A global projection synchronization method of a four-element value memristor neural network based on open-loop control and application thereof

Abstract

The application belongs to the field of memristor neural network and secret communication, and particularly relates to a global projection synchronization method of a four-element value memristor neural network based on open-loop control and application thereof. The method is different from the traditional separation of the system into a real number system and three complex number systems, but the system is regarded as a whole for research. Meanwhile, a discrete multi-time delay memristor neural network is used to establish a corresponding drive system and response system, and an open-loop controller is designed, so that the transmission of the encrypted plaintext signal in the channel can achieve better security effect. Compared with the traditional chaotic neural network, the application has better security effect, lower network energy consumption, and provides a better solution for encrypted communication.

Description

Technical Field

[0001] This invention relates to the fields of memristor neural networks and secure communication, specifically to a global projection synchronization method based on a quaternary memristor neural network with open-loop control and its application. Background Technology

[0002] With the advent of the Internet of Things era, communication technology is developing rapidly, leading to increasingly higher demands for communication security and confidentiality. However, existing communication and encryption methods have certain shortcomings, necessitating the continuous development of new communication encryption methods to meet the demand for high reliability. Due to the wide spectral density, strong nonlinearity, non-periodicity, and noise-like characteristics of chaotic signals, they were used for secure communication in the 1990s. In 1983, Professor Cai Shaotang proposed the famous Cai circuit, pioneering the theory of chaotic communication. In 1990, Pecora and Carroll of the U.S. Naval Research Laboratory first proposed chaotic synchronization based on the drive-response synchronization method. Since then, research on chaotic secure communication has entered a new stage, proposing many new synchronization methods and encryption technologies. In recent years, ultra-high-dimensional memristor chaotic circuits and systems have become a research hotspot and new field for scholars.

[0003] Memristors are considered the fourth type of passive circuit element, and these novel circuit elements possess many unique characteristics. In terms of practical applications, memristors primarily include: novel non-volatility, secure communication, and neural networks. Researchers have discovered that memristors resemble neurons in the human brain. Due to this property, an increasing number of researchers are constructing memristor-based neural networks, using memristors to replace resistors to simulate the human brain and study the dynamic behavior of neural networks. Therefore, combining memristors with neural networks for secure communication can significantly improve security performance.

[0004] Over the past few decades, Real-Valued Neural Networks (RVNNs) and Complex-Valued Neural Networks (CVNNs) have been widely applied in signal processing, associative memory, and automatic intelligent control due to their respective characteristics. However, CVNNs and RVNNs have certain limitations when dealing with multidimensional data. Considering this, some researchers have proposed Quadruple-Valued Neural Networks (QVNNs) to handle multidimensional data. Therefore, it is necessary to study the dynamic behavior of QVNNs. Furthermore, since memristors consume no energy and possess memory properties, research on quadruple memristor neural networks has significant practical implications.

[0005] In secure communication, the transmitted signals need to be converted without distortion at the receiving end, which leads to the concept of synchronization. The essence of synchronization control is to force one system to track another system by applying an appropriate controller.

[0006] To date, neural network synchronization has been successfully applied in numerous fields such as secure communication, public channel cryptography, and neurocryptography. Synchronization between chaotic systems and neural networks has become an important research area. Meanwhile, there are many research achievements in synchronization, including projection synchronization, anti-synchronization, phase synchronization, full synchronization, exponential synchronization, and Mittag-Leffler synchronization. Among these, projection synchronization refers to the ability of a neural network to synchronize to a scaling factor, indicating that different types of synchronization can be achieved by selecting different projection coefficients. When the projection coefficients are 1, 0, and -1, full synchronization, stable synchronization, and anti-synchronization can be achieved, respectively. Summary of the Invention

[0007] To achieve the above objectives, the present invention provides a global projection synchronization method based on an open-loop controlled quaternary memristor neural network, the synchronization method comprising the following steps:

[0008] S1: Description of a discrete multi-delay quaternion-valued memristor neural network;

[0009] S2: Design an open-loop controller;

[0010] S3: Implementation of the communication encryption scheme.

[0011] It needs further explanation that S1 specifically refers to:

[0012] ①. Establish a discrete multi-time-delay quaternary memristor neural network driven system:

[0013]

[0014] Where D α The notation for fractional derivatives, where α represents the order, 0 < α < 1; x i (t)=(x1(t),...,x n (t)) T Let c represent the state variable of the i-th neuron. i τ is a positive constant. j For discrete time delay, I i Let f represent the external input vector, which is a constant vector. i (·) and g i (·) is a non-linear activation function, a ij (x j (t)) and b ij (x j (t) represents the weights for connecting the memristors, and their values ​​are as follows:

[0015]

[0016]

[0017]

[0018]

[0019]

[0020]

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027]

[0028]

[0029]

[0030]

[0031] ②. Establish a discrete multi-delay quaternary memristor neural network response system:

[0032]

[0033] Where D α The notation for the fractional derivative, where α represents the order (0 < α < 1); and c represents the state variable of the i-th neuron. i τ is a positive constant. j For discrete time delay, I i Let f represent the external input vector, which is a constant vector. i (·) and g i (·) is a non-linear activation function, a ij (x j (t)) and b ij (x j (t) is the connection weight of the memristor, and its value is the same as that of the driver x. i (t)=(x1(t),...,x n (t)) T System, U i (t) represents the controller to be designed.

[0034] Further explanation is needed regarding S2, which specifically refers to:

[0035] ③. Construct the error function

[0036] ④. Controller design.

[0037] It needs further explanation that ③. the construction of the error function is specifically as follows:

[0038] Define the error function as: e i (t)=y i (t)-βx i (t), where i = 1, 2, ..., n, β ∈ R represents the projection factor, which reflects the synchronization ratio between the driving network and the response network;

[0039] The design of the controller, as described in section ④, is as follows:

[0040] Select the following controller: U i (t)=U i1 (t)+U i2 (t)+U i3 (t)

[0041]

[0042] Where k1=k2=2 are arbitrary positive constants, and β=2 are projection coefficients.

[0043] Further explanation is needed regarding step S3, which specifically includes:

[0044] ⑤. Because the signals processed within a computer are all binary signals, it is necessary to discretize the communication content into a binary bit stream signal M. s (k), the discretized state of the driving system, modulates the above two signals to obtain the modulated signal C. s (k).

[0045] ⑥. Place X i (k) and C s (k) Transmission from the sending end to the receiving end, i.e., the receiving end of the response system, is designed with a synchronization controller to receive X. i (k) and the response system Y i (k) Data is collected, and then the state of the response system is adjusted to synchronize with the state of the drive system.

[0046] ⑦. Next, the communication signal is transferred from C by the demodulation unit. s Separate from (k) to obtain the decrypted signal R s (k), due to X i (k) and Y i(k) Synchronization, therefore M s (k)=R s (k) This completes the entire process of secure communication.

[0047] Further explanation is needed regarding the application of a global projection synchronization method based on an open-loop controlled quaternary memristor neural network in secure communication.

[0048] The technical effects and advantages provided by the present invention in the above technical solution are as follows:

[0049] Unlike traditional separation techniques, this invention treats the fractional-order quaternion-valued memristor neural network (FOQVMNN) as a whole, significantly reducing system energy consumption. Furthermore, based on real-valued neural networks (RVNN) and complex-valued neural networks (CVNN), a quaternion-valued neural network (QVNN) is proposed for processing high-dimensional data, improving security performance.

[0050] To avoid decomposing QVNN into two CVNNs or four RVNNs, a new quaternion sign function is introduced based on the real and complex number sign functions. Simultaneously, a novel open-loop controller is designed to ensure the global projection synchronization criterion of FOQVMNN with multiple delays. Applying this to the field of secure communication significantly increases the complexity of secure communication systems and enhances the difficulty of cracking them.

[0051] A novel 1-norm Lyapunov function is established based on the quaternion sign function. Furthermore, based on the designed open-loop controller and the proposed lemma, some sufficient conditions for ensuring global projection synchronization of the system are given.

[0052] The invention provides a wider range of applications, including secure transmission of audio, text, images, and video. Attached Figure Description

[0053] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0054] Figure 1 This is a block diagram of the overall structure of encrypted communication;

[0055] Figure 2 This is a flowchart illustrating the design of the global projection synchronization method based on open-loop control of a fractional-order quaternary memristor neural network in Embodiment 2 of the present invention.

[0056] Figure 3aThis is a real part diagram of the trajectory graphs of x1(t) and y1(t) without an open-loop controller in Embodiment 2 of the present invention;

[0057] Figure 3b This is the imaginary part of the trajectory diagrams of x1(t) and y1(t) without an open-loop controller in Embodiment 2 of the present invention;

[0058] Figure 3c This is the imaginary part of the trajectory diagrams of x1(t) and y1(t) without an open-loop controller in Embodiment 2 of the present invention;

[0059] Figure 3d This is the imaginary part of the trajectory diagrams of x1(t) and y1(t) without an open-loop controller in Embodiment 2 of the present invention;

[0060] Figure 4a This is a real part diagram of the trajectory of x2(t) and y2(t) without an open-loop controller in Embodiment 2 of the present invention;

[0061] Figure 4b This is the imaginary part of the trajectory diagrams of x2(t) and y2(t) without an open-loop controller in Embodiment 2 of the present invention;

[0062] Figure 4c This is the imaginary part of the trajectory diagrams of x2(t) and y2(t) without an open-loop controller in Embodiment 2 of the present invention;

[0063] Figure 4d This is the imaginary part of the trajectory diagrams of x2(t) and y2(t) without an open-loop controller in Embodiment 2 of the present invention;

[0064] Figure 5 This is the error system state trajectory diagram without an open-loop controller in Embodiment 2 of the present invention;

[0065] Figure 6a This is a real part diagram of the trajectory of x1(t) and y1(t) under the open-loop controller in Embodiment 2 of the present invention;

[0066] Figure 6b This is the imaginary part of the trajectory diagrams of x1(t) and y1(t) under the open-loop controller in Embodiment 2 of the present invention;

[0067] Figure 6c This is the imaginary part of the trajectory diagrams of x1(t) and y1(t) under the open-loop controller in Embodiment 2 of the present invention;

[0068] Figure 6d This is the imaginary part of the trajectory diagrams of x1(t) and y1(t) under the open-loop controller in Embodiment 2 of the present invention;

[0069] Figure 7aThis is a real part diagram of the trajectory of x2(t) and y2(t) under the addition of an open-loop controller in Embodiment 2 of the present invention;

[0070] Figure 7b This is the imaginary part of the trajectory diagrams of x2(t) and y2(t) under the open-loop controller in Embodiment 2 of the present invention;

[0071] Figure 7c This is the imaginary part of the trajectory diagrams of x2(t) and y2(t) under the open-loop controller in Embodiment 2 of the present invention;

[0072] Figure 7d This is the imaginary part of the trajectory diagrams of x2(t) and y2(t) under the open-loop controller in Embodiment 2 of the present invention;

[0073] Figure 8 This is the error system state trajectory diagram with an open-loop controller added in Embodiment 2 of the present invention. Detailed Implementation

[0074] To provide a clearer explanation and description of the technical solution and implementation of the present invention, several preferred specific embodiments for implementing the technical solution of the present invention are described below.

[0075] The following description is exemplary in nature and is not intended to limit the scope, application, or use of this disclosure. It should be understood that in all these figures, the same or similar reference numerals indicate the same or similar parts and features. The figures are merely schematic representations of the concept and principles of embodiments of this disclosure and do not necessarily show the specific dimensions and scale of each embodiment. Specific details or structures of embodiments of this disclosure may be exaggerated in particular portions of certain figures. The disclosures of various publications, patents, and published patent specifications cited herein are incorporated herein by reference in their entirety. The technical solutions of this invention will be clearly and completely described below in conjunction with embodiments of the invention. Obviously, the described embodiments are only a part of the embodiments of this invention.

[0076] Example 1

[0077] This embodiment provides a global projection synchronization method based on an open-loop controlled quaternary memristor neural network. This method is used to achieve global projection synchronization between the driving network and the response network of a fractional-order quaternary memristor neural network system. The projection e... i The specific steps of the synchronization method are as follows:

[0078] First, define the system's error function, let:

[0079] e i (t)=y i (t)-βx i (t)

[0080] Where, x i (t) represents the state variables of the driving system; y i (t) represents the state variables of the response system; β represents the projection factor, which reflects the synchronization ratio between the driving system and the response system.

[0081] Next, design the open-loop controller U. i (t) is:

[0082] U i (t)=U i1 (t)+U i2 (t)+U i3 (t)

[0083]

[0084] Where, k i This indicates the gain of the controller.

[0085] In this embodiment, the driving system model of the fractional-order quaternion-valued memristor neural network is as follows:

[0086]

[0087] Where D α The notation for fractional derivatives, where α represents the order, 0 < α < 1; x i (t)=(x1(t),...,x n (t)) T Let c represent the state variable of the i-th neuron. i τ is a positive constant. j For discrete time delay, I i Let f represent the external input vector, which is a constant vector. i (·) and g i (·) is a non-linear activation function, a ij (x j (t)) and b ij (x j (t) is the connection memristor weight.

[0088] In this embodiment, the response system model of the fractional-order quaternion-valued memristor neural network is as follows:

[0089]

[0090] Where D α The notation for fractional derivatives, where α represents the order, 0 < α < 1; x i (t)=(x1(t),...,x n (t)) T Let c represent the state variable of the i-th neuron.i τ is a positive constant. j For discrete time delay, I i Let f represent the external input vector, which is a constant vector. i (·) and g i (·) is a non-linear activation function, a ij (x j (t)) and b ij (x j (t) is the connection weight of the memristor, U i (t) represents the controller to be designed.

[0091] Example 2

[0092] This embodiment mainly includes two parts:

[0093] The first part provides a theoretical proof of the effectiveness of the synchronization controller designed in the projection synchronization method of the fractional-order quaternary memristor neural network in Example 1.

[0094] The second part uses numerical simulation to verify the theoretical analysis in the first part.

[0095] (Theoretical proofs and simulation experiments are not intended to limit the present invention. In other embodiments, simulation experiments may not be performed, or other experimental schemes may be used to verify the performance of the neural network system.)

[0096] I. Theoretical Proof

[0097] 1. Conditional Assumptions:

[0098] First, in general studies of projection synchronization in quaternion-valued memristor neural networks, the system is usually divided into four subsystems, including one real part system and three imaginary parts systems. However, since this paper introduces a quaternion-valued sign function and related fractional inequalities, it is not necessary to divide the system into four subsystems; instead, the system is studied as a whole.

[0099] Secondly, considering the discontinuity of the memristor weights, under the meaning of the Filioppov solution, based on the theory of differential inclusion and extremum mapping, we can obtain the following driving-response system and error system:

[0100] Drive system:

[0101]

[0102] Response system:

[0103]

[0104] Error system:

[0105]

[0106] These are the results after differential inclusion and extremum mapping, respectively.

[0107] in

[0108]

[0109]

[0110]

[0111]

[0112] Among them, T j Indicates the jump time, T j >0.

[0113] For any system's driver and response networks, if global projection synchronization is to be achieved through a designed open-loop controller, the following conditions must be met:

[0114] H1-vH2>0

[0115] Where v>1

[0116]

[0117]

[0118] 2. Derivation and Proof

[0119] Construct a Lyapunov function as follows:

[0120]

[0121] according to

[0122]

[0123] have

[0124]

[0125] Based on the properties of quaternions, the above inequality can be rearranged to obtain:

[0126]

[0127] By Lipschitz conditions:

[0128] |f i (x)-f i (x')|1≤F i|x-x'|1

[0129] |g(x)-g i (x')|1≤G i |x-x'|1

[0130] have:

[0131]

[0132]

[0133]

[0134]

[0135]

[0136] in

[0137]

[0138]

[0139] The above four parts can be summarized as follows:

[0140]

[0141] According to the fractional Razumikhin theorem:

[0142] D α V(t)≤-H1V(t)+H2V(t-τ j )≤-(H1-vH2)V(t)

[0143] in

[0144]

[0145]

[0146] In summary, the synchronization method provided in this embodiment can achieve global projection synchronization of fractional-order quaternary memristor neural networks.

[0147] II. Numerical Simulation

[0148] In this embodiment, taking a two-dimensional fractional-order quaternary memristor neural network system with multiple time delays as an example, the model of the driving system of the neural network system is determined as follows:

[0149]

[0150] in

[0151] τ1=0.2, τ2=0.8, c1=c2=1, I i (t)=(0,0) T , i = 1, 2.

[0152] The quaternion-valued memristor connection weights satisfy:

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[0167]

[0168]

[0169] Meanwhile, the corresponding response system model of the two-dimensional fractional-order quaternary memristor neural network system with multiple time delays is as follows:

[0170]

[0171] The values ​​for some parameters are as follows: projection coefficient β = 2, control gain k1 = k2 = 2, v = 1.2, and Lipschitz constant N. i =M i=1, (i = 1, 2) to ensure H1 - vH2 > 0, and the values ​​of the other parameters are consistent with those in the drive system.

[0172] in, Figure 2 Figure 1 is a flowchart of a global projection synchronization method based on an open-loop control fractional-order quaternary memristor neural network in Embodiment 1 of the present invention; Figure 3 is a trajectory diagram of x1(t) and y1(t) without an open-loop controller in Embodiment 2 of the present invention (the diagram contains one real part and three imaginary parts, the real part being...). Figure 3a The three imaginary parts are: Figure 3b , Figure 3c and Figure 3d Figure 4 shows the trajectories of x2(t) and y2(t) without an open-loop controller in Embodiment 2 of the present invention (the figure contains one real part and three imaginary parts, the real part being...). Figure 4a The three imaginary parts are: Figure 4b , Figure 4c and Figure 4d ); Figure 5 Figure 6 shows the error system state trajectory diagram without an open-loop controller in Embodiment 2 of the present invention; Figure 7 shows the trajectory diagrams of x1(t) and y1(t) with an open-loop controller in Embodiment 2 of the present invention (the figure contains one real part diagram and three imaginary parts diagrams, the real part diagram is...). Figure 6a The three imaginary parts are: Figure 6b , Figure 6c and Figure 6d Figure 7 shows the trajectories of x2(t) and y2(t) with an open-loop controller added in Embodiment 2 of the present invention (the figure contains one real part and three imaginary parts, the real part being...). Figure 7a The three imaginary parts are: Figure 7b , Figure 7c and Figure 7d ); Figure 8 This is the error system state trajectory diagram with an open-loop controller added in Embodiment 2 of the present invention.

[0173] In summary, the trend of the curves in the simulation results obtained from the simulation experiment shows that the fractional-order quaternary memristor neural network provided in this embodiment can achieve global projection synchronization of the system under an open-loop controller.

[0174] Example 3

[0175] This embodiment builds upon Embodiment 2, achieving global projection synchronization of the driver-response system and applying it to secure communication.

[0176] like Figure 1 As shown, in a communication system with a signal transmitter, a signal receiver, and a channel, the method for implementing secure communication using a fractional-order quaternary memristor neural network system is as follows:

[0177] ⑤. Because the signals processed within a computer are all binary signals, it is necessary to discretize the communication content into a binary bit stream signal M. s (k), the discretized state of the driving system, modulates the above two signals to obtain the modulated signal C. s (k).

[0178] ⑥. Place X i (k) and C s (k) Transmission from the sending end to the receiving end, i.e., the receiving end of the response system, is designed with a synchronization controller to receive X. i (k) and the response system Y i (k) collects data and then adjusts the state of the response system to synchronize it with the state of the drive system.

[0179] ⑦. Next, the communication signal is transferred from C by the demodulation unit. s Separate from (k) to obtain the decrypted signal R s (k), due to X i (k) and Y i (k) Synchronization, therefore C s (k)=R s (k).

[0180] The foregoing has only described certain exemplary embodiments of the present invention by way of illustration. Undoubtedly, those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the foregoing drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A global projection synchronization method based on a quaternary memristor neural network with open-loop control, characterized in that: The synchronization method includes the following steps: S1: Description of a discrete multi-delay quaternion-valued memristor neural network; S2: Design an open-loop controller; Design an open-loop controller for: in, Indicates the gain of the controller. Indicates the projection factor; S3: Implementation of the communication encryption scheme; Specifically, S1 is: ①. Establish a discrete multi-time-delay quaternary memristor neural network driven system: in The notation for fractional derivatives, Indicates the order, ; Indicates the first The state variables of each neuron For positive integers, For discrete time delay, This represents the external input vector, which is a constant vector. and It is a non-linear activation function. and These are the connection weights for the memristors, and their values ​​are as follows: ②. Establish a discrete multi-delay quaternary memristor neural network response system: in The notation for fractional derivatives, Indicates the order, ; Indicates the first The state variables of each neuron For positive integers, For discrete time delay, This represents the external input vector, which is a constant vector. and It is a non-linear activation function. and It connects the memristor weights, and its value is the same as that of the driver. system, The controller to be designed.

2. The global projection synchronization method based on a quaternary memristor neural network with open-loop control according to claim 1, characterized in that: Specifically, S2 is: ③. Construct the error function ④. Controller design.

3. The global projection synchronization method based on a quaternary memristor neural network with open-loop control according to claim 2, characterized in that: The specific construction of the error function mentioned in ③ is as follows: Define the error function as: ,in , The projection factor represents the synchronization ratio between the driving network and the response network.

4. The global projection synchronization method based on a quaternary memristor neural network with open-loop control according to claim 1, characterized in that: Step S3 specifically includes: ⑤. Because the signals processed within a computer are all binary signals, it is necessary to discretize the communication content into a binary bit stream signal. , To obtain the modulated signal, the two signals are modulated to represent the discretized state of the driving system. ; ⑥. and The data is transmitted from the sending end to the receiving end, and the receiving end, i.e., the response system, is designed with a synchronization controller to receive the data. With response system Data is collected, and then the state of the response system is adjusted to synchronize with the state of the drive system. ; ⑦. Next, the communication signal is converted from... by the demodulation unit. The decryption signal is extracted from the sample. ,because and Synchronization, therefore This completes the entire process of secure communication.

5. The application of the global projection synchronization method based on open-loop control quaternary memristor neural network according to any one of claims 1-4 in secure communication.

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