Secret communication method based on mixed time delay fuzzy neural network

Abstract

The invention belongs to the technical field of new-generation information, and particularly relates to a secret communication method based on a mixed time-delay fuzzy neural network, and the method comprises the steps: building a driving system and a response system based on the mixed time-delay fuzzy neural network; a projection synchronization error is set, a finite time quantitative projection synchronization controller is designed, and the response system realizes finite time projection synchronization of the response system and the driving system under the action of the finite time quantitative projection synchronization controller, so that secret communication is realized. According to the invention, the time-varying time lag and the finite distributed time lag are introduced into the fuzzy neural network, and the finite time quantitative projection synchronization controller is designed, so that the problem of finite time projection synchronization based on the mixed time lag fuzzy neural network is solved, and the complexity and security of secret communication are improved by the proposed secret communication method.

Description

Technical Field

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

[0002] In the practical application of neural networks, in order to cope with changing real-world problems, neural networks need to exhibit complex dynamic states. Therefore, it is necessary to study complex and general neural network systems. In addition, in practical engineering applications, due to the unknown characteristics and uncertainties of the system, the fuzzy theory plays an important role in the modeling of neural network systems. Therefore, studying fuzzy 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 achieving neural network synchronization in infinite time, achieving projective synchronization of neural networks in finite time has more profound significance for the field of new generation information technology.

[0004] Bandwidth constraints in network communication systems limit the transmission speed of information on communication channels. Introducing quantization control can reduce its impact on control performance, relieve the transmission pressure on communication channels, and save economic costs. Summary of the Invention

[0005] The object of the present invention is to provide a secure communication method based on a hybrid time-delay fuzzy neural network, which can achieve finite-time projective synchronization based on a hybrid time-delay fuzzy 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 hybrid time-delay fuzzy neural network includes the following steps:

[0007] Step S1: Establish a drive system and a response system based on a hybrid time-delay fuzzy neural network, specifically including the following steps:

[0008] Respectively establish a drive system and a response system based on a hybrid time-delay fuzzy neural network:

[0009]

[0010] Where time t ≥ 0, i = 1, 2,..., n; j = 1, 2,..., n; n represents the number of neurons in the fuzzy neural network; x i (t) represents the state of the i-th neuron in the drive system at time t; α i represents the damping coefficient of the i-th neuron, α i satisfies α i > 0; a ij 、bij and c ij represents the connection weight; d ij is a feedforward element; h ij and m ij are the minimum fuzzy feedback elements; k ij and n ij are the maximum fuzzy feedback elements; T ij and S ij represent the minimum fuzzy feedforward element and the maximum fuzzy feedforward element respectively; f j (x j (t)) represents the activation function of the j-th neuron without time delay in the fuzzy neural network, f j (x j (t - σ(t))) represents the activation function of the j-th neuron with time-varying discrete time delay in the fuzzy neural network; y i (t) represents the state of the i-th neuron in the response system at time t; f j (y j (t)) represents the activation function of the j-th neuron without time delay in the response system, f j (y j (t - σ(t))) represents the activation function of the j-th neuron with time-varying discrete time delay in the response system; σ(t) and τ(t) represent the discrete time delay and the distributed time delay of the neuron information transmission at time t respectively, and satisfy are constants; each of the above activation functions satisfies the Lipschitz condition, that is and |f j (·)| ≤ M j , where and ω are arbitrary real numbers, L j is a positive constant, M j is a positive constant; and represent the finite-time quantization projection synchronization controller; ∧ and ∨ represent the "fuzzy AND" and "fuzzy OR" operators respectively, and for any real numbers and ω satisfy the following conditions:

[0011]

[0012] V j (t) represents the input of the j-th neuron; 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 S2: Based on the drive system and response system of the hybrid time-delay fuzzy neural network established in Step S1, set the projection synchronization error;

[0014] Step S3: Based on the projection synchronization error constructed in Step S2, design a finite-time quantization projection synchronization controller, and apply the finite-time quantization projection synchronization controller to the response system, so that the response system projects and synchronizes with the drive system within a finite time T, thereby realizing the secure communication method.

[0015] Further, Step S2 is specifically as follows:

[0016] Based on the drive system and response system of the hybrid time-delay fuzzy neural network constructed in Step S1, set the projection synchronization error of the drive system and the response system as:

[0017] e i (t) = y i (t) - βx i (t)

[0018] In the formula, β represents the projection coefficient.

[0019] Further, Step S3 specifically includes the following contents:

[0020] Step S31: Based on the projection synchronization error constructed in Step S2, design a finite-time quantization projection synchronization controller:

[0021]

[0022] where λ i , η i and θ i are positive controller gains; 0 < ν < 1; sign(·) is the sign function; g(e i (t)) is the quantization value of the error e i (t), g(e i (t)) = (1 + Δ)e i (t), Δ is the quantization error, is the sector boundary, 0 < δ < 1; the controller gains λ i and θ i satisfy the following inequalities:

[0023] -2α i -2λ i (1 + δ) ≤ 0

[0024]

[0025] Step S32: Apply the finite-time quantization projection synchronization controller to the response system, such that the response system projects synchronously with the drive system within a finite time T;

[0026] Step S33: After the drive system and the response system are in projection synchronization, the sender obtains the chaotic signal generated by the drive system as the encryption signal x i (t), and the receiver obtains the chaotic signal generated by the response system as the decryption signal y i (t);

[0027] Step S34: The sender performs an encryption operation on the encryption signal x i (t) and the plaintext signal s i (t) to obtain the ciphertext signal h i (t), h i (t) = x i (t) + s i (t);

[0028] Step S35: The sender sends the ciphertext signal h i (t) through a channel, and the receiver receives the ciphertext signal h i (t) through the channel;

[0029] Step S36: The receiver performs a decryption operation on the received ciphertext signal h i (t) and the decryption signal y i (t) to obtain the decrypted plaintext signal ss i (t), ss i (t) = h i (t) - y i (t) / β.

[0030] Further, the finite time T in Step S3 is:

[0031]

[0032] Compared with the prior art, the beneficial effects of the present invention are:

[0033] 1. In the present invention, a fuzzy operator, time-varying time delay, and finite distributed time delay are introduced into the neural network. Compared with other first-order neural networks, it has more complex dynamic behaviors, further increasing the difficulty of cracking secure communication.

[0034] 2. A finite-time quantization projection synchronization controller is designed in the present invention. The synchronization convergence time of this type can be optimized by adjusting the initial value, enabling the neural network to achieve the desired synchronization characteristics within a controllable time and realizing the reasonable optimization of resources. At the same time, after the quantizer is introduced into the control system, it can reduce the burden on the communication channel and the impact of bandwidth constraints on the system performance, saving system resources. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The drawings are used to provide a further understanding of the present invention and constitute a part of the specification. They are used together with Embodiment 1 of the present invention to explain the present invention and do not constitute a limitation to the present invention.

[0036] In the drawings:

[0037] Figure 1 is a flowchart of a secure communication method based on a hybrid time-delay fuzzy neural network according to the present invention;

[0038] Figure 2 is a change trajectory diagram of the drive system and the response system without the action of a controller, where (a) is a trajectory diagram of y 1 (t) and x 1 (t); (b) is a trajectory diagram of y 2 (t) and x 2 (t);

[0039] Figure 3 is a change trajectory diagram of the projection synchronization error e 1 (t) and e 2 (t);

[0040] Figure 4 is a change trajectory diagram of the drive system and the response system under the action of a finite-time quantization projection synchronization controller, where (a) is a trajectory diagram of y 1 (t) and x 1 (t); (b) is a trajectory diagram of y 2 (t) and x 2 (t);

[0041] Figure 5 is an error trajectory diagram under the action of a finite-time quantization projection synchronization controller, where (a) is a change trajectory diagram of the projection synchronization error e 1 (t) and e 2 (t); (b) is a change trajectory diagram of g(e 1 (t)) and g(e 2 (t)). Detailed implementation mode

[0042] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0043] Embodiment 1:

[0044] As Figure 1 shown, this embodiment provides a secure communication method based on a hybrid time-delay fuzzy neural network. The synchronization control method includes the following steps:

[0045] Step S1: Establish a drive system and a response system based on a hybrid time-delay fuzzy neural network, specifically including the following steps:

[0046] Respectively establish a drive system and a response system based on a hybrid time-delay fuzzy neural network:

[0047]

[0048] In the formula, time t≥0, i = 1, 2,..., n; j = 1, 2,..., n; n represents the number of neurons in the fuzzy neural network; x i (t) represents the state of the i-th neuron in the drive system at time t; α i represents the damping coefficient of the i-th neuron, α i satisfies α i >0; a ij , b ij and c ij represent connection weights; d ij is a feedforward element; h ij and m ij are fuzzy feedback minimum elements; k ij and n ij are fuzzy feedback maximum elements; T ij and S ij respectively represent the fuzzy feedforward minimum element and the fuzzy feedforward maximum element; f j (x j (t)) represents the activation function of the j-th neuron in the fuzzy neural network without time delay, f j (x j (t - σ(t))) represents the activation function of the j-th neuron in the fuzzy neural network with time-varying discrete time delay; y i (t) represents the state of the i-th neuron in the response system at time t; fj (y j (t)) represents the activation function without time delay of the j-th neuron in the said response system, f j (y j (t - σ(t))) represents the activation function with time-varying discrete time delay of the j-th neuron in the said response system; σ(t) and τ(t) respectively represent the discrete time delay and distributed time delay of neuron information transmission at time t, and satisfy is a constant; each of the above activation functions satisfies the Lipschitz condition, that is and |f j (·)| ≤ M j , where and ω are arbitrary real numbers, L j is a positive constant, M j is a positive constant; and represent the finite-time quantization projection synchronization controller; ∧ and ∨ respectively represent the "fuzzy AND" and "fuzzy OR" operators, and for any real numbers and ω satisfy the following conditions:

[0049]

[0050]

[0051] V j (t) represents the input of the j-th neuron; 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;

[0052] Step S2: According to the drive system and response system based on the hybrid time-delay fuzzy neural network established in Step S1, set the projection synchronization error;

[0053] Step S3: According to the projection synchronization error constructed in Step S2, design a finite-time quantization projection synchronization controller, and apply the finite-time quantization projection synchronization controller to the said response system, so that the said response system is projection synchronized with the said drive system within a finite time T, thereby realizing the secure communication method.

[0054] In this embodiment, Step S2 is specifically:

[0055] According to the drive system and response system based on the hybrid time-delay fuzzy neural network constructed in Step S1, set the projection synchronization error between the said drive system and response system as:

[0056] e i (t) = y i (t) - βx i (t)

[0057] Where β represents the projection coefficient.

[0058] In this embodiment, step S3 specifically includes the following content:

[0059] Step S31: Design a finite-time quantization projection synchronization controller according to the projection synchronization error constructed in step S2:

[0060]

[0061] Where λ i , η i and θ i are positive controller gains; 0 < ν < 1; sign(·) is the sign function; g(e i (t)) is the quantization value of the error e i (t), g(e i (t)) = (1 + Δ)e i (t), Δ is the quantization error, is the sector boundary, 0 < δ < 1; the controller gains λ i and θ i satisfy the following inequalities:

[0062] -2α i -2λ i (1 + δ) ≤ 0

[0063]

[0064] Step S32: Apply the finite-time quantization projection synchronization controller to the response system so that the response system is projection synchronized with the drive system within a finite time T;

[0065] Step S33: After the drive system and the response system are projection synchronized, the sender obtains the chaotic signal generated by the drive system as the encryption signal x i (t), and the receiver obtains the chaotic signal generated by the response system as the decryption signal y i (t);

[0066] Step S34: The sender performs an encryption operation on the encryption signal x i (t) and the plaintext signal s i (t) to obtain the ciphertext signal h i (t), h i (t) = x i (t) + si (t);

[0067] Step S35: The sender sends the ciphertext signal h i (t) through the channel, and the receiver receives the ciphertext signal h i (t) through the channel;

[0068] Step S36: The receiver performs a decryption operation on the received ciphertext signal h i (t) and the decryption signal y i (t) to obtain the decrypted plaintext signal ss i (t), ss i (t)=h i (t)-y i (t) / β;

[0069] In this embodiment, the finite time T in step S3 is:

[0070]

[0071] It should be noted that in the present invention, by introducing a fuzzy operator, time-varying time delay, and finite distributed time delay into the neural network, compared with other first-order neural networks, it has more complex dynamic behaviors, which further increases the difficulty of cracking the secure communication. In the present invention, a finite-time quantization projection synchronization controller is designed, and the synchronization convergence time of this type can be optimized by adjusting the initial value, so that the neural network can achieve the desired synchronization characteristics within a controllable time, realizing the reasonable optimization of resources. At the same time, after the quantizer is introduced into the control system, it can reduce the burden on the communication channel and the influence of bandwidth constraints on the system performance, saving system resources.

[0072] Embodiment 2:

[0073] In this embodiment, taking a hybrid time-delay fuzzy neural network containing two neurons as an example, the drive system and the response system are determined as follows:

[0074]

[0075]

[0076] The specific parameters are as follows: i = 1, 2; j = 1, 2; t ≥ 0; the time-varying time delay σ(t)=1.01|sin(t)|; the finite distributed time delay τ(t)=1.01|sin(t)|; f 1 (x 1 (t))=tanh(x 1 (t)); f 2 (x 2 (t))=tanh(x 2 (t)); f1 (x 1 (t - τ(t))) = tanh(x 1 (t - 1.01|sin(t)|)); f 2 (x 2 (t - τ(t))) = tanh(x 2 (t - 1.01|sin(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(t))) = tanh(y 1 (t - 1.01|sin(t)|)); f 2 (y 2 (t - τ(t))) = tanh(y 2 (t - 1.01|sin(t)|)); β = 1.5; α 1 = α 2 = 3; a 11 = 0.3, a 12 = 0.1, a 21 = -0.1, a 22 = 0.2; b 11 = -0.4, b 12 = 0.2, b 21 = 0.3, b 22 = 0.1; c 11 = -。04, c 12 = 0.2, c 21 = 0.3, c 22 = 0.1; d 11 = 0.4, d 12 = 0.2, d 21 = -0.25, d 22 = 0.3; T 11 = 1, T 12 = -1, T 21 = -0.9, T 22 = 1; S 11 = -1, S 12 = 1, S 21 = 0.9, S 22 = -1; h 11 = -0.6, h It should be noted that there seems to be an unclear or incorrect expression "-。04" in the original text which is retained as is in the translation.12 = 0.5, h 21 = -0.4, h 22 = 0.8; k 11 = -1, k 12 = 2, k 21 = -2, k 22 = 1.8; 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) = 1, V 2 (t) = 1; I 1 (t) = 4cos(t), I 2 (t) = 4sin(t), take I i = 4; Let M j = 1, δ = 0.25;

[0077] According to the above parameter settings, and the inequality:

[0078] -2α i -2λ i (1 + δ) ≤ 0

[0079]

[0080] The value range of the parameter can be obtained as: λ 1 ≥ 0, λ 2 ≥ 0, θ ≥ 2.65; Then according to the requirements of the finite-time quantization synchronization controller η i > 0, 0 < ν < 1; Take λ 1 = λ 2 = 1, θ = 2.9, η 1 = η 2 = 0.7, ν = 0.9, and the upper bound of time T = 5.18 is obtained.

[0081] For the drive system, response system and finite-time quantization synchronization controller under the above-set parameters, perform numerical simulations on them. The initial values of the drive system and response system are set as: x 1 (0) = 1, x 2 (0) = -1.5, y 1 (0) = -1, y 2 (0) = 0.5.

[0082] The specific simulation experiment results are as follows: Figure 2Trajectory diagrams of the drive system and the response system without the action of a controller, where (a) shows the trajectory diagrams of y 1 (t) and x 1 (t); (b) shows the trajectory diagrams of y 2 (t) and x 2 (t); Figure 3 Trajectory diagrams of the projection synchronization errors e 1 (t) and e 2 (t) without the action of a controller; Figure 4 Trajectory diagrams of the drive system and the response system under the action of a finite-time quantization projection synchronization controller, where (a) shows the trajectory diagrams of y 1 (t) and x 1 (t) under the action of a finite-time quantization projection synchronization controller; (b) shows the trajectory diagrams of y 2 (t) and x 2 (t) under the action of a finite-time quantization projection synchronization controller; Figure 5 Error trajectory diagrams under the action of a finite-time quantization projection synchronization controller, where (a) shows the trajectory diagrams of the projection synchronization errors e 1 (t) and e 2 (t) under the action of a finite-time quantization projection synchronization controller; (b) shows the trajectory diagrams of g(e 1 (t)) and g(e 2 (t)) under the action of a finite-time quantization projection synchronization controller; where Figures 2 - 3 It shows that the drive system and the response system cannot achieve synchronization without the action of a controller; Figures 4 - 5 The trajectory shows that the response system achieves projection synchronization with the drive system under the action of a finite-time quantization projection synchronization controller, verifying the synchronization performance.

[0083] Finally, it should be noted that the above are only preferred examples of the present invention and are not used to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A secure communication method based on a hybrid time-delay fuzzy neural network, characterized in that: The following steps are involved: Step S1: Establishing a driving system and a response system based on a hybrid time-delay fuzzy neural network, specifically including the following steps: The driving system and response system based on hybrid time-delay fuzzy neural network are established respectively: Wherein, time t≥0, i=1, 2, ..., n; j=1, 2, ..., n; n represents the number of neurons in the fuzzy neural network; x i (t) represents the state of the i-th neuron in the driving system at time t; α i represents the damping coefficient of the i-th neuron, α i Satisfy α i >0;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 neural network without time lag, f j (x j (t-σ(t))) represents the activation function of the j-th neuron in the fuzzy neural network containing time-varying discrete time lag; y i (t) represents the state of the i-th neuron in the response system at time t; 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-σ(t))) represents the activation function of the jth neuron in the response system with a time-varying discrete time delay; σ(t) and τ(t) represent the discrete time delay and distributed time delay of neuron information transmission at time t, respectively, and satisfy 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 represents a finite-time quantized projective synchronization controller; ∧ 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; 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 S2: according to the driving system and the response system based on the hybrid time-delay fuzzy neural network established in step S1, setting the projection synchronization error; Step S3: According to the projection synchronization error constructed in step S2, a finite-time quantitative projection synchronization controller is designed, and the finite-time quantitative projection synchronization controller is applied to the response system, so that the response system is projected and synchronized with the driving system within a finite time T, thereby realizing a confidential communication method.

2. The secure communication method based on a hybrid time-delay fuzzy neural network according to claim 1 is characterized in that: Step S2 is specifically as follows: According to the drive system and response system based on the hybrid time-delay fuzzy neural network constructed in step S1, the projection synchronization error of the drive system and the response system is set to: e i (t)=y i (t)-βx i (t) Where β represents the projection coefficient.

3. The secure communication method based on a hybrid time-delay fuzzy neural network according to claim 2 is characterized in that: Step S3 specifically includes the following steps: Step S31: According to the projection synchronization error constructed in step S2, a finite time quantized projection synchronization controller is designed: Among them, λ i , η i and θ i is a positive controller gain; 0<ν<1; sign(·) is the sign function; g(e i (t)) is the error e i The quantized value of (t), g(e i (t))=(1+Δ)e i (t), Δ is the quantization error, is a sector boundary, 0<δ<1; controller gain λ i and θ i The following inequalities are satisfied: -2a i -2min i (1+δ)≤0 Step S32: applying the finite time quantized projection synchronization controller to the response system, so that the response system is projection synchronized with the drive system within a finite time T; Step S33: After the projection synchronization between the driving system and the response system, the transmitting end obtains the chaotic signal generated by the driving 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 ciphertext 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) / β.

4. The secure communication method based on a hybrid time-delay fuzzy neural network according to claim 3 is characterized in that: The limited time T in step S3 is:

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