Secure communication method based on time-varying and time-delay fuzzy CG neural network

Abstract

The present invention belongs to the field of new generation information technology, and specifically relates to a secure communication method based on a time-varying time-delay fuzzy CG neural network. The method establishes a drive system and a response system based on a time-varying time-delay fuzzy CG neural network; sets a synchronization error, designs a fixed-time quantized synchronization controller, and the response system, under the action of the fixed-time quantized synchronization controller, realizes fixed-time synchronization between the response system and the drive system, thereby realizing secure communication. The present invention introduces time-varying time delay into the fuzzy CG neural network, and designs a fixed-time quantized synchronization controller, which solves the problem of fixed-time synchronization based on the time-varying time-delay fuzzy CG neural network, and the proposed secure communication method improves the complexity and security of secure communication.

Description

Technical Field

[0001] The present invention relates to the field of new generation information technology, and in particular to a secure communication method based on a time-varying and time-delay fuzzy CG neural network. Background Art

[0002] In the practical application of neural networks, in order to cope with the ever-changing real-world problems, neural networks need to present complex dynamic states, so it is necessary to study complex and universal CG neural network systems. In addition, in actual engineering applications, due to the existence of certain unknown characteristics and uncertainties in the system, fuzzy theory plays an important role in the modeling of neural network systems. Therefore, the study of fuzzy CG neural networks has potential application value in the field of new generation information technology.

[0003] There are a large number of synchronization phenomena in nature and many disciplines. Compared with the research on realizing neural network synchronization in infinite time, realizing neural network synchronization in finite time has a more profound significance for the new generation of information technology. However, the initial values ​​of most neural networks and chaotic systems are uncertain, and the upper bound of synchronization time cannot be obtained in actual situations. Therefore, fixed time synchronization is introduced. In the fixed time synchronization strategy, the initial value is independent of the upper bound of the neural network synchronization time. Then, by adjusting the gain of the controller, the upper bound of the synchronization time is adjusted by the gain, thereby realizing the fixed time synchronization of the neural network.

[0004] Bandwidth constraints in network communication systems limit the transmission speed of information on communication channels. The introduction of quantitative control can reduce its impact on control performance, alleviate the transmission pressure of communication channels, and save economic costs. Summary of the invention

[0005] The purpose of the present invention is to provide a secure communication method based on a time-varying, time-delay fuzzy CG neural network, which can achieve fixed time synchronization based on a time-varying, time-delay fuzzy CG neural network and improve the security of secure communication.

[0006] To achieve the above object, the present invention provides the following technical solution, a secure communication method based on a time-varying and time-delay fuzzy CG neural network, comprising the following steps:

[0007] Step S1: Establishing a driving system and a response system based on a time-varying and time-delay fuzzy CG neural network, specifically including the following steps:

[0008] Step S11: Establishing a time-varying and time-delay fuzzy CG neural network driving system:

[0009]

[0010] In the formula, the coefficient ε i is a constant, and time t≥0, i=1, 2, ..., n; j=1, 2, ..., n; n represents the number of neurons in the fuzzy CG neural network; x i (t) represents the state of the i-th neuron of the fuzzy CG neural network at time t; α i represents the damping coefficient of the i-th neuron, α i Satisfy α i >0;p i (·) represents the magnification function, and there exists a positive constant p i and H i The amplification function p i (·) satisfies the inequality: 0 <p i (χ)≤p i ,|p i (χ)-p i (ψ)|≤H i |χ-ψ|, where χ and ψ are arbitrary real numbers; β i (·) represents the behavior function, and there exists a positive constant J i The amplification function p i (·) and the behavior function β i (·) satisfies the inequality: a ij 、b ij and c ij represents the connection weight; d ij is the feedforward element; h ij and m ij is the minimum element of fuzzy feedback; k ij and n ij is the largest element of fuzzy feedback; T ij and S ij They represent the minimum fuzzy feedforward element and the maximum fuzzy feedforward element respectively; f j (x j (t)) represents the activation function of the jth neuron in the fuzzy CG neural network without time lag, f j (x j (t-τ ij (t))) represents the activation function of the j-th neuron in the fuzzy CG neural network containing time-varying time lag, represents the activation function of the jth neuron of the fuzzy CG neural network with neutral time lag, τ ij (t) represents the information transmission delay of neurons at time t, and satisfies is a constant; the above activation functions all satisfy the Lipschitz condition, that is and |f j (·)|≤M j ,in and ω are any real numbers, L jis a positive constant, M j is a positive constant; ∧ and ∨ represent the "fuzzy AND" and "fuzzy OR" operators respectively, and for any real number and ω satisfy the following conditions:

[0011]

[0012] V j (t) represents the input of the jth neuron and satisfies in is a positive constant; I i (t) represents the bias of the i-th neuron and satisfies |I i (t)|≤I i , where I i is a positive constant;

[0013] Step S12: According to the driving system established in step S11, a corresponding response system is established:

[0014]

[0015] Wherein, time t≥0, i=1, 2, ..., n; j=1, 2, ..., n; n represents the number of neurons in the fuzzy CG neural network; y i (t) represents the state of the i-th neuron of the response system at time t; w i (t) represents the z in the response system corresponding to the z in the drive system i (t) parameter; f j (y j (t)) represents the activation function of the jth neuron in the response system without time delay, f j (y j (t-τ ij (t))) represents the activation function of the jth neuron in the response system including time-varying delay, represents the activation function of the jth neuron in the response system with neutral time delay; the above activation functions all satisfy the Lipschitz condition, that is, and |f j (·)|≤M j ,in and ω are any real numbers, L j is a positive constant, M j is a positive constant; and represents a fixed-time quantized synchronous controller;

[0016] Step S2: according to the driving system and the response system based on the time-varying and time-delay fuzzy CG neural network established in step S1, setting the synchronization error;

[0017] Step S3: According to the synchronization error constructed in step S2, a fixed-time quantized synchronization controller is designed, and the fixed-time quantized synchronization controller is applied to the response system so that the response system is synchronized with the drive system, thereby realizing a confidential communication method.

[0018] Furthermore, step S2 is specifically as follows:

[0019] According to the drive system and response system based on the time-varying and time-delay fuzzy CG neural network constructed in step S1, the synchronization error of the drive system and the response system is set as:

[0020]

[0021] Furthermore, step S3 specifically includes the following contents:

[0022] Step S31: Design a fixed-time quantized synchronization controller according to the synchronization error constructed in step S2:

[0023]

[0024] Among them, σ 1 , σ 2 , λ, μ and θ are positive controller gains; 0<η<1, ψ>1; sign(·) is the sign function; g(e 1i (t)) is the error e 1i The quantized value of (t), g(e 1i (t))=(1+Δ)e 1i (t), Δ is the quantization error, is a sector boundary, 0<δ<1; g(e 2i (t)) is the error e 2i (t), where g(e 2i (t))=(1+Δ)e 2i (t); controller gain σ 1 , σ 2 and θ satisfy the following inequalities:

[0025]

[0026]

[0027] Step S32: applying the fixed-time quantized synchronization controller to the response system, so that the response system is synchronized with the drive system;

[0028] Step S33: After the drive system is synchronized with the response system, the sending end obtains the chaotic signal generated by the drive system as the encrypted signal x i (t), the receiving end obtains the chaotic signal generated by the response system as the decryption signal y i (t);

[0029] Step S34: The transmitting end encrypts the signal x i (t) and the plaintext signal s i (t) Perform encryption operation to obtain the ciphertext signal h i (t), h i (t) = x i (t)+s i (t);

[0030] Step S35: The transmitting end sends the ciphertext signal h through the channel i (t), the receiving end receives the ciphertext signal h through the channel i (t);

[0031] Step S36: The receiving end receives the plaintext signal h i (t) and the decrypted signal y i (t) Perform decryption operation to obtain the decrypted plaintext signal ss i (t), ss i (t) = h i (t)-y i (t).

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] 1. In the present invention, fuzzy operators and time-varying delays are introduced into the CG neural network, which has more complex dynamic behaviors than other first-order neural networks, and increases the difficulty of cracking confidential communications.

[0034] 2. The present invention designs a fixed-time synchronous quantization controller. This type of synchronous convergence time is independent of the initial value of the system and is only related to the parameters of the controller, so that the neural network can achieve the desired synchronization characteristics within a controllable time and achieve reasonable optimization of resources. At the same time, after the quantizer is introduced into the control system, the burden of the communication channel and the impact of bandwidth constraints on system performance can be reduced, saving system resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a flow chart of a secure communication method based on time-varying and time-delay fuzzy CG neural network of the present invention;

[0036] Figure 2is the change trajectory diagram of the driving system and the response system without the action of the controller, where (a) is the x 1 (t) and y 1 (t) is the trajectory of x; (b) is the trajectory of x without the controller 2 (t) and y 2 (t) is the trajectory of z without the controller; (c) is the trajectory of z without the controller 1 (t) and w 1 (t) is the trajectory of z without the controller; (d) is the trajectory of z without the controller 2 (t) and w 2 (t) trajectory diagram;

[0037] Figure 3 is the synchronization error e without controller action 11 (t), e 12 (t), e 21 (t) and e 22 (t) change trajectory diagram;

[0038] Figure 4 is the change trajectory diagram of the driving system and the response system under the action of the fixed-time quantized synchronous controller, where (a) is the change trajectory diagram of x under the action of the fixed-time quantized synchronous controller 1 (t) and y 1 (t) is the trajectory of x; (b) is the trajectory of x under the action of fixed-time quantized synchronous controller 2 (t) and y 2 (t) is the trajectory diagram; (c) is the trajectory diagram of z under the action of fixed-time quantized synchronous controller 1 (t) and w 1 (t) is the trajectory diagram; (d) is the trajectory diagram of z under the action of fixed-time quantized synchronous controller 2 (t) and w 2 (t) trajectory diagram;

[0039] Figure 5 is the error trajectory diagram under the action of fixed-time quantized synchronous controller, where (a) is the synchronization error e under the action of fixed-time quantized synchronous controller 11 (t), e 12 (t), e 21 (t) and e 22 (t) is the changing trajectory of g(e) under the action of fixed-time quantized synchronous controller; (b) is the changing trajectory of g(e) under the action of fixed-time quantized synchronous controller 11 (t))、g(e 12 (t))、g(e 21 (t)) and g(e 22 (t))’s changing trajectory. DETAILED DESCRIPTION

[0040] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0041] Embodiment 1:

[0042] like Figure 1 As shown, this embodiment provides a secure communication method based on a time-varying and time-delay fuzzy CG neural network, the method comprising the following steps:

[0043] Step S1: Establishing a driving system and a response system based on a time-varying and time-delay fuzzy CG neural network, specifically including the following steps:

[0044] Step S11: Establishing a time-varying and time-delay fuzzy CG neural network driving system:

[0045]

[0046] In the formula, the coefficient ε i is a constant, and time t≥0, i=1, 2, ..., n; j=1, 2, ..., n; n represents the number of neurons in the fuzzy CG neural network; x i (t) represents the state of the i-th neuron of the fuzzy CG neural network at time t; α i represents the damping coefficient of the i-th neuron, α i Satisfy α i >0;p i (·) represents the magnification function, and there exists a positive constant p i and H i The amplification function p i (·) satisfies the inequality: 0 <p i (χ)≤p i ,|p i (χ)-p i (ψ)|≤H i |χ-ψ|, where χ and ψ are arbitrary real numbers; β i (·) represents the behavior function, and there exists a positive constant J i The amplification function p i (·) and the behavior function β i (·) satisfies the inequality: a ij 、b ij and c ij represents the connection weight; d ij is the feedforward element; hij and m ij is the minimum element of fuzzy feedback; k ij and n ij is the largest element of fuzzy feedback; T ij and S ij They represent the minimum fuzzy feedforward element and the maximum fuzzy feedforward element respectively; f j (x j (t)) represents the activation function of the jth neuron in the fuzzy CG neural network without time lag, f j (x j (t-τ ij (t))) represents the activation function of the j-th neuron in the fuzzy CG neural network containing time-varying time lag, represents the activation function of the jth neuron of the fuzzy CG neural network with neutral time lag, τ ij (t) represents the information transmission delay of neurons at time t, and satisfies is a constant; the above activation functions all satisfy the Lipschitz condition, that is and |f j (·)|≤M j ,in and ω are any real numbers, L j is a positive constant, M j is a positive constant; ∧ and ∨ represent the "fuzzy AND" and "fuzzy OR" operators respectively, and for any real number and ω satisfy the following conditions:

[0047]

[0048] V j (t) represents the input of the jth neuron and satisfies in is a positive constant; I i (t) represents the bias of the i-th neuron and satisfies |I i (t)|≤I i , where I i is a positive constant;

[0049] Step S12: According to the driving system established in step S11, a corresponding response system is established:

[0050]

[0051] Wherein, time t≥0, i=1, 2, ..., n; j=1, 2, ..., n; n represents the number of neurons in the fuzzy CG neural network; y i (t) represents the state of the i-th neuron of the response system at time t; w i(t) represents the z in the response system corresponding to the z in the drive system i (t) parameter; f j (y j (t)) represents the activation function of the jth neuron in the response system without time delay, f j (y j (t-τ ij (t))) represents the activation function of the jth neuron in the response system including time-varying delay, represents the activation function of the jth neuron in the response system with neutral time delay; the above activation functions all satisfy the Lipschitz condition, that is, and |f j (·)|≤M j ,in and ω are any real numbers, L j is a positive constant, M j is a positive constant; and represents a fixed-time quantized synchronous controller;

[0052] Step S2: according to the driving system and the response system based on the time-varying and time-delay fuzzy CG neural network established in step S1, setting the synchronization error;

[0053] Step S3: According to the synchronization error constructed in step S2, a fixed-time quantized synchronization controller is designed, and the fixed-time quantized synchronization controller is applied to the response system so that the response system is synchronized with the drive system, thereby realizing a confidential communication method.

[0054] Furthermore, step S2 is specifically as follows:

[0055] According to the drive system and response system based on the time-varying and time-delay fuzzy CG neural network constructed in step S1, the synchronization error of the drive system and the response system is set as:

[0056]

[0057] Furthermore, step S3 specifically includes the following contents:

[0058] Step S31: Design a fixed-time quantized synchronization controller according to the synchronization error constructed in step S2:

[0059]

[0060] Among them, σ 1 , σ 2 , λ, μ and θ are positive controller gains; 0<η<1, ψ>1; sign(·) is the sign function; g(e 1i (t)) is the error e1i The quantized value of (t), g(e 1i (t))=(1+Δ)e 1i (t), Δ is the quantization error, is a sector boundary, g(e 2i (t)) is the error e 2i (t), where g(e 2i (t))=(1+Δ)e 2i (t); controller gain σ 1 , σ 2 and θ satisfy the following inequalities:

[0061]

[0062] Step S32: applying the fixed-time quantized synchronization controller to the response system, so that the response system is synchronized with the drive system;

[0063] Step S33: After the drive system is synchronized with the response system, the sending end obtains the chaotic signal generated by the drive system as the encrypted signal x i (t), the receiving end obtains the chaotic signal generated by the response system as the decryption signal y i (t);

[0064] Step S34: The transmitting end encrypts the signal x i (t) and the plaintext signal s i (t) Perform encryption operation to obtain the ciphertext signal h i (t), h i (t) = x i (t)+s i (t);

[0065] Step S35: The transmitting end sends the ciphertext signal h through the channel i (t), the receiving end receives the ciphertext signal h through the channel i (t);

[0066] Step S36: The receiving end receives the plaintext signal h i (t) and the decrypted signal y i (t) Perform decryption operation to obtain the decrypted plaintext signal ss i (t), ss i (t) = h i (t)-y i (t).

[0067] It is worth noting that, in the present invention, fuzzy operators and time-varying delays are introduced into the CG neural network, which has more complex dynamic behaviors than other first-order neural networks, and increases the difficulty of cracking confidential communications. A fixed-time synchronous quantization controller is designed in the present invention. This type of synchronous convergence time is independent of the initial value of the system and is only related to the parameters of the controller, so that the neural network can achieve the desired synchronization characteristics within a controllable time and realize reasonable optimization of resources. At the same time, after the quantizer is introduced into the control system, the burden of the communication channel and the impact of bandwidth constraints on system performance can be reduced, saving system resources.

[0068] Embodiment 2:

[0069] This embodiment mainly includes two parts:

[0070] The first is to theoretically prove the effectiveness of a secure communication method based on a time-varying, time-delay fuzzy CG neural network proposed in Example 1.

[0071] Secondly, the synchronization performance of the fuzzy CG neural network driving system and response system with time-varying delay in Example 1 is verified by numerical simulation.

[0072] (Theoretical proof and simulation experiment are not used to limit the present invention. In other embodiments, simulation experiment may not be performed, and other experimental schemes may be used to test and verify the performance of the neural network system.)

[0073] 1. Theoretical Proof

[0074] Define the synchronization error between the drive system and the response system: e 1i (t) = y i (t)-x i (t), e 2i (t) = w i (t)-z i (t), the synchronous error system can be obtained from the driving system and the response system as follows

[0075]

[0076] The following are the definitions and lemmas that will be used in the proof:

[0077] Definition 1: For a fixed time T that is completely independent of the initial value of the system max >0, if all t≥T max , both have And|y i (t)-x i (t)|=0,|w i (t)-z i(t)|=0, then the driving system and the response system are called max Achieve fixed time synchronization within

[0078] Lemma 1: Assume there exists a regular, positive definite and radially unbounded function V(t): R n →R + ∪{0}, so that any solution of the error system satisfies the inequality:

[0079]

[0080] in, Then the upper bound of time T max It is expressed by the following formula:

[0081]

[0082] Lemma 2: Assume u 1 ,u 2， …,u n ≥0,0<p≤1,q> 1, then

[0083]

[0084] Next, construct the Lyapunov functional:

[0085]

[0086] Then, the derivative of the constructed Lyapunov functional is calculated:

[0087]

[0088]

[0089]

[0090] According to the bounded activation function, the following inequality can be obtained:

[0091]

[0092]

[0093] And according to the amplification function p i (·), behavior function β i (·) and neuron j input V j (t) is defined, then We can further get:

[0094]

[0095] Since the parameter σ 1 , σ2 and θ satisfy the following inequalities:

[0096]

[0097] Then it can be deduced that:

[0098]

[0099] According to Lemma 2, we can get:

[0100]

[0101] Based on Lemma 1, we can get 2λ(1+δ) η >0, T max as follows:

[0102]

[0103] Therefore, according to Definition 1 and Lemma 1, It can be seen that under the action of the fixed-time quantized synchronous controller, the drive system and the response system are max Fixed time synchronization is achieved within.

[0104] 2. Numerical Simulation

[0105] In this embodiment, taking a time-varying and time-delay fuzzy CG neural network containing two neurons as an example, the driving system and the response system are determined as follows:

[0106]

[0107]

[0108] The specific parameters are as follows: i = 1, 2; j = 1, 2; t ≥ 0; time-varying lag τ 12 (t) = cos 2 (t), τ 21 (t) = sin 2 (t), f 1 (x 1 (t)) = tanh(x 1 (t)); f 2 (x 2 (t)) = tanh(x 2 (t)); f 1 (x 1 (t-τ 21 (t)))=tanh(x) 1 (t-sin 2(t)));f 2 (x 2 (t-τ 12 (t)))=tanh(x 2 (t-cos 2 (t)));f 2 (x 2 (t-τ 22 (t)))=tanh(x 2 (t-cos 2 (t))); f 1 (y 1 (t))=tanh(y 1 (t));f 2 (y 2 (t))=tanh(y 2 (t)); f 1 (y 1 (t-τ 21 (t)))=tanh(y 1 (t-sin 2 (t)));f 2 (y 2 (t-τ 12 (t)))=tanh(y 2 (t-cos 2 (t)));f 2 (y 2 (t-τ 22 (t)))=tanh(y 2 (t-cos 2 (t))); β 1 (x 1 (t))=0.4x 1 (t);β 2 (x 2 (t))=0.4x 2 (t);β 1 (y 1 (t))=0.4y 1 (t);β 2 (y 2 (t))=0.4y 2 (t);ε 1 =ε 2 =1;α 1 =α 2 =4;a 11 =-1、a12 =1, a 21 =1, a 22 =-1; b 11 =-2, b 12 =3, b 21 =3, b 22 =-2; c 11 =-1, c 12 =-1.5, c 21 =1, c 22 =-2; d 11 =-0.4, d 12 =-0.2, d 21 =-0.25, d 22 =-0.3; T 11 =-2, T 12 =1, T 21 =1, T 22 =-4; S 11 =-3, S 12 =1, S 21 =1, S 22 =-3; h 11 =-3, h 12 =1.5,h 21 =1.5,h 22 =3; k 11 =3, k 12 =-1.5, k 21 =1.5, k 22 =-3; m 11 =-2, m 12 =1.5, m 21 =1.4, m 22 =1.8; n 11 =-2.6, n 12 =3.5, n 21 =-2.6, n 22 =-2.8; external input V 1 (t) = 5sin(t), V 2 (t) = 5cos(t), take I 1 (t) = 3cos(t), I 2 (t) = 3sin(t), take I i =3; let M j =1, J i =0.12, H i =0.05; p i =0.4, δ=0.25;

[0109] According to the above parameter settings and inequality:

[0110]

[0111] The parameter value ranges are: 1 ≥2.559,σ 2 ≥0.959, θ≥11.24; then according to the requirements of the fixed time quantized synchronous controller λ>0, μ>0, 0<η<1, ψ>1; take σ 1 =3,σ 2 =1,θ=11.5,λ=1,μ=1,η=0.5,ψ=1.5; According to Lemma 1, we can get T max =3.491.

[0112] The drive system, response system and fixed time quantized synchronous controller are numerically simulated under the above parameters. The initial values ​​of the drive system and response system are set as: 1 (0) = 0, x 2 (0) = -2, z 1 (0) = 0, z 2 (0) = -1, y 1 (0) = 1, y 2 (0) = 0, w 1 (0) = 2, w 2 (0)=0, t>0.

[0113] The specific simulation experiment results are as follows: Figure 2 is the change trajectory diagram of the driving system and the response system without the action of the controller, where (a) is the x 1 (t) and y 1 (t) is the trajectory of x; (b) is the trajectory of x without the controller 2 (t) and y 2 (t) is the trajectory of z without the controller; (c) is the trajectory of z without the controller 1 (t) and w 1 (t) is the trajectory of z without the controller; (d) is the trajectory of z without the controller 2 (t) and w 2 (t) trajectory diagram; Figure 3 is the synchronization error e without controller action 11 (t), e 12 (t), e 21 (t) and e 22 (t) change trajectory diagram; Figure 4 is the change trajectory diagram of the driving system and the response system under the action of the fixed-time quantized synchronous controller, where (a) is the change trajectory diagram of x under the action of the fixed-time quantized synchronous controller 1 (t) and y 1 (t) is the trajectory of x; (b) is the trajectory of x under the action of fixed-time quantized synchronous controller2 (t) and y 2 (t) is the trajectory diagram; (c) is the trajectory diagram of z under the action of fixed-time quantized synchronous controller 1 (t) and w 1 (t) is the trajectory diagram; (d) is the trajectory diagram of z under the action of fixed-time quantized synchronous controller 2 (t) and w 2 (t) trajectory diagram; Figure 5 is the error trajectory diagram under the action of fixed-time quantized synchronous controller, where (a) is the synchronization error e under the action of fixed-time quantized synchronous controller 11 (t), e 12 (t), e 21 (t) and e 22 (t) is the changing trajectory of g(e) under the action of fixed-time quantized synchronous controller; (b) is the changing trajectory of g(e) under the action of fixed-time quantized synchronous controller 11 (t))、g(e 12 (t))、g(e 21 (t)) and g(e 22 (t)) change trajectory diagram. Among them, Figure 2 and Figure 3 It shows that the drive system and the response system cannot be synchronized without the action of the controller; Figure 4 and Figure 5 The trajectory shows that the response system is synchronized with the drive system under the action of the fixed-time quantized synchronization controller, verifying the synchronization performance.

[0114] Finally, it should be noted that the above description is only a preferred example of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or replace some of the technical features therein by equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A secure communication method based on time-varying and time-delay fuzzy CG neural network, characterized in that: The following steps are involved: Step S1: Establishing a driving system and a response system based on a time-varying and time-delay fuzzy CG neural network, specifically including the following steps: Step S11: Establishing a time-varying and time-delay fuzzy CG neural network driving system: In the formula, the coefficient ε i is a constant, and time t≥0, i=1, 2, ..., n; j=1, 2, ..., n; n represents the number of neurons in the fuzzy CG neural network; x i (t) represents the state of the i-th neuron of the fuzzy CG neural network at time t; α i represents the damping coefficient of the i-th neuron, α i Satisfy α i >0;p i (·) represents the magnification function, and there exists a positive constant p i and H i The amplification function p i (·) satisfies the inequality: 0 <p i (χ)≤p i ,|p i (χ)-p i (ψ)|≤H i |χ-ψ|, where χ and ψ are arbitrary real numbers; β i (·) represents the behavior function, and there exists a positive constant J i The amplification function p i (·) and the behavior function β i (·) satisfies the inequality: χ≠ψ; a ij , b ij and c ij represents the connection weight; d ij is the feedforward element; h ij and m ij is the minimum element of fuzzy feedback; k ij and n ij is the largest element of fuzzy feedback; T ij and S ij They represent the minimum fuzzy feedforward element and the maximum fuzzy feedforward element respectively; f j (x j (t)) represents the activation function of the jth neuron in the fuzzy CG neural network without time lag, f j (x j (t-τ ij (t))) represents the activation function of the j-th neuron in the fuzzy CG neural network containing time-varying time lag, represents the activation function of the jth neuron of the fuzzy CG neural network with neutral time lag, τ ij (t) represents the information transmission delay of neurons at time t, and satisfies is a constant; the above activation functions all satisfy the Lipschitz condition, that is and |f j (·)|≤M j ,in and ω are any real numbers, L j is a positive constant, M j is a positive constant; ∧ and ∨ represent the "fuzzy AND" and "fuzzy OR" operators respectively, and for any real number and ω satisfy the following conditions: V j (t) represents the input of the jth neuron and satisfies in is a positive constant; I i (t) represents the bias of the i-th neuron and satisfies |I i (t)|≤I i , where I i is a positive constant; Step S12: According to the driving system established in step S11, a corresponding response system is established: Wherein, time t≥0, i=1, 2, ..., n; j=1, 2, ..., n; n represents the number of neurons in the fuzzy CG neural network; y i (t) represents the state of the i-th neuron of the response system at time t; w i (t) represents the z in the response system corresponding to the z in the drive system i (t) parameter; f j (y j (t)) represents the activation function of the jth neuron in the response system without time delay, f j (y j (t-τ ij (t))) represents the activation function of the jth neuron in the response system including time-varying delay, represents the activation function of the jth neuron in the response system with neutral time delay; the above activation functions all satisfy the Lipschitz condition, that is, and |f j (·)|≤M j ,in and ω are any real numbers, L j is a positive constant, M j is a positive constant; and represents a fixed-time quantized synchronous controller; Step S2: according to the driving system and the response system based on the time-varying and time-delay fuzzy CG neural network established in step S1, a synchronization error is set; Step S3: designing a fixed-time quantized synchronization controller according to the synchronization error constructed in step S2, and applying the fixed-time quantized synchronization controller to the response system so that the response system is synchronized with the drive system, thereby realizing a confidential communication method; Step S2 is specifically as follows: According to the drive system and response system based on the time-varying and time-delay fuzzy CG neural network constructed in step S1, the synchronization error of the drive system and the response system is set as: Step S3 specifically includes the following steps: Step S31: Design a fixed-time quantized synchronization controller according to the synchronization error constructed in step S2: where σ1, σ2, λ, μ, and θ are positive controller gains; 0<η<1, ψ>1; sign(·) is the sign function; g(e 1i (t)) is the error e 1i The quantized value of (t), g(e 1i (t))=(1+Δ)e 1i (t), Δ is the quantization error, is a sector boundary, 0<δ<1; g(e 2i (t)) is the error e 2i (t), where g(e 2i (t))=(1+Δ)e 2i (t); the controller gains σ1, σ2 and θ satisfy the following inequalities: Step S32: applying the fixed-time quantized synchronization controller to the response system, so that the response system is synchronized with the drive system; Step S33: After the drive system is synchronized with the response system, the sending end obtains the chaotic signal generated by the drive system as the encrypted signal x i (t), the receiving end obtains the chaotic signal generated by the response system as the decryption signal y i (t); Step S34: The transmitting end encrypts the signal x i (t) and the plaintext signal s i (t) Perform encryption operation to obtain the ciphertext signal h i (t), h i (t) = x i (t)+s i (t); Step S35: The transmitting end sends the ciphertext signal h through the channel i (t), the receiving end receives the ciphertext signal h through the channel i (t); Step S36: The receiving end receives the plaintext signal h i (t) and the decrypted signal y i (t) Perform decryption operation to obtain the decrypted plaintext signal ss i (t), ss i (t) = h i (t)-y i (t).

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