Fractional order multi-mode memristor neural network finite time synchronization control method and system

Abstract

The invention relates to the technical field of memristive neural networks, and provides a fractional order multi-mode memristive neural network finite time synchronization control method and system, and the method comprises the following steps: fusing an activation function with time delay and an activation function without time delay according to a fractional order neural network, constructing a driving system and a response system of the fractional order multi-mode memristor neural network, and further determining an error system; the method comprises the following steps: constructing a finite time state feedback synchronous controller by considering interaction among neurons, external input, time delay and error state, acting the finite time state feedback synchronous controller on a response system, adjusting the working state of each neuron memristor, and realizing synchronization of the response system and a driving system. The finite time synchronization control theory is fused with the fractional order multi-mode memristor neural network, multiple factors are considered to construct the feedback controller, and synchronization of the fractional order multi-mode memristor neural network within the finite time is achieved.

Description

Technical Field

[0001] The present disclosure relates to the technical field related to memristor neural networks, and more specifically, to a fractional-order multimodal memristor neural network finite-time synchronization control method and system. Background Art

[0002] The statements in this section merely provide background information related to the present disclosure and do not necessarily constitute prior art.

[0003] Memristive Neural Networks (MNN) is a new type of neural network architecture that uses memristors as basic components to build neural networks. Memristors are electronic components that can store and remember the history of current and have characteristics such as adaptability, nonlinearity, and variable impedance. This characteristic of memristors gives them an advantage in simulating the synaptic transmission of biological neurons, because the synaptic connection between neurons in biological neural networks will be strengthened or weakened according to usage, similar to the plasticity of memristors. In memristive neural networks, memristors are used to simulate synapses in neural networks, store information, and dynamically adjust the intensity of signal transmission, thereby achieving functions such as learning, memory, and reasoning. The nonlinear characteristics of memristors enable the network to optimize the connection strength in a more efficient way when performing adaptive learning, thereby improving the processing power and storage density of the network.

[0004] The synchronization of memristor neural networks generally refers to the coordination of the activities or update processes of different parts of the network (such as neurons or synapses). During the training of a neural network, especially when using memristors for adjustment, multiple elements of the network may need to be synchronized in order to accurately reflect the learning process or signal transmission. The synchronization of memristor neural networks has a wide range of applications in many fields, such as biological system modeling, electronic circuit optimization, image encryption technology, confidential communication technology, and oscillator design. However, due to the complex dynamic characteristics of memristor neural networks, especially in application scenarios where efficient collaboration is required, synchronization becomes a key factor in improving system efficiency and reliability. The synchronization problem of memristor neural networks has always been one of the research hotspots. However, since it is difficult for memristor neural networks to achieve synchronization through internal regulation, their performance in group dynamics behavior is limited. The existing technology mostly adopts asymptotic synchronization, that is, the system state is synchronized through long-term dynamic adjustment. However, this method has obvious limitations: it takes a long time to achieve synchronization, and it is difficult to meet the requirements of efficiency and timeliness in actual application scenarios. For example, in a communication system, if the signal synchronization process takes too long, it will seriously affect the efficiency and reliability of information transmission.

[0005] In contrast, finite-time synchronization can achieve synchronization of system states within a limited time interval through a specific control strategy, which can significantly improve communication efficiency. However, the inventors found that there are few studies on finite-time synchronization of memristor neural networks, and the technical means are still imperfect. For the traditional method of finite-time synchronization of memristor neural networks, a strategy based on fixed parameter feedback control is adopted. Since this method is difficult to flexibly adjust the control intensity according to the real-time state of the network, it has poor adaptability when dealing with dynamic changes in network structure or external interference, and it is very easy to have synchronization delays or even synchronization failures. The memristor itself exhibits strong nonlinear resistance characteristics, and its resistance change has a complex relationship with current and voltage. This makes the overall dynamic behavior of the memristor neural network highly nonlinear. The existing fractional-order finite-time synchronization controller uses a controller derived from the integer-order theorem, which makes the design of the controller very complex. Therefore, when applied to memristor neural networks, there are problems of complex calculations and unsimplified controllers, which in turn affects the efficiency and accuracy of the synchronization control of the memristor neural network. Summary of the invention

[0006] In order to solve the above problems, the present invention proposes a finite-time synchronization control method and system for a fractional-order multimodal memristor neural network, which integrates the finite-time synchronization control theory with the fractional-order multimodal memristor neural network, constructs a feedback controller considering multiple factors, and realizes the finite-time synchronization of the fractional-order multimodal memristor neural network.

[0007] In order to achieve the above objectives, the present disclosure adopts the following technical solutions:

[0008] One or more embodiments provide a fractional-order multimodal memristor neural network finite-time synchronization control method, comprising the following steps:

[0009] According to the fractional-order neural network, the activation function with delay and the activation function without delay are integrated to construct the driving system and response system of the fractional-order multimodal memristor neural network.

[0010] According to the driving system and response system of the constructed fractional-order multimodal memristor neural network, the corresponding synchronization error is set, and then the error system is established;

[0011] Considering the interaction between neurons, external input, time delay and error state, a finite-time state feedback synchronization controller is constructed. The finite-time state feedback synchronization controller is applied to the response system to adjust the working state of each neuron memristor and achieve synchronization between the response system and the drive system.

[0012] One or more embodiments provide a fractional-order multimodal memristor neural network finite-time synchronous control system, including:

[0013] The system building module is configured to build a driving system and a response system of a fractional-order multimodal memristor neural network by fusing an activation function with a time delay and an activation function without a time delay according to a fractional-order neural network;

[0014] The error system determination module is configured to set a corresponding synchronization error according to a driving system and a response system of the constructed fractional-order multimodal memristor neural network, thereby establishing an error system;

[0015] The feedback synchronization control module is configured to consider the interaction between neurons, external input, time delay and error state, construct a finite-time state feedback synchronization controller, apply the finite-time state feedback synchronization controller to the response system, adjust the working state of each neuron memristor, and achieve synchronization between the response system and the drive system.

[0016] An electronic device includes a memory and a processor, and computer instructions stored in the memory and executed on the processor. When the computer instructions are executed by the processor, the steps in the above-mentioned fractional-order multi-modal memristor neural network finite-time synchronization control method are completed.

[0017] A computer-readable storage medium is used to store computer instructions. When the computer instructions are executed by a processor, the steps in the above-mentioned fractional-order multi-modal memristor neural network finite-time synchronization control method are completed.

[0018] Compared with the prior art, the present invention has the following beneficial effects:

[0019] The present disclosure can determine an accurate error function by constructing a fractional-order multimodal memristor neural network model including a drive system and a response system with a time delay function and without a time delay. Based on the constructed error function, a feedback controller is constructed based on multiple factors, thereby enabling the system to achieve a synchronous state within a limited time range.

[0020] The advantages of the present disclosure and the advantages of additional aspects will be described in detail in the following specific embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The accompanying drawings constituting a part of the present disclosure are used to provide a further understanding of the present disclosure. The exemplary embodiments of the present disclosure and the description thereof are used to explain the present disclosure but do not constitute a limitation of the present disclosure.

[0022] Figure 1 is a flowchart of a synchronous control method according to Embodiment 1 of the present disclosure;

[0023] Figure 2 is the drive system x in the simulation example of Embodiment 1 of the present disclosure 1 (t), x 2(t) Side view of the phase diagram structure;

[0024] Figure 3 is the driving system x in the simulation example of Embodiment 1 of the present disclosure without applying the controller 1 (t), x 2 (t) state change trajectory diagram;

[0025] Figure 4 is the driving system x in the simulation example of Embodiment 1 of the present disclosure when the controller is applied 1 (t), x 2 (t) The state change trajectory reaches a consistent graph;

[0026] Figure 5 In the simulation example of Embodiment 1 of the present disclosure, under the control of the synchronous controller, the error system E i (t) Graph of reaching synchronization. DETAILED DESCRIPTION

[0027] The present disclosure is further described below in conjunction with the accompanying drawings and embodiments.

[0028] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present disclosure. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present disclosure belongs.

[0029] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present disclosure. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof. It should be noted that, in the absence of conflict, the various embodiments in the present disclosure and the features in the embodiments can be combined with each other. The embodiments will be described in detail below in conjunction with the accompanying drawings.

[0030] Example 1

[0031] In the technical solutions disclosed in one or more embodiments, Figures 1 to 5 As shown, a fractional-order multi-modal memristor neural network finite-time synchronization control method comprises the following steps:

[0032] Step S1: Based on the fractional-order neural network, the activation function with time delay and the activation function without time delay are integrated to construct the driving system x of the fractional-order multimodal memristor neural network. i (t) and the response system y i (t);

[0033] Step S2: Based on the constructed fractional-order multimodal memristor neural network driving system x i (t) and the response system y i (t), set the corresponding synchronization error, and then establish the error system E i (t);

[0034] Step S3: Considering the interaction between neurons, external input, time delay and error state, a finite-time state feedback synchronous controller U is constructed. i (t), the finite-time state feedback synchronous controller acts on the response system y i (t), adjust the working state of each neuron memristor to realize the response system y i (t) and drive system x i (t) synchronization.

[0035] In this embodiment, by constructing a fractional-order multimodal memristor neural network model including a drive system and a response system with a time delay function and without a time delay, an accurate error function can be determined. Based on the constructed error function, a feedback controller is constructed based on multiple factors, thereby enabling the system to achieve a synchronous state within a limited time range.

[0036] A memristor is a component with memory function, and its resistance value can change according to the historical changes of the current or voltage passing through it. Memristor neural network utilizes this characteristic of memristors, and uses memristors as each neuron node to store and process information by simulating the changes of synaptic weights in biological neural networks. Memristor neural network synchronization is the synchronization of neurons in each memristor neural network.

[0037] In step S3, a response system y is generated. i (t) The control input U of the memristor on each neuron node i (t), control response system y i (t) Each neuron is synchronized with each neuron of the driving system within a limited time, including: synchronization of weight updates, synchronization of neuron activities, and synchronization of computational processes;

[0038] Synchronization of weight updates: The weights of multiple neurons or synapses in the network (i.e., the impedance of the memristor) may need to be updated synchronously to ensure the overall learning effect of the network during training. Synchronization between different layers or neurons can accelerate network convergence and avoid over-activation or inactivity of some neurons.

[0039] Synchronization of neuronal activity: In some cases, neurons may need to be activated synchronously within certain time steps to improve network performance, especially when using parallel computing or processing large-scale data.

[0040] Synchronization of computing processes: In hardware implementation, due to the physical properties of memristors and the increase in network size, it may be necessary to synchronize the operations of multiple memristors through parallel computing to ensure that the overall performance of the network is not affected by delays or erroneous transmission.

[0041] In step S1, the construction process of the driving system and the response system is as follows:

[0042] Step S11: Fusion of activation functions with time delay and activation functions without time delay to establish a driving system x of a fractional-order multimodal memristor neural network i (t), as follows:

[0043]

[0044] Among them, ∈ represents the order of the fractional-order system, x i (t) represents the state of the i-th neuron in the driving system at time t; x j (t) represents the state of the jth neuron in the driving system at time t; t is time, greater than or equal to 0; C i represents the self-inhibition rate of the neuron, which is a constant. Indicates that there is no activation function with time delay in the drive system, g(x j (t-τ ι (t))) represents the activation function with time delay in the drive system, and all the activation functions mentioned above satisfy the Lipschitz condition, and the Lipschitz constant is set to τ ι (t) represents the delay, m represents the number of delays, and satisfies 0≤τ ι (t)≤1,I i Refers to the external input conditions of the drive system;

[0045] Step S12: Fusion of activation functions with time delay and activation functions without time delay to establish the response system y of the fractional-order multimodal memristor neural network i (t), as follows:

[0046]

[0047]

[0048] In the formula, y i (t) represents the state of the i-th neuron in the response system at time t, Indicates that there is no activation function for the response system, g(y j (t-τ ι(t)) represents the activation function with time delay in the response system. All the activation functions mentioned above satisfy the Lipschitz condition, and the Lipschitz constant is τ ι (t) represents the delay, m represents the number of delays, and satisfies 0≤τ ι (t)≤1,J i Refers to the external input of the response system, U i (t) refers to the designed feedback controller; N represents the number of neurons contained in the driving system and the response system;

[0049] are the memristor connection weight values, satisfying the following conditions respectively:

[0050]

[0051] in, are all set constants. is the set switching threshold.

[0052] Further technical solutions, activation function and g use trigonometric functions, preferably, a tangent function.

[0053] The drive system x constructed in this embodiment i (t) and the response system y i (t) constitutes a fractional-order multimodal memristor neural network model, which incorporates external input and multiple time delay elements; the external input signal directly or indirectly regulates the dynamic behavior of the entire system by affecting the state of the neural network nodes. The external input signal serves as a control variable and can adjust the state of the system in real time, thereby achieving fine control over the dynamic behavior of the system; the introduction of multiple time delay elements enables the system to have more complex time correlation characteristics, which can regulate the synchronization speed and error amplitude through time delay, thereby accelerating the synchronization speed; in this embodiment, by integrating fractional-order characteristics, external input and multiple time delay elements into the fractional-order multimodal memristor neural network model, the system not only retains the nonlinear characteristics of the traditional neural network, but also exhibits more complex and richer dynamic behaviors.

[0054] In step S2, the process of constructing the error system is as follows:

[0055] Step S21: Drive system x of the fractional-order multimodal memristor neural network established in step S1 i (t) and the response system y i (t), the synchronization error between the driving system and the response system is assumed to be:

[0056] E i (t) = yi (t)-x i (t); (3)

[0057] Step S22: Establishing an error system: Based on the synchronization error set in step S21, combined with the specific expressions of the drive system and the response system, a specific synchronization error system is obtained, and the expression is as follows:

[0058]

[0059] In step 3, a Lyapunov function is constructed according to the synchronization error set in step S2, and a finite-time state feedback synchronization controller is designed, and the finite-time state feedback synchronization controller is applied to the response system so that the response system is synchronized with the drive system for a finite time;

[0060] Step 31 constructs the Lyapunov function V(t) according to the synchronization error set in step S2, and the specific expression is given as:

[0061]

[0062] The constructed Lyapunov function set in this step is used to derive sufficient conditions for the existence of the controller, and the controller is set according to the selected Lyapunov function;

[0063] Step 32: Considering the interaction between neurons, external input, time delay and error state, a finite-time state feedback synchronization controller is designed as:

[0064]

[0065] Wherein, i=1, 2, ..., N; ι=1, 2, ..., m; n1, n2, n3, n4, p1 and q1 are all set values ​​greater than zero; sgn(E i (t)) represents the synchronization error E i (t) is a sign function; ζ i , η i represents the constant that satisfies the control gain;

[0066] The controller parameters set need to meet the synchronous control gain, as follows:

[0067]

[0068] in, represents the maximum supremum value of the connection weight of the memristor, H is the Lipschitz constant, represents the maximum supremum value of the connection weight of the memristor, M represents the upper bound of the activation function, which is a constant. 0 Represents the upper bound of the external input of the response system, I 0 Represents the upper bound of the external input to the drive system.

[0069] The controller designed above can achieve fractional-order finite-time stability. This controller is more general and can directly change the controller parameter n according to the selected finite-time stability theorem. 1 、n 2 When the selected finite-time stability theorem (Lemma 1) is in a degenerate form, the controller parameters can be set according to the degenerate theorem form.

[0070] In the controller constructed above:

[0071] -η in the first line of formula (5) i (E i Item (t) is used to process the interaction between neurons. Its main purpose is to directly suppress the error and make the state of the error system gradually tend to 0 through the negative feedback mechanism.

[0072] The second line of formula (5) is the time delay and error processing term, which helps the system to make more comprehensive adjustments based on the historical trend of the error, compensate for the system response lag caused by time delay, and improve the stability and robustness of the system;

[0073] The third line of formula (5) is the error state processing term, which is used to make the error state become 0. It is a constant term that provides a basic adjustment benchmark and is independent of the historical value of the error.

[0074] Step 33: Apply the finite-time state feedback synchronization controller constructed by formula (5) to the response system, so that the response system is synchronized with the drive system within a finite time.

[0075] The control method of this embodiment implements a fractional-order multimodal memristor neural network finite-time synchronization control method, which is a more effective synchronization control method than an asymptotic synchronization control method, because the synchronization time of the asymptotic synchronization control method is infinite in theory, while the finite-time synchronization control method ensures that the response system is synchronized with the drive system within a finite time.

[0076] Furthermore, the stability theorem involved in this embodiment is also more universal and has wider applicability. When the parameters are properly selected, it can be degenerated into the existing fractional order theorem. The finite time stability theorem of this embodiment includes Lemma 1 and Lemma 2. The judgment conditions of the stability theorem are as follows:

[0077]

[0078] Where, ∈ represents the order of the fractional-order system; α, β are real numbers greater than or equal to 0; c, δ, θ are all constants greater than 0, and θ ≥ δ;

[0079] Specifically, if there exists a positive definite, unbounded continuous function V(·)∈([t0,+∞),R + )satisfy Then the system can achieve synchronization within a limited time;

[0080] Lemma 2: If the function F is continuous and 0<∈<1, then the following equation is true Where sgn represents the sign function;

[0081] The existing fractional order theorem is relatively conservative. The stability theorem involved in this embodiment is more general and has wider applicability. When the parameters α and β are respectively selected to be equal to 0, it can be degenerated into the existing form, which is more universal. The addition of the term with parameters α and β realizes the error E i The processing of nonlinear terms related to the negative power of (t) and the nonlinear adjustment mechanism help the system to achieve better control performance within different error ranges and enhance the effectiveness of stability verification.

[0082] Furthermore, the stability of the proposed finite-time state feedback synchronization controller is proved based on the set stability theorem and Lyapunov function, and the finite-time stability of the error system is verified;

[0083] The effectiveness of the feedback controller designed for the synchronization control method of the above-mentioned fractional-order multimodal memristor neural network is theoretically proved below; and with the help of numerical simulation, the drive system and response system built by the fractional-order multimodal memristor neural network in the implementation are verified to confirm whether they have achieved the synchronization state;

[0084] Based on the finite-time stability theorem, the finite-time stability of the error system is proved in combination with the controller. The specific process is as follows:

[0085] The Lyapunov function is constructed as:

[0086]

[0087] According to Lemma 2, we can find the fractional derivative of the Lyapunov function:

[0088]

[0089] Add the controller. It is worth noting that the controller parameters need to satisfy the control gain of the controller, and we get:

[0090]

[0091] According to the content of Lemma 1 and Lyapunov's asymptotic stability theorem, it can be known that the synchronization error asymptotically tends to 0, that is, the drive system and the response system can achieve synchronization under the action of the finite-time synchronization controller.

[0092] The following numerical simulation is performed. In this embodiment, the driving system constructed by the fractional-order multimodal memristor neural network model is in the following specific form:

[0093]

[0094] Similarly, the response system is as follows:

[0095]

[0096] Among them, the following parameters are selected: ∈ = 0.98; i = 1, 2; C1 = 0.7, C2 = 0.677; activation function

[0097]

[0098] g(x j (t-τ ι (t)))=tanh(x) j (t-τ ι (t)));

[0099] τ 1 (t)=0.9|sin(t)|,

[0100]

[0101]

[0102] g(y j (t-τ ι (t))) = tanh(y j (t-τ ι (t)));

[0103] I 1 =1.2sin(t);

[0104] I 2 =0.9sin(t);

[0105] x(0)=[-2,2] T ,J 1 =1.1sin(t),J 2 =0.5sin(t),y(0)=[2,12] T ;

[0106]

[0107]

[0108] The controller parameters involved in this embodiment are: 1 =2.3,η 2 =2.3; p i ι =3.2; ζ 1 =ζ 2 =5.8; n 1 =0.61, n 2 =0.25, n 3 =0.2, n 4 =0.9; p 1 =1, p 2 =1.3;

[0109]

[0110] The numerical simulation operation is carried out according to the parameters given above. Figure 2 The figure shows the phase diagram of the driving system. By observing and analyzing the diagram, it can be found that the system is in a chaotic state.

[0111] Figure 3 It is the change trajectory of the states of the driving system and the response system under the condition that no controller is applied. Figure 3 In the figure, the upper figure shows the state change trajectories of the first drive system and the response system, x1 is the first drive system, y1 is the first response system, and the lower figure shows the state change trajectories of the second drive system and the response system, x2 is the second drive system and y2 is the second response system. It can be clearly seen from the figure that when there is no controller, the two systems cannot be synchronized.

[0112] Figure 4 When the finite-time state feedback synchronous controller of this embodiment is set for control, the drive system and the response system can maintain a consistent state within a limited time.

[0113] Figure 5 Under the condition of applying the finite-time state feedback synchronous controller of this embodiment, the error can gradually tend to 0 within a finite time. In the figure, e1 is the error system corresponding to the first simulated drive-response system in this example, e2 is the error system corresponding to the second drive-response system, and data is the data of the error system movement.

[0114] Example 2

[0115] Based on Example 1, this embodiment provides a fractional-order multimodal memristor neural network finite-time synchronization control system, including:

[0116] The system building module is configured to build a driving system and a response system of a fractional-order multimodal memristor neural network by fusing an activation function with a time delay and an activation function without a time delay according to a fractional-order neural network;

[0117] The error system determination module is configured to set a corresponding synchronization error according to a driving system and a response system of the constructed fractional-order multimodal memristor neural network, thereby establishing an error system;

[0118] The feedback synchronization control module is configured to consider the interaction between neurons, external input, time delay and error state, construct a finite-time state feedback synchronization controller, apply the finite-time state feedback synchronization controller to the response system, adjust the working state of each neuron memristor, and achieve synchronization between the response system and the drive system.

[0119] It should be noted here that the various modules in this embodiment correspond one-to-one to the various steps in Example 1, and the specific implementation process is the same, which will not be repeated here.

[0120] Example 3

[0121] This embodiment provides an electronic device, including a memory and a processor, and computer instructions stored in the memory and running on the processor. When the computer instructions are executed by the processor, the steps in the fractional-order multimodal memristor neural network finite-time synchronization control method of Example 1 are completed.

[0122] Example 4

[0123] This embodiment provides a computer-readable storage medium for storing computer instructions. When the computer instructions are executed by a processor, the steps in the fractional-order multimodal memristor neural network finite-time synchronization control method of Embodiment 1 are completed.

[0124] The above description is only a preferred embodiment of the present disclosure and is not intended to limit the present disclosure. For those skilled in the art, the present disclosure may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present disclosure shall be included in the protection scope of the present disclosure.

[0125] Although the above describes the specific implementation methods of the present disclosure in conjunction with the accompanying drawings, it is not intended to limit the scope of protection of the present disclosure. Technical personnel in the relevant field should understand that on the basis of the technical solution of the present disclosure, various modifications or variations that can be made by those skilled in the art without creative work are still within the scope of protection of the present disclosure.

Claims

1. A fractional-order multimodal memristor neural network finite-time synchronization control method, characterized in that: The steps include: According to the fractional-order neural network, the activation function with time delay and the activation function without time delay are integrated to construct the driving system and response system of the fractional-order multimodal memristor neural network. According to the driving system and response system of the constructed fractional-order multimodal memristor neural network, the corresponding synchronization error is set, and then the error system is established; Considering the interaction between neurons, external input, time delay and error state, a finite-time state feedback synchronization controller is constructed. The finite-time state feedback synchronization controller is applied to the response system to adjust the working state of each neuron memristor and achieve synchronization between the response system and the drive system.

2. The fractional-order multi-modal memristor neural network finite-time synchronization control method according to claim 1, characterized in that: The activation function with delay and the activation function without delay are integrated to establish the driving system of fractional-order multimodal memristor neural network. By integrating activation functions with time delay and activation functions without time delay, a response system of fractional-order multimodal memristor neural network is established.

3. The fractional-order multi-modal memristor neural network finite-time synchronization control method according to claim 2, characterized in that: The activation function uses the tangent function.

4. The fractional-order multi-modal memristor neural network finite-time synchronization control method according to claim 1, characterized in that: Considering the interaction between neurons, external input, time delay and error state, the finite-time state feedback synchronous controller is designed as: U i (t)=-η i (E i (t)) +n1E i (t) -p1 -n2E i (t) -q1 -n3E i (t)-sgn(E i (t))n4 Wherein, i=1, 2, ..., N; ι=1, 2, ..., m; n1, n2, n3, n4, p1 and q1 are all set values ​​greater than zero; sgn(E i (t)) represents the synchronization error E i (t) is a sign function; ζ i , η i is the set constant that satisfies the control gain of the controller.

5. The fractional-order multi-modal memristor neural network finite-time synchronization control method according to claim 1, characterized in that: A finite-time stability theorem is constructed to verify the control stability of the finite-time state feedback synchronous controller. The judgment conditions of the stability theorem are as follows: Wherein, ∈ represents the order of the fractional-order system; α, β are real numbers greater than or equal to 0; c, δ, θ are all constants greater than 0, and θ ≥ δ.

6. The fractional-order multi-modal memristor neural network finite-time synchronization control method according to claim 5, characterized in that: Based on the constructed finite-time stability theorem and Lyapunov function, the control stability of the finite-time state feedback synchronous controller is judged.

7. A fractional-order multimodal memristor neural network finite-time synchronous control system, characterized in that: include: The system building module is configured to build a driving system and a response system of a fractional-order multimodal memristor neural network by fusing an activation function with a time delay and an activation function without a time delay according to a fractional-order neural network; The error system determination module is configured to set a corresponding synchronization error according to a driving system and a response system of the constructed fractional-order multimodal memristor neural network, thereby establishing an error system; The feedback synchronization control module is configured to consider the interaction between neurons, external input, time delay and error state, construct a finite-time state feedback synchronization controller, apply the finite-time state feedback synchronization controller to the response system, adjust the working state of each neuron memristor, and achieve synchronization between the response system and the drive system.

8. The fractional-order multimodal memristor neural network finite-time synchronous control system according to claim 7, characterized in that: include: Considering the interaction between neurons, external input, time delay and error state, the finite-time state feedback synchronous controller is designed as: U i (t)=-η i (E i (t)) Wherein, i=1, 2, ..., N; ι=1, 2, ..., m; n1, n2, n3, n4, p1 and q1 are all set values ​​greater than zero; sgn(E i (t)) represents the synchronization error E i (t) is a sign function; ζ i , η i is the set constant that satisfies the control gain of the controller.

9. An electronic device, characterized in that: The invention comprises a memory and a processor and computer instructions stored in the memory and executed on the processor, wherein when the computer instructions are executed by the processor, the steps in the fractional-order multimodal memristor neural network finite-time synchronization control method as described in any one of claims 1 to 6 are completed.

10. A computer-readable storage medium, characterized in that: Used to store computer instructions, which, when executed by a processor, complete the steps in the fractional-order multimodal memristor neural network finite-time synchronization control method described in any one of claims 1 to 6.

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