-state time function is expressed as: if Or, if Take real numbers , make get hour Find the minimum value ,therefore, ； Construct an energy function to verify the preset time stability of the synchronization error system; Determine the conditions for the drive system and response system to achieve preset time synchronization and verify them through simulation.

2. The preset time synchronization control method for a time-delay memristor neural network according to claim 1, characterized in that, The driving system for constructing a time-delay memristor neural network includes: in, Indicates the state of a neuron. Indicates the neuronal self-inhibition rate. and Indicates connection weights. Let represent the activation function that satisfies the Lipschitz condition, with the Lipschitz constants set as . Indicates time delay, Indicates external input; Based on set-valued mapping and differential inclusion theory, system (1) is transformed into the following form: in, Indicates by and The generated convex closure, Therefore, there exist real numbers. Make: 。 3. The preset time synchronization control method for a time-delay memristor neural network according to claim 2, characterized in that, Constructing a response system for a time-delay memristor neural network includes: According to set-valued mappings and differential inclusion, there exist real numbers ,have to in, It is the controller to be designed. and This indicates the state of a neuron.

4. The preset time synchronization control method for the time-delay memristor neural network according to claim 3, characterized in that, Based on the synchronization error settings of the drive system and response system, a complete synchronization error system is established, including: Let synchronization error The error system is as follows: Since the drive-response system has different initial values, the purpose of subtraction is to transform the synchronization problem of the drive-response system into the stability problem of the error system.

5. The preset time synchronization control method for a time-delay memristor neural network according to claim 1, characterized in that, Constructing an energy function to verify the preset time stability of the synchronization error system includes: Differentiate the Lyapunov function: Among them, real numbers .

6. The preset time synchronization control method for a time-delay memristor neural network according to claim 5, characterized in that, The conditions for achieving preset time synchronization between the drive system and the response system are determined, including: The drive system (1) and the response system (4) can achieve preset time synchronization under the action of the controller (6), then the feedback gain .

7. The preset time synchronization control method for a time-delay memristor neural network according to claim 6, characterized in that, Simulation verification includes: Assuming the driver-response system is two-dimensional, the relevant parameter settings are as follows: Initial conditions: Neuronal self-inhibition rate: Activation function: External input: Memristor connection weights: ； ； ； ； The system's preset time synchronization is independent of the initial value. Three different initial values ​​are set as follows: Group 1: Group 2: Group 3: .

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