Adaptive chaotic synchronous controller design method and secret communication method based on MANN and DH-PGA

Abstract

The invention provides a self-adaptive chaotic synchronous controller design method and a secret communication method based on an MANN and a DH-PGA algorithm. The method is used for solving the synchronization problem of the three-dimensional chaotic system under the conditions of uncertainty and external disturbance. By introducing the memristor and the DH-PGA algorithm, the controller not only shows strong robustness when facing system uncertainty and external disturbance, but also can improve the synchronization precision and stability of the system through adaptive adjustment. Generally speaking, the chaotic synchronous controller based on the MANN and the DH-PGA provides an effective solution for synchronization of a complex nonlinear system, and particularly shows excellent performance in scenes with high real-time requirements and limited computing resources.

Description

Technical Field

[0001] The present invention relates to chaos synchronization control technology, in particular to the design of an adaptive nonlinear robust controller used in communication and control systems, and belongs to the fields of automatic control, information security and cryptography, and in particular to an adaptive chaos synchronization controller design method and a confidential communication method based on MANN and DH-PGA algorithms. Background Art

[0002] Since the theory of chaotic systems was proposed, it has gradually become an important field of scientific research. Chaotic synchronization is a key branch of this field, which aims to make the state variables of multiple chaotic systems consistent or maintain a specific relationship through specific control methods. This technology has broad application prospects in many fields such as communication, security and signal processing. However, traditional control methods such as feedback control and sliding mode control have problems such as design redundancy and lack of flexibility, making it difficult to effectively cope with the challenges of complex dynamic systems. Summary of the invention

[0003] The purpose of the present invention is to solve the problems in the prior art and propose an adaptive chaos synchronization controller design method and a confidential communication method based on MANN and DH-PGA algorithms.

[0004] The present invention is implemented by the following technical scheme. The present invention proposes a design method of an adaptive chaotic synchronization controller based on MANN and DH-PGA algorithms. The design method includes two parts:

[0005] Design of MANN: The activation function in RBFNN is replaced with a memristor model to form a neural network MANN activated by a memristor. The mathematical expression of the memristor model is as follows:

[0006]

[0007] Where M(q) is the resistance value of the memristor at time t, which depends on the charge q(t) and the external voltage V(t); α is the weight parameter that controls the amplitude of the resistance change; tanh is the hyperbolic tangent function, which limits the combined effect of charge and voltage to a limited range, ensuring that the change in resistance presents an adaptive nonlinear characteristic; M0 is a constant that represents the offset of the initial state of the memristor; q(t) is a function that depends on the input quantity, which is understood as the intrinsic state variable of the memristor, reflecting the memory effect of the memristor; V(t) is the dynamic external condition or input drive term of the memristor; β,γ are model parameters;

[0008] DH-PGA algorithm design: The particle swarm of the PSO algorithm and the population of the GA are merged to form a larger mixed population. The optimization process in each iteration is executed alternately by the PSO algorithm and the GA. In specific operations, the PSO algorithm and the GA each update individual solutions through different strategies and share the global optimal solution, thus forming a collaborative optimization mechanism.

[0009] Furthermore, in the design process of MANN, the specific expression of q(t) is as follows

[0010]

[0011] The relationship followed by the memristor is expressed as:

[0012]

[0013] Applying the memristor model to the activation function of the neuron, the resulting activation function can be formalized as:

[0014]

[0015] Where e is expressed as equation (8);

[0016]

[0017] Among them, the parameters M0, α, β, γ are all 3×1 matrices, and i is both the number of inputs and the number of neurons;

[0018] When using equation (6) as the activation function, the controller design is expressed as:

[0019] u(t)=W T Ψ(e) (9).

[0020] Furthermore, in the DH-PGA algorithm design process, after each iteration, the optimal solutions of PSO and GA are synchronized to ensure that each algorithm can utilize the optimal solution found by the other part; the combined formula is as follows:

[0021]

[0022] In this process, no matter the global optimal solution found by the PSO algorithm or the GA, it will be updated to global_best_position and used by both the PSO algorithm and the GA in the next iteration.

[0023] Furthermore, in the design of the DH-PGA algorithm, the fitness function selected is:

[0024]

[0025] Where T is the simulation termination time, x is / im (t) is the value of the i-th state variable of the master (slave) system at time t, x is (t)-x im (t) is the error between the master system and the slave system at the i-th state variable.

[0026] Furthermore, during the GA optimization process, the selection pressure coefficient pressure is dynamically adjusted according to the population diversity, and its calculation formula is as follows:

[0027] pressure=1+(2-1)·(1+exp(-diversity)) (11)

[0028]

[0029] Where diversity is the diversity of the population, Var(x i ) is the variance of each individual genetic variable, n is the size of the population;

[0030] Equation (11) indicates that as diversity increases, the selection pressure will decrease, thereby maintaining the diversity of the population; next, roulette selection is performed, with probability P i Represents the probability of each individual being selected:

[0031]

[0032] Cost i is the fitness function value of the i-th individual;

[0033] Assume there are two parent-child bodies P1={p11,p12,…,p1 l} and P2={p21,p22,…,p2 l}, where l is the length of the individual; select multiple crossover points, assuming that the two crossover points c1 and c2 satisfy 1≤c1<c2≤l, then the generated offspring O={o1,o2,…,o l} can be expressed as:

[0034]

[0035] The mutation method selects Gaussian mutation; in addition, the crossover rate C r and mutation rate M r It is dynamically adjusted and adaptively regulated through population diversity;

[0036]

[0037] in is the initial crossover rate 0.4, The initial mutation rate is 0.4.

[0038] Furthermore, the inertia weight ω is dynamically adjusted during the PSO optimization process; the inertia weight is adjusted using an exponential decay method:

[0039] ω=ω min +(ω max -ω min )·e -0.01·λ (17)

[0040] where ω min and ω max are the minimum and maximum values ​​of the inertia weight, respectively, and λ is the current number of iterations.

[0041] Furthermore, the acceleration coefficients c1 and c2 are dynamically adjusted during the PSO optimization process; the acceleration coefficients c1 and c2 respectively determine the degree of dependence of the particle on the individual optimal position and the global optimal position when updating the position; the acceleration coefficient is dynamically adjusted using an exponential function through the following formula:

[0042]

[0043] where c 1,max and c 1,min are the initial maximum and minimum values ​​of acceleration c1, λ is the current iteration number, α is the total number of iterations, and c 2,max and c 2,min are the initial maximum and minimum values ​​of acceleration c2 respectively;

[0044] The PSO algorithm iterates the optimization process by updating the speed and position of each particle; the update formulas for speed and position are as follows:

[0045] v i (k+1)=ω·v i (k)+c1(p i -x i (k))+c2(gx i (k)) (20)

[0046] x i (k+1)=x i (k)+v i (k+1) (21)

[0047] where v i (k) is the velocity of particle i at the kth iteration, x i (k) is the position of particle i at the kth iteration, p i is the individual optimal position of particle i, and g is the optimal position of the particle group.

[0048] The present invention also proposes a secure communication method, which is implemented based on the controller; the secure communication method uses the linear combination of the state variables of the master system as the synchronization signal, and the slave system is also in the same way, specifically: during the communication process, the synchronization signal sent by the sender is [f 1m ,f 2m ,f 3m ],[f 1m ,f 2m ,f 3m ]The expression is as follows

[0049]

[0050] The receiver generates [f 1s ,f 2s ,f 3s ]; In this method, the sender linearly combines the state variables of the main system and sends the combined data [f 1m ,f 2m ,f 3m ] is sent to the receiver as a synchronization signal; the receiver’s response system also uses a linear combination method to obtain [f 1s ,f 2s ,f 3s ], and finally [f 1m -f 1s ,f 2m -f 2s ,f 3m -f 3s ] as the input of the memristive neural controller.

[0051] The present invention also proposes an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the steps of the adaptive chaos synchronization controller design method and the confidential communication method based on the MANN and DH-PGA algorithms.

[0052] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the adaptive chaos synchronization controller design method and the confidential communication method based on the MANN and DH-PGA algorithms.

[0053] Compared with the prior art, the present invention has the following beneficial effects:

[0054] (1) The present invention integrates neural network and memristor and proposes an adaptive memristor neural controller design scheme, which can cope with the uncertainty and external disturbance in the system and improve the robustness and synchronization accuracy of the system.

[0055] (2) The present invention combines PSO and GA optimization algorithms, which can not only improve the optimization efficiency of controller parameters in complex systems, but also effectively avoid falling into local optimal solutions and achieve better synchronization and control performance.

[0056] (3) In combination with the neural controller design of the present invention, a new confidential communication scheme is proposed. By using the linear combination of the main system state variables as the synchronization signal, the security of system communication is guaranteed, greatly improving the practical application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0058] Figure 1 It is the overall block diagram of the controller design of the present invention.

[0059] Figure 2 Schematic diagram of the behavior of the memristor under different conditions, where (a) the IV curve changes with the input frequency when the maximum input amplitude is fixed; (b) the IV curve changes with the maximum input amplitude when the input frequency is fixed.

[0060] Figure 3 This is the relationship diagram of the input layer, hidden layer, and output layer of MANN.

[0061] Figure 4 is in Δf(x 1s ,x 2s ,x 3s ) under the traditional drive-response synchronization method; (a) xz phase diagram when the initial values ​​of the master and slave systems are both [1,1,1]; (b) xz phase diagram when the initial values ​​of the master system are [0.1,20,30] and the initial values ​​of the slave system are [1,2,3].

[0062] Figure 5 It is the timing diagram and synchronization time diagram of the state variables of the master and slave systems when the initial values ​​of the master system are [0.1, 20, 3] and the initial values ​​of the slave system are [10, 0.2, 0.03]; (ac) corresponds to the x, y, z timing diagram of the MANN controller of the present invention.

[0063] Figure 6 It is the error diagram of the state variables of the master and slave systems when the initial values ​​of the master system are [0.1, 20, 3] and the initial values ​​of the slave system are [10, 0.2, 0.03]; (ac) corresponds to the errors of x, y, and z of the MANN controller of the present invention.

[0064] Figure 7 This is the attractor phase diagram of the master-slave system when the initial values ​​of the master system are [0.1, 20, 3] and the initial values ​​of the slave system are [10, 0.2, 0.03].

[0065] Figure 8 It is the waveform diagram of u(t) generated by the MANN controller.

[0066] Fig. 9 This is a schematic diagram of the original, masked, received, recovered and errors signals of the MANN controller when the initial values ​​of the master system are [0.1, 20, 3] and the initial values ​​of the slave system are [10, 0.2, 0.03].

[0067] Fig.10 It is a confidential communication flow chart. DETAILED DESCRIPTION

[0068] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the drawings 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.

[0069] The present invention proposes a design scheme of an adaptive chaos synchronization controller based on memristor and neural network, aiming to improve the robustness and synchronization accuracy of the system, especially in dealing with uncertainty and external disturbances. The controller significantly improves the synchronization performance of the system by adaptively adjusting parameters. In combination with the neural controller design scheme of the present invention, a new confidential communication scheme is proposed. By using the linear combination of the main system state variables as the synchronization signal, the security of the system communication is guaranteed, and the practical application value is greatly improved. The overall design block diagram of the chaotic system synchronization is shown in the figure. Figure 1 shown.

[0070] The present invention focuses on the synchronization problem of a general three-dimensional continuous chaotic system. A typical three-dimensional continuous chaotic system model can be represented by the following state equation:

[0071]

[0072] Among them, x1, x2, x3 are the state variables of the system, α, β, λ are the system parameters, and functions f, g, h, ψ are smooth continuous functions.

[0073] The slave system is defined as:

[0074]

[0075] Where Δf(x1,x2,x3) represents the modeling uncertainty or external disturbance, and u(t) is the control signal.

[0076] Specifically, combined Figure 1-Figure 10 The present invention proposes a design method of an adaptive chaotic synchronization controller based on MANN and DH-PGA algorithms. The design method includes two parts:

[0077] Design of MANN: The activation function in RBFNN is replaced with a memristor model to form a memristor-activated neural network (MANN); the internal state of the memristor is not only related to the current input, but also to the historical input, showing a "memory"-like property. This memory effect makes the memristor network more efficient in processing time series data and dynamic systems. In contrast, the traditional RBF network cannot directly process the dependencies in the time series data because the activation function is fixed, which makes the controller more flexible and robust when dealing with complex dynamic systems. The mathematical expression of the memristor model is as follows:

[0078]

[0079] Where M(q) is the resistance value of the memristor at time t, which depends on the charge q(t) and the external voltage V(t); α is the weight parameter that controls the amplitude of the resistance change; tanh is the hyperbolic tangent function, which limits the combined effect of charge and voltage to a limited range, ensuring that the change in resistance presents an adaptive nonlinear characteristic; M0 is a constant that represents the offset of the initial state of the memristor; q(t) is a function that depends on the input quantity, which is understood as the intrinsic state variable of the memristor, reflecting the memory effect of the memristor; V(t) is the dynamic external condition or input drive term of the memristor; β,γ are model parameters; Figure 2 The nonlinear relationship between current I and voltage V in equation (3) is depicted, as well as the hysteresis effect. Figure 2 The typical hysteresis curve of the memristor is shown, indicating its memory characteristics and response to input frequency and voltage. This hysteresis characteristic is the historical response of the memristor to simulate biological synapses and dynamic systems, which is very useful for dynamic system modeling and simulation.

[0080] DH-PGA algorithm design: The particle swarm of the PSO algorithm and the population of the GA are merged to form a larger mixed population. The optimization process in each iteration is executed alternately by the PSO algorithm and the GA. In specific operations, the PSO algorithm and the GA each update individual solutions through different strategies and share the global optimal solution, thus forming a collaborative optimization mechanism.

[0081] In the design process of MANN, the specific expression of q(t) is as follows

[0082]

[0083] The relationship followed by the memristor is expressed as:

[0084]

[0085] Applying the memristor model to the activation function of the neuron, the resulting activation function can be formalized as:

[0086]

[0087] Where e is expressed as equation (8);

[0088]

[0089] Experimental verification shows that when the number of neurons is 3, a very good effect has been achieved, so the parameters M0, α, β, and γ are all 3×1 matrices, and i is both the number of inputs and the number of neurons;

[0090] In RBFNN, the input layer and the hidden layer are not connected by a weight matrix like in traditional neural networks, but the Euclidean distance between the input and the center of each hidden neuron (the center value can be regarded as the parameter of the hidden neuron) is calculated. The MANN neural network used in the present invention also skips the linear transformation step in the traditional neural network, directly converts the input into a matrix form, and then substitutes the activation function for nonlinear transformation, thereby simplifying the processing of the input to the hidden layer. It only needs to set the weight matrix in the hidden layer and the output layer. The structure diagram of MANN is as follows: Figure 3 shown.

[0091] When using equation (6) as the activation function, the controller design is expressed as:

[0092] u(t)=W T Ψ(e) (9).

[0093] The fitness function is a key concept in optimization algorithms such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). It is used to measure the quality of a solution, that is, to evaluate the "fitness" or "goodness" of a candidate solution (or individual). Through the fitness function, the optimization algorithm can select solutions with better performance and guide the algorithm to iterate in a better direction. The fitness function is equivalent to an objective function in the optimization algorithm, which is used to provide a score for each solution. In the design of the DH-PGA algorithm, the fitness function selected is:

[0094]

[0095] Where T is the simulation termination time, x is / im (t) is the value of the i-th state variable of the master (slave) system at time t, x is (t)-x im (t) is the error between the master system and the slave system at the i-th state variable.

[0096] Obviously, the smaller the value of IAE, the better. By integrating the error in the entire simulation time interval, the deviation between the master system and the slave system can be evaluated globally. Compared with focusing only on a certain moment or a certain state variable, IAE takes into account the cumulative effect of errors in the entire time range, so as to better reflect the global control performance of the system. The integral form of IAE enables it to accumulate and evaluate the errors of the entire system, rather than just the errors at a certain point in time or an instant. This makes it easier for the DH-PGA algorithm to find the global optimal solution and less likely to fall into local minima. This is particularly important for the control of chaotic systems, because chaotic systems themselves are highly sensitive and complex, and local small errors may be amplified without global evaluation.

[0097] Genetic algorithm is an optimization algorithm based on natural selection and genetic mechanism, which is inspired by the biological evolution process. GA gradually optimizes the solution of the problem by simulating genetic variation, crossover and selection. GA simulates the evolutionary process in nature. The core idea is "survival of the fittest". It gradually evolves the solution in the population and approaches the optimal solution. It is often used to solve complex optimization problems. For the selection part, an adaptive selection pressure method is used to select the parent. The selection pressure is achieved by adjusting the fitness value (by adjusting the pressure parameter). The individuals with better fitness have a higher probability of being selected. This adaptive selection pressure mechanism enhances the selection probability of excellent individuals, while traditional GA is often a simple roulette selection or ranking selection. During the GA optimization process, the selection pressure coefficient pressure is dynamically adjusted according to the diversity of the population. The calculation formula is as follows:

[0098] pressure=1+(2-1)·(1+exp(-diversity)) (11)

[0099]

[0100] Where diversity is the diversity of the population, Var(x i ) is the variance of each individual genetic variable, n is the size of the population;

[0101] Equation (11) indicates that as diversity increases, the selection pressure will decrease, thereby maintaining the diversity of the population; next, roulette selection is performed, with probability P i Represents the probability of each individual being selected:

[0102]

[0103] Cost i is the fitness function value of the ith individual; in the adaptive selection, the pressure coefficient pressure is introduced to exponentially amplify the fitness value of the individual, making the probability of individuals with better fitness being selected greater.

[0104] Multipoint crossover is a genetic recombination method that generates new offspring individuals by exchanging multiple gene fragments of two parent individuals. It introduces more variation between the parent and offspring, increasing the diversity of the population. Suppose there are two parent offspring P1 = {p11, p12, …, p1 l} and P2={p21,p22,…,p2 l}, where l is the length of the individual (the number of genes); select multiple crossover points, assuming that the two crossover points c1 and c2 satisfy 1≤c1<c2≤l, then the generated offspring O={o1,o2,…,o l} can be expressed as:

[0105]

[0106] DH-PGA uses two random crossover points to exchange multiple gene fragments between parents. This method can better maintain and propagate favorable gene fragments than traditional single-point crossover, improving the diversity and global search ability of the algorithm. The mutation method selects Gaussian mutation; in addition, the crossover rate C r and mutation rate M r It is dynamically adjusted and adaptively regulated through population diversity;

[0107]

[0108] in is the initial crossover rate 0.4, The initial mutation rate is 0.4. When the diversity is large, the crossover rate increases, and more gene exchanges help maintain diversity, while the mutation rate decreases to avoid excessive disturbance. When the diversity is small, the crossover rate decreases to reduce the interference of excessive crossover on local search, while the mutation rate increases to increase gene mutations to prevent the population from falling into the local optimum.

[0109] The core idea of ​​the PSO (particle swarm optimization) algorithm is to find the global optimal solution to the problem through information sharing between individual particles. The optimization and improvement of the PSO part includes dynamically adjusting the inertia weight ω during the PSO optimization process; the inertia weight determines the speed and range of the particle search. In the early stage of the algorithm, a larger weight is needed to maintain the global search capability, while in the later stage, a smaller weight is needed to enhance the local search capability. Use exponential decay to adjust the inertia weight:

[0110] ω=ω min +(ω max -ω min )·e -0.01·λ (17)

[0111] where ω min and ω max are the minimum and maximum values ​​of the inertia weight, respectively, and λ is the current iteration number. This approach can maintain early exploration and late development while making a smooth transition.

[0112] The optimization and improvement of the PSO part also includes dynamically adjusting the acceleration coefficients c1 and c2 during the PSO optimization process; the acceleration coefficients c1 and c2 respectively determine the degree of dependence of the particle on the individual optimal position and the global optimal position when updating the position; in order to improve the convergence speed and optimization effect, the exponential function is used to dynamically adjust the acceleration coefficient through the following formula:

[0113]

[0114] where c 1,max and c 1,min are the initial maximum and minimum values ​​of acceleration c1, λ is the current iteration number, α is the total number of iterations, and c 2,max and c 2,min are the initial maximum and minimum values ​​of acceleration c2, respectively. This setting makes particles rely more on their own experience (larger c1) in the early stage of the search, and more on group experience (larger c2) in the later stage, so as to converge more efficiently.

[0115] The PSO algorithm iterates the optimization process by updating the speed and position of each particle; the update formulas for speed and position are as follows:

[0116] v i (k+1)=ω·v i (k)+c1(p i -x i (k))+c2(gx i (k)) (20)

[0117] x i (k+1)=x i(k)+v i (k+1) (21)

[0118] where v i (k) is the velocity of particle i at the kth iteration, x i (k) is the position of particle i at the kth iteration, p i is the individual optimal position of particle i, and g is the optimal position of the particle group.

[0119] The particle swarm of the PSO algorithm and the population of the GA are merged to form a larger mixed population. The optimization process in each iteration is performed alternately by the PSO algorithm and the GA. In specific operations, the PSO algorithm and the GA each update individual solutions through different strategies and share the global optimal solution, thus forming a collaborative optimization mechanism. This combination can make full use of the fast convergence characteristics of the PSO algorithm and the diversity retention ability of the GA, so that the algorithm can quickly approach the optimal solution in the early stage and avoid falling into the local optimum in the later stage. After each iteration, the optimal solutions of the PSO and GA are synchronized to ensure that each algorithm can use the optimal solution found by the other part. The merging formula is as follows:

[0120]

[0121] In this process, the global optimal solution found by both the PSO algorithm and the GA will be updated as global_best_position and used by both the PSO algorithm and the GA in the next iteration. The combination of the PSO algorithm and the GA can not only take advantage of the fast convergence of the PSO algorithm, but also maintain the diversity of the population through the GA to avoid falling into the local optimum. The PSO is mainly responsible for accelerating convergence, while the GA is responsible for maintaining a balance between global search and local development.

[0122] The present invention also proposes a secure communication method, which is implemented based on the controller; the secure communication method uses the linear combination of the state variables of the master system as the synchronization signal, and the slave system is also in the same way, which has been verified to be able to achieve synchronization, specifically: during the communication process, the synchronization signal sent by the sender is [f 1m ,f 2m ,f 3m ],[f 1m ,f 2m ,f 3m ]The expression is as follows

[0123]

[0124] The receiver generates [f 1s ,f 2s ,f 3s]; In this method, the sender linearly combines the state variables of the main system and sends the combined data [f 1m ,f 2m ,f 3m ] is sent to the receiver as a synchronization signal; the receiver’s response system also uses a linear combination method to obtain [f 1s ,f 2s ,f 3s ], and finally [f 1m -f 1s ,f 2m -f 2s ,f 3m -f 3s ] as the input of the memristive neural controller.

[0125] Next, the confidentiality of the secure communication method is verified as follows: an n-dimensional square matrix A is used as the coefficient matrix, and its non-homogeneous linear equation system Ax=y is

[0126]

[0127] The solution of equation (23) depends mainly on the properties of the coefficient matrix A. Only when A is a non-invertible matrix (det(A) = 0) and the constant vector y is in the column space of A, then the system of equations has infinite solutions. In this case, the set of solutions can be expressed as any linear combination of a particular solution plus the solution space of the homogeneous linear system of equations Ax = 0.

[0128] However, not all matrices A are irreversible. In addition, it has been verified that the synchronization effect of irreversible coefficient matrices is worse than that of reversible coefficient matrices. Therefore, in order to maintain universality, the present invention selects a 3×4 matrix B as the coefficient matrix, and its non-homogeneous linear equation system Bx=y. For example, the 3D square matrix A is selected as

[0129]

[0130] It has been verified that det(A)=4≠0, which means that when an attacker knows the form of the matrix A, it will be easy to obtain the unique solution, that is, the state variable of the main system, which is unsafe.

[0131] Consider a 3×4 matrix B, which is a matrix A with an additional column C = [1,1,1] T

[0132]

[0133] The physical meaning of C is the time interval dt of the discretization of the chaotic system. Since the time intervals of the master and slave systems are the same by default, the dt part can be offset when making the difference.

[0134] Since y is in the column space of A, that is, y can be expressed as a linear combination of the column vectors of A, then the system of equations has a solution. Since A is a 3×4 matrix, its rank is at most 3, and the number of unknowns is 4. Since the number of unknowns is greater than the number of equations, the solution space of the system of equations will have degrees of freedom (at least one free variable), and therefore there will be infinite solutions.

[0135] Verify the solution set of B, first list the augmented matrix of B

[0136]

[0137] In this simplified augmented matrix, the expression of the solution of equation (26) can be summarized as

[0138]

[0139] Because the variable x4 can take any value, the non-homogeneous linear system of equations does have infinite solutions. This is because there is a free variable t, and the solution space is infinite in one dimension. In fact, the solution set of the system of equations is any linear combination of the special solution plus the solution space of the homogeneous linear system of equations Bx=0. Since the dimension of the solution space of the system of equations is 4-rank (A), in this case, the dimension of the solution space is at least 1, resulting in infinite solutions. Therefore, even if the attacker intercepts the synchronization signal and the ciphertext at the same time, he cannot directly infer the state of the main system, so it is difficult to crack the ciphertext.

[0140] Example

[0141] The most classic Lorenz system is used as the benchmark synchronization system for research. The Lorenz system is widely used in the study of chaos synchronization and control due to its simple form and typical chaotic characteristics. This paper will use the Lorenz system as an example to verify the effectiveness and advantages of the new method in dealing with system uncertainty and external disturbances.

[0142] The Lorenz system can assign the function in system (1) to:

[0143]

[0144] Substituting equation (28) into system (1), we can obtain the main system

[0145]

[0146] Substituting equation (29) into system (2), we can obtain the system

[0147]

[0148] Where Δf(x 1s ,x 2s ,x 3s)=2sin(πx 1s )(1+cos(πx 3s )), set a=10, b=8 / 3, r=28.

[0149] The present invention takes the traditional drive-response synchronization as an example. When the initial value difference between the master and slave systems is too large, and accompanied by modeling uncertainty or external error Δf(x 1s ,x 2s ,x 3s ), the synchronization performance will deteriorate. Figure 4 As shown, it can be clearly found that when there is external interference, even if the master and slave initial values ​​are the same, a small error will occur. However, when the initial value changes, the error will increase significantly. This verifies that the use of the controller cannot be ignored, and the controller needs to be robust enough to deal with these uncertainties and external interference.

[0150] The DH-PGA parameters and the internal parameters of the MANN controller set by the present invention are shown in Tables 1 and 2. 1s ,x 2s ,x 3s ) and the initial value difference, the initial value of the master system is set to [0.1, 20, 3], and the initial value of the slave system is set to [10, 0.2, 0.03], and the initial value of the two is set to differ by 100 times to verify the universality of the controller. Figure 5 As shown, the time required for synchronization is shown using the timing diagram of the state variables of the master-slave system, such as Figure 6 As shown in Figure 2, the master-slave system state variable error is used to compare the synchronization efficiency. Figure 7 The attractor phase diagram after synchronization from 200 to 3500 points is depicted. The present invention significantly improves the stability and efficiency of synchronization while ensuring a shorter synchronization time. Figure 8 The waveform of the control signal u(t) is given. The experimental results show that when the initial value difference is large and is subject to external interference, the controller proposed in the present invention has good robustness, can effectively reduce the error, and ensure the stable synchronization of the system.

[0151] Table 1. Parameters of MANN controller

[0152]

[0153] Table 2. Parameters optimized for the DH-PGA algorithm

[0154]

[0155] In order to verify the feasibility of data encryption transmission, Fig. 9As shown in the figure, the process of encrypting and decrypting the signal is realized. The original data is m(t) = 2sin(2πt)·(1+9cos(5πt)). In the encryption stage, an exclusive OR (XOR) operation is used, using the state variable x m (maskedMsg) confuses the original data (originalMsg). Even if the data (receivedMsg) is intercepted, its meaning cannot be easily understood. As can be seen from the above, the solution space of the sent synchronization signal is one-dimensional and infinite. Even if the synchronization signal and data (receivedMsg) are intercepted at the same time, it is difficult to get the original data (originalMsg). The flow chart is as follows Fig.10 Of course, you can also choose a more complex encryption method, which will greatly increase security.

[0156] The present invention proposes a chaotic synchronization controller based on a neural network (MANN) activated by a memristor and DH-PGA combining a genetic algorithm (GA) and a particle swarm optimization (PSO), which is used to solve the synchronization problem of a three-dimensional chaotic system under uncertainty and external disturbance conditions. By introducing memristors and the DH-PGA algorithm, the controller not only exhibits strong robustness in the face of system uncertainty and external disturbances, but also improves the synchronization accuracy and stability of the system through adaptive adjustment. In general, the chaotic synchronization controller based on the MANN and DH-PGA algorithms proposed in the present invention provides an effective solution for the synchronization of complex nonlinear systems, especially in scenarios with high real-time requirements and limited computing resources.

[0157] The present invention also proposes an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the processor executes the computer program, it implements the steps of the adaptive chaos synchronization controller design method and the confidential communication method based on the MANN and DH-PGA algorithms.

[0158] The present invention also proposes a computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the steps of the adaptive chaos synchronization controller design method and the confidential communication method based on the MANN and DH-PGA algorithms.

[0159] The memory in the embodiments of the present application may be a volatile memory or a non-volatile memory, or may include both volatile and non-volatile memories. Among them, the non-volatile memory may be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory may be a random access memory (RAM), which is used as an external cache. By way of example and not limitation, many forms of RAM are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), and direct RAM bus RAM (DRRAM). It should be noted that the memory of the method described in the present invention is intended to include, but is not limited to, these and any other suitable types of memory.

[0160] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions may be transmitted from a website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (digital subscriber line, DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode to another website site, computer, server or data center. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may be a magnetic medium (eg, a floppy disk, a hard disk, a magnetic tape), an optical medium (eg, a high-density digital video disc (DVD)), or a semiconductor medium (eg, a solid state disc (SSD)).

[0161] In the implementation process, each step of the above method can be completed by an integrated logic circuit of hardware in a processor or an instruction in the form of software. The steps of the method disclosed in conjunction with the embodiment of the present application can be directly embodied as a hardware processor for execution, or a combination of hardware and software modules in a processor for execution. The software module can be located in a storage medium mature in the art such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in a memory, and the processor reads the information in the memory and completes the steps of the above method in conjunction with its hardware. To avoid repetition, it is not described in detail here.

[0162] It should be noted that the processor in the embodiment of the present application can be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method embodiment can be completed by an integrated logic circuit of hardware in the processor or an instruction in the form of software. The above processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components. The methods, steps and logic block diagrams disclosed in the embodiments of the present application can be implemented or executed. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc. The steps of the method disclosed in the embodiment of the present application can be directly embodied as a hardware decoding processor to perform, or the hardware and software modules in the decoding processor can be combined and performed. The software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in a memory, and the processor reads the information in the memory and completes the steps of the above method in combination with its hardware.

[0163] The above is a detailed introduction to the adaptive chaotic synchronization controller design method and confidential communication method based on MANN and DH-PGA algorithms proposed in the present invention. Specific examples are used in this article to illustrate the principles and implementation methods of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea. At the same time, for general technical personnel in this field, according to the idea of ​​the present invention, there will be changes in the specific implementation method and application scope. In summary, the content of this specification should not be understood as a limitation on the present invention.

Claims

1. A design method for an adaptive chaotic synchronization controller based on MANN and DH-PGA algorithms, characterized in that: The design method consists of two parts: Design of MANN: The activation function in RBFNN is replaced with a memristor model to form a neural network MANN activated by a memristor. The mathematical expression of the memristor model is as follows: Where M(q) is the resistance value of the memristor at time t, which depends on the charge q(t) and the external voltage V(t); α is the weight parameter that controls the amplitude of the resistance change; tanh is the hyperbolic tangent function, which limits the combined effect of charge and voltage to a limited range, ensuring that the change in resistance presents an adaptive nonlinear characteristic; M0 is a constant that represents the offset of the initial state of the memristor; q(t) is a function that depends on the input quantity, which is understood as the intrinsic state variable of the memristor, reflecting the memory effect of the memristor; V(t) is the dynamic external condition or input drive term of the memristor; β,γ are model parameters; DH-PGA algorithm design: The particle swarm of the PSO algorithm and the population of the GA are merged to form a larger mixed population. The optimization process in each iteration is executed alternately by the PSO algorithm and the GA. In specific operations, the PSO algorithm and the GA each update individual solutions through different strategies and share the global optimal solution, thus forming a collaborative optimization mechanism.

2. The method according to claim 1, characterized in that In the design process of MANN, the specific expression of q(t) is as follows The relationship followed by the memristor is expressed as: Applying the memristor model to the activation function of the neuron, the resulting activation function can be formalized as: Where e is expressed as equation (8); Among them, the parameters M0, α, β, γ are all 3×1 matrices, and i is both the number of inputs and the number of neurons; When using equation (6) as the activation function, the controller design is expressed as: u(t)=W T Ψ(e) (9)。 3. The method according to claim 2, characterized in that During the DH-PGA algorithm design process, after each iteration, the optimal solutions of PSO and GA are synchronized to ensure that each algorithm can utilize the optimal solution found by the other part; the combined formula is as follows: In this process, no matter the global optimal solution found by the PSO algorithm or the GA, it will be updated to global_best_position and used by both the PSO algorithm and the GA in the next iteration.

4. The method according to claim 1, characterized in that In the DH-PGA algorithm design, the fitness function selected is: Where T is the simulation termination time, x is / im (t) is the value of the i-th state variable of the master (slave) system at time t, x is (t)-x im (t) is the error between the master system and the slave system at the i-th state variable.

5. The method according to claim 1, characterized in that During the GA optimization process, the selection pressure coefficient pressure is dynamically adjusted according to the population diversity. The calculation formula is as follows: pressure=1+(2-1)·(1+exp(-diversity)) (11) Where diversity is the diversity of the population, Var(x i ) is the variance of each individual genetic variable, n is the size of the population; Equation (11) indicates that as diversity increases, the selection pressure will decrease, thereby maintaining the diversity of the population; next, roulette selection is performed, with probability P i Represents the probability of each individual being selected: Cost i is the fitness function value of the i-th individual; Assume there are two parent-child bodies P1={p11,p12,…,p1 l } and P2={p21,p22,…,p2 l }, where l is the length of the individual; select multiple crossover points, assuming that the two crossover points c1 and c2 satisfy 1≤c1<c2≤l, then the generated offspring O={o1,o2,…,o l } can be expressed as: The mutation method selects Gaussian mutation; in addition, the crossover rate C r and mutation rate M r It is dynamically adjusted and adaptively regulated through population diversity; in is the initial crossover rate 0.4, The initial mutation rate is 0.

4.

6. The method according to claim 1, characterized in that Dynamically adjust the inertia weight ω during the PSO optimization process; use exponential decay to adjust the inertia weight: oh = oh min +(ω max -oh min )·e -0.01·λ (17) where ω min and ω max are the minimum and maximum values ​​of the inertia weight, respectively, and λ is the current number of iterations.

7. The method according to claim 1, characterized in that The acceleration coefficients c1 and c2 are dynamically adjusted during the PSO optimization process; the acceleration coefficients c1 and c2 respectively determine the degree of dependence of the particle on the individual optimal position and the global optimal position when updating the position; the exponential function is used to dynamically adjust the acceleration coefficient through the following formula: where c 1,max and c 1,min are the initial maximum and minimum values ​​of acceleration c1, λ is the current iteration number, α is the total number of iterations, and c 2,max and c 2,min are the initial maximum and minimum values ​​of acceleration c2 respectively; The PSO algorithm iterates the optimization process by updating the speed and position of each particle; the update formulas for speed and position are as follows: v i (k+1)=ω·v i (k)+c1(p i -x i (k))+c2(g-x i (k)) (20) x i (k+1)=x i (k)+v i (k+1) (21) where v i (k) is the velocity of particle i at the kth iteration, x i (k) is the position of particle i at the kth iteration, p i is the individual optimal position of particle i, and g is the optimal position of the particle group.

8. A confidential communication method, characterized in that: The secure communication method is implemented based on the controller of claim 1; the secure communication method uses the linear combination of the state variables of the master system as the synchronization signal, and the slave system is the same, specifically: during the communication process, the synchronization signal sent by the sender is [f 1m ,f 2m ,f 3m ],[f 1m ,f 2m ,f 3m ]The expression is as follows The receiver generates [f 1s ,f 2s ,f 3s ]; In this method, the sender linearly combines the state variables of the main system and sends the combined data [f 1m ,f 2m ,f 3m ] is sent to the receiver as a synchronization signal; the receiver’s response system also uses a linear combination method to obtain [f 1s ,f 2s ,f 3s ], and finally [f 1m -f 1s ,f 2m -f 2s ,f 3m -f 3s ] as the input of the memristive neural controller.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.

10. A computer-readable storage medium for storing computer instructions, characterized in that: When the computer instructions are executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

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