Design method of adaptive chaotic synchronization controller and secret communication method based on mann and dh-pga algorithm

Abstract

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

Description

Technical Field

[0001] This invention relates to chaotic synchronization control technology, particularly to the design of adaptive nonlinear robust controllers for use in communication and control systems. It belongs to the fields of automatic control, information security, and cryptography, and specifically relates to an adaptive chaotic synchronization controller design method and a secure communication method based on the MANN and DH-PGA algorithms. Background Technology

[0002] Since their theoretical introduction, chaotic systems have gradually become an important area of ​​scientific research. Chaotic synchronization is a key branch of this field, aiming to achieve consistency or maintain specific relationships between the state variables of multiple chaotic systems 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 suffer from problems such as design redundancy and insufficient flexibility, making it difficult to effectively cope with the challenges of complex dynamic systems. Summary of the Invention

[0003] The purpose of this invention is to solve the problems in the prior art by proposing an adaptive chaotic synchronization controller design method and a secure communication method based on the MANN and DH-PGA algorithms.

[0004] This invention is achieved through the following technical solution: This invention proposes an adaptive chaotic synchronization controller design method based on the MANN and DH-PGA algorithms. The design method comprises two parts:

[0005] MANN Design: The activation function in RBFNN is replaced with a memristor model, forming the MANN neural network activated by memristors; 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 a weighting parameter that controls the magnitude of the resistance change; tanh is a hyperbolic tangent function that limits the combined effect of charge and voltage within a finite range, ensuring that the resistance change exhibits adaptive nonlinear characteristics; M0 is a constant representing the offset of the memristor's initial state; q(t) is a function dependent on the input quantity, which can be 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 driving term of the memristor; β and γ are model parameters;

[0008] DH-PGA Algorithm Design: The particle swarm optimization (PSO) algorithm and the population optimization (GA) algorithm are merged to form a larger-scale hybrid population. The optimization process in each iteration is executed alternately by the PSO algorithm and the GA algorithm. In practice, the PSO algorithm and the GA algorithm 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 that memristors follow is expressed as:

[0012]

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

[0014]

[0015] Where e is represented by equation (8);

[0016]

[0017] Where 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 equation (6) is used as the activation function, the controller design is expressed as:

[0019] u(t) = W T Ψ(e) (9).

[0020] Furthermore, in the design process of the DH-PGA algorithm, 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 merging formula is as follows:

[0021]

[0022] In this process, the global optimal solution found by both the PSO algorithm and GA will be updated to global_best_position and used by both the PSO algorithm and 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 pressure coefficient is dynamically adjusted based on population diversity, and its calculation formula is as follows:

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

[0028]

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

[0030] Equation (11) indicates that as diversity increases, selection pressure decreases, thus maintaining population diversity; next, a roulette wheel selection is performed with probability P. i This represents the probability that each individual is selected:

[0031]

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

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

[0034]

[0035] The mutation method chosen was Gaussian mutation; in addition, the crossover rate C r and the rate of variation M r It is dynamically adjusted, and adaptive adjustments are made through population diversity.

[0036]

[0037] in The initial crossover rate is 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 These are the minimum and maximum values ​​of the inertia weight, respectively, and λ is the current iteration number.

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

[0042]

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

[0044] The PSO algorithm iteratively optimizes the process by updating the velocity and position of each particle; the formulas for updating velocity 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 in the kth iteration, x i (k) is the position of particle i in the kth iteration, p i is the optimal position of particle i, and g is the optimal position of the particle swarm.

[0048] This invention also proposes a secure communication method, which is implemented based on the aforementioned controller; the secure communication method uses a linear combination of the state variables of the master system as a synchronization signal, and the slave system does the same, specifically: during communication, 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] in the same way. 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 Finally, [f] 1m -f 1s ,f 2m -f 2s ,f 3m -f 3s [This serves as the input to the memristor 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 the processor executes the computer program to implement the steps of the adaptive chaotic synchronization controller design method and the secure 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 chaotic synchronization controller design method and the secure communication method based on the MANN and DH-PGA algorithms.

[0053] Compared with the prior art, the beneficial effects of the present invention are:

[0054] (1) This invention integrates neural networks and memristors and proposes an adaptive memristor neural controller design scheme that can cope with uncertainties and external disturbances in the system and improve the robustness and synchronization accuracy of the system.

[0055] (2) This 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 getting trapped in local optima and achieve better synchronization and control performance.

[0056] (3) Based on the neural controller design scheme of the present invention, a new secure 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, which greatly improves the practical application value. Attached Figure Description

[0057] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0058] Figure 1 This is an overall block diagram of the controller design of this invention.

[0059] Figure 2 These are schematic diagrams showing the behavior of a memristor under different conditions, where (a) is the IV curve as the input frequency changes when the maximum input amplitude is fixed; and (b) is the IV curve as the maximum input amplitude changes when the input frequency is fixed.

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

[0061] Figure 4 It is in Δf(x) 1s ,x 2s ,x 3s Under the following conditions, attractor phase diagrams using the traditional drive-response synchronization method are shown: (a) xz phase diagram with initial values ​​of [1,1,1] for both master and slave systems; (b) xz phase diagram with initial values ​​of [0.1,20,30] for the master system and [1,2,3] for the slave system.

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

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

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

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

[0066] Figure 9 This is a diagram showing the original, masked, received, recovered, and error signals of the MANN controller when the initial value of the master system is [0.1, 20, 3] and the initial value of the slave system is [10, 0.2, 0.03].

[0067] Figure 10 This is a flowchart of secure communication. Detailed Implementation

[0068] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0069] This invention proposes an adaptive chaotic synchronization controller design based on memristors and neural networks, aiming to improve the robustness and synchronization accuracy of the system, particularly in dealing with uncertainties and external disturbances. This controller significantly improves the system's synchronization performance by adaptively adjusting parameters. Combined with the neural controller design of this invention, a novel secure communication scheme is proposed. By using a linear combination of the master system's state variables as the synchronization signal, the security of system communication is guaranteed, greatly enhancing its practical application value. The overall design block diagram of the chaotic system synchronization is shown below. Figure 1 As shown.

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

[0071]

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

[0073] The system is defined as follows:

[0074]

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

[0076] Specifically, in combination Figures 1-10 This invention proposes a design method for an adaptive chaotic synchronization controller based on the MANN and DH-PGA algorithms. The design method comprises two parts:

[0077] The design of MANN involves replacing the activation function in RBFNN with a memristor model, forming a memristor-activated neural network (MANN). The internal state of the memristor is related not only to the current input but also to historical inputs, exhibiting a "memory"-like characteristic. This memory effect makes memristor networks more efficient in processing time-series data and dynamic systems. In contrast, traditional RBF networks, due to their fixed activation function, cannot directly handle dependencies in time-series data, making 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 a weighting parameter that controls the magnitude of the resistance change; tanh is a hyperbolic tangent function that limits the combined effect of charge and voltage within a finite range, ensuring that the resistance change exhibits adaptive nonlinear characteristics; M0 is a constant representing the offset of the memristor's initial state; q(t) is a function dependent on the input quantity, which can be 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 driving term of the memristor; β and γ are model parameters; Figure 2 Describe the nonlinear relationship between current I and voltage V in equation (3), as well as the hysteresis effect. Figure 2 The typical hysteresis curve of a memristor is shown, illustrating its memory characteristics and response to input frequency and voltage. This hysteresis characteristic is used by memristors to simulate the historical response of biological synapses and dynamic systems, and is very useful for dynamic system modeling and simulation.

[0080] DH-PGA Algorithm Design: The particle swarm optimization (PSO) algorithm and the population optimization (GA) algorithm are merged to form a larger-scale hybrid population. The optimization process in each iteration is executed alternately by the PSO algorithm and the GA algorithm. In practice, the PSO algorithm and the GA algorithm 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 that memristors follow is expressed as:

[0084]

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

[0086]

[0087] Where e is represented by equation (8);

[0088]

[0089] Experiments have shown that a good effect is achieved when the number of neurons is 3. Therefore, the parameters M0, α, β, 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 hidden layers are not connected via weight matrices as in traditional neural networks. Instead, the Euclidean distance between the input and the center of each hidden neuron (the center value can be considered as a parameter of the hidden neuron) is calculated. The MANN neural network used in this invention also skips the linear transformation step in traditional neural networks, directly converting the input into a matrix form and then substituting it into the activation function for a non-linear transformation. This simplifies the processing from input to hidden layers; only weight matrices need to be set in the hidden and output layers. The structure diagram of MANN is shown below. Figure 3 As shown.

[0091] When equation (6) is used 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 measures the quality of a solution, evaluating the "fitness" or "goodness" of a candidate solution (or individual). Through the fitness function, the optimization algorithm selects better-performing solutions and guides it to iterate towards a better outcome. The fitness function in the optimization algorithm is equivalent to an objective function, providing a score for each solution. In the DH-PGA algorithm design, the chosen fitness function 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] Clearly, a smaller IAE value is better. By integrating the error over the entire simulation time interval, the deviation between the master and slave systems can be globally evaluated. Compared to focusing only on a single moment or a single state variable, IAE considers the cumulative effect of error over the entire time range, thus better reflecting the global control performance of the system. The integral form of IAE allows it to accumulate and evaluate the error of the entire system, rather than just the error at a single point in time or instant. This makes it easier for the DH-PGA algorithm to find the global optimum and less likely to get trapped in local minima. This is particularly important for the control of chaotic systems, because chaotic systems are inherently highly sensitive and complex, and small local errors can be amplified without global evaluation.

[0097] Genetic Algorithms (GAs) are optimization algorithms based on natural selection and genetic mechanisms, inspired by biological evolution. GAs gradually optimize solutions by simulating genetic mutation, crossover, and selection. GAs mimic natural evolution, with the core idea of ​​"survival of the fittest," progressively evolving solutions within the population to approach the optimal solution. They are commonly used to solve complex optimization problems. For the selection part, an adaptive selection pressure method is used for parent selection. Selection pressure is achieved by adjusting the fitness value (by adjusting the pressure parameter). Individuals with better fitness have a higher probability of being selected. This adaptive selection pressure mechanism enhances the selection probability of superior individuals, whereas traditional GAs often use simple roulette wheel selection or ranking selection. During the GA optimization process, the selection pressure coefficient (pressure) is dynamically adjusted based on population diversity. Its calculation formula is as follows:

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

[0099]

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

[0101] Equation (11) indicates that as diversity increases, selection pressure decreases, thus maintaining population diversity; next, a roulette wheel selection is performed with probability P. i This represents the probability that each individual is selected:

[0102]

[0103] Cost i It is the fitness function value of the i-th individual; in adaptive selection, the pressure coefficient is introduced, which exponentially amplifies the fitness value of individuals, making individuals with better fitness more likely to be selected.

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

[0105]

[0106] DH-PGA uses two random crossover points to exchange multiple gene segments between parents. This method better preserves and propagates beneficial gene segments than traditional single-point crossover, improving the algorithm's diversity and global search capability. Gaussian mutation is chosen as the mutation method; furthermore, the crossover rate C... r and the rate of variation M r It is dynamically adjusted, and adaptive adjustments are made through population diversity.

[0107]

[0108] in The initial crossover rate is 0.4. The initial mutation rate is 0.4. When diversity is high, the crossover rate increases, and more gene exchange helps maintain diversity, while the mutation rate decreases to avoid excessive perturbation. When diversity is low, the crossover rate decreases to reduce the interference of excessive crossover on local searches, while the mutation rate increases to increase gene mutations to prevent the population from getting trapped in local optima.

[0109] The core idea of ​​the Particle Swarm Optimization (PSO) algorithm is to find the global optimum of a problem through information sharing among individual particles. Optimizations and improvements to PSO include dynamically adjusting the inertia weight ω during the optimization process. The inertia weight determines the speed and range of the particle search; a larger weight is needed in the early stages of the algorithm to maintain global search capability, while a smaller weight is needed in later stages to enhance local search capability. The inertia weight is adjusted using an exponential decay method.

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

[0111] Where ω min and ω max These are the minimum and maximum values ​​of the inertia weight, respectively, and λ is the current iteration number. This approach allows for a smooth transition while maintaining both early exploratory and later developmental aspects.

[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 determine the degree of dependence of the particle on the individual optimal position and the global optimal position when updating its position, respectively; in order to improve the convergence speed and optimization effect, the acceleration coefficients are dynamically adjusted using an exponential function, expressed by the following formula:

[0113]

[0114] Where c 1,max and c 1,min These are the initial maximum and minimum values ​​of acceleration c1, respectively, where λ is the current iteration number, α is the total number of iterations, and c is the maximum and minimum values ​​of acceleration c1. 2,max and c 2,min These are the initial maximum and minimum values ​​of acceleration c2, respectively. This setting allows particles to rely more on their own experience (larger c1) in the early stages of the search, and more on the collective experience (larger c2) in the later stages, thus converging more efficiently.

[0115] The PSO algorithm iteratively optimizes the process by updating the velocity and position of each particle; the formulas for updating velocity 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 in the kth iteration, x i (k) is the position of particle i in the kth iteration, p i is the optimal position of particle i, and g is the optimal position of the particle swarm.

[0119] The particle swarm optimization (PSO) algorithm and the GA (Graphical Approach) population are merged to form a larger hybrid population. In each iteration, the optimization process is performed alternately by the PSO and GA components. Specifically, the PSO and GA algorithms update their individual solutions using different strategies and share the global optimum, thus forming a collaborative optimization mechanism. This combination fully utilizes the fast convergence of the PSO algorithm and the diversity preservation capability of the GA algorithm, enabling the algorithms to quickly approach the optimal solution in the early stages while avoiding getting trapped in local optima in the later stages. After each iteration, the optimal solutions of the PSO and GA algorithms are synchronized to ensure that each algorithm can utilize the optimal solution found by the other component. The merging formula is as follows:

[0120]

[0121] In this process, the global optimal solution found by both the PSO algorithm and GA is updated to `global_best_position` and used by both algorithms in the next iteration. The combination of PSO and GA not only leverages the fast convergence of PSO but also maintains population diversity through GA, avoiding getting trapped in local optima. PSO primarily accelerates convergence, while GA maintains a balance between global search and local exploitation.

[0122] This invention also proposes a secure communication method, which is implemented based on the aforementioned controller. The secure communication method uses a linear combination of the state variables of the master system as a synchronization signal, and the slave system follows the same method. Verification has shown that synchronization can be achieved. Specifically, during communication, 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] in the same way. 1s ,f 2s ,f 3sIn 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 Finally, [f] 1m -f 1s ,f 2m -f 2s ,f 3m -f 3s [This serves as the input to the memristor neural controller.]

[0125] Next, the confidentiality of this secure communication method is verified. Specifically, 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 solutions to equation (23) depend primarily on the properties of the coefficient matrix A. Only if 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 infinitely many solutions. In this case, the set of solutions can be represented as a particular solution plus any linear combination of the solution space of the homogeneous linear system of equations Ax = 0.

[0128] However, not all matrices A are non-invertible. Furthermore, it has been verified that non-invertible coefficient matrices have worse synchronization performance than invertible coefficient matrices. Therefore, to maintain generality, this invention chooses a 3×4 matrix B as the coefficient matrix, whose non-homogeneous linear equation system is Bx = y. For example, the 3D square matrix A is chosen as...

[0129]

[0130] It has been verified that det(A) = 4 ≠ 0, which means that if an attacker knows the form of matrix A, they can easily obtain a unique solution, i.e., the state variables of the main system, which is insecure.

[0131] Consider a 3×4 matrix B, which is 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 parts can cancel each other out when the difference is calculated.

[0134] Since y lies in the column space of A, meaning y can be represented as a linear combination of the column vectors of A, the system of equations has a solution. Since A is a 3×4 matrix, its rank is at most 3, while the number of unknowns is 4. Because 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), thus resulting in infinitely many solutions.

[0135] To verify the solution set of B, first list the augmented matrix of B.

[0136]

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

[0138]

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

[0140] Example

[0141] This study uses the classic Lorenz system as the benchmark synchronization system. Due to its simple form and typical chaotic properties, the Lorenz system is widely used in research on chaotic synchronization and control. This invention will use the Lorenz system as an example to verify the effectiveness and advantages of the new method in dealing with system uncertainties and external disturbances.

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

[0143]

[0144] Substituting equation (28) into system (1) yields the main system.

[0145]

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

[0147]

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

[0149] This invention takes 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 When this happens, synchronization performance will deteriorate. For example... Figure 4 As shown, it can be clearly seen that when there is external interference, even if the initial values ​​of the master and slave are the same, a small error will still occur. However, when the initial values ​​change, the error will increase significantly. This verifies that the use of a controller is indispensable, and the controller needs to have sufficient robustness to cope with these uncertainties and external interference.

[0150] The DH-PGA parameters and the internal parameters of the MANN controller set in this invention are shown in Tables 1 and 2. Considering Δf(x) 1s ,x 2s ,x 3s Under the influence of the difference between the initial values ​​and the actual initial values, the initial value of the main system is set to [0.1, 20, 3], and the initial value of the slave system is set to [10, 0.2, 0.03]. The initial values ​​are then differed by a factor of 100 to verify the controller's versatility. Figure 5 As shown, a timing diagram of the state variables of the master-slave system is used to display the time required for synchronization, such as... Figure 6 As shown, the synchronization efficiency is compared using the error of the master-slave system state variables. Figure 7 The attractor phase diagrams after synchronization at 200 to 3500 points are depicted. This 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. Experimental results show that, under conditions of large initial value differences and external disturbances, the controller proposed in this invention has good robustness, can effectively reduce errors, and ensure stable system synchronization.

[0151] Table 1. Parameters of MANN controller

[0152]

[0153] Table 2. Parameters for DH-PGA Algorithm Optimization

[0154]

[0155] To verify the feasibility of encrypted data transmission, such as Figure 9As shown, the process of encrypting and decrypting the signal is implemented. The original data is m(t) = 2sin(2πt)·(1+9cos(5πt)). In the encryption stage, the XOR operation is used, with the state variable x of the main system as the decryption method. m (maskedMsg) obfuscates the original data (originalMsg). Even if the data (receivedMsg) is intercepted, its meaning cannot be easily understood. Furthermore, as mentioned above, the solution space of the transmitted synchronization signal is one-dimensional and infinite. Even if the synchronization signal and the data (receivedMsg) are intercepted simultaneously, it is still difficult to obtain the original data (originalMsg). The flowchart is as follows. Figure 10 As shown. Of course, more complex encryption methods can also be chosen, which will greatly increase security.

[0156] This invention proposes a chaotic synchronization controller based on a memristor-activated neural network (MANN) and a DH-PGA algorithm combining genetic algorithm (GA) and particle swarm optimization (PSO) to solve the synchronization problem of three-dimensional chaotic systems under conditions of uncertainty and external disturbances. 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 summary, the chaotic synchronization controller based on the MANN and DH-PGA algorithms proposed in this invention provides an effective solution for the synchronization of complex nonlinear systems, especially performing well in scenarios with high real-time requirements and limited computational resources.

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

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

[0160] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as 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, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available media may be magnetic media (e.g., floppy disks, hard disks, magnetic tapes), optical media (e.g., high-density digital video discs (DVDs)), or semiconductor media (e.g., solid-state disks (SSDs)).

[0161] In implementation, each step of the above method can be completed by integrated logic circuits in the processor's hardware or by instructions in software. The steps of the method disclosed in the embodiments of this application can be directly implemented by a hardware processor, or by a combination of hardware and software modules in the processor. The software modules can reside in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads information from the memory and, in conjunction with its hardware, completes the steps of the above method. To avoid repetition, detailed descriptions are omitted here.

[0162] It should be noted that the processor in the embodiments of this application can be an integrated circuit chip with signal processing capabilities. During implementation, each step of the above method embodiments can be completed by the integrated logic circuitry in the processor's hardware or by instructions in software form. The 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 gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the methods disclosed in the embodiments of this application can be directly embodied as being executed by a hardware decoding processor, or executed by a combination of hardware and software modules in the decoding processor. The software modules can be located in random access memory, flash memory, read-only memory, programmable read-only memory, electrically erasable programmable memory, registers, or other mature storage media in the art. This storage medium is located in memory, and the processor reads the information in the memory and, in conjunction with its hardware, completes the steps of the above methods.

[0163] The above provides a detailed description of the adaptive chaotic synchronization controller design method and secure communication method based on the MANN and DH-PGA algorithms proposed in this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A design method for an adaptive chaotic synchronization controller based on the MANN and DH-PGA algorithms, characterized in that, The design method consists of two parts: MANN Design: The activation function in RBFNN is replaced with a memristor model, forming the MANN neural network activated by memristors; the mathematical expression of the memristor model is as follows: (3) in It is a memristor in time t The resistance value at any given moment depends on the charge. and external voltage ; It is a weighting parameter that controls the magnitude of the resistance change; It is a hyperbolic tangent function, which limits the combined effect of charge and voltage to a finite range, ensuring that the change in resistance exhibits adaptive nonlinear characteristics; It is a constant representing the offset of the initial state of the memristor; It is a function that depends on the input quantity, and can be understood as the intrinsic state variable of the memristor, reflecting the memory effect of the memristor; It is the dynamic external condition or input drive term of the memristor; These are model parameters; DH-PGA Algorithm Design: The particle swarm optimization (PSO) algorithm and the population optimization (GA) algorithm are merged to form a larger-scale hybrid population. The optimization process in each iteration is executed alternately by the PSO algorithm and the GA algorithm. In practice, the PSO algorithm and the GA algorithm 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, During the design process of MANN, The specific expression is as follows (4) The relationship that memristors follow is expressed as: (5) Applying the memristor model to the activation function of a neuron, the resulting activation function can be formalized as: (6) (7) in e It is represented as equation (8); (8) in, It is the system's state variable. m Represents the main system. s Represents from the system; parameters Both are 3×1 matrices. i It is both the number of inputs and the number of neurons; When equation (6) is used as the activation function, the controller design is expressed as: (9)。 3. The method according to claim 2, characterized in that, In the design process of the DH-PGA algorithm, 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 merging formula is as follows: (22) During this process, both the global optimum found by the PSO algorithm and the global optimum found by GA will be updated to... global _ best _ position It is used by both the PSO algorithm and GA in the next iteration.

4. The method according to claim 1, characterized in that, In the design of the DH-PGA algorithm, the selected fitness function is: (10) in T This is the simulation termination time. Is it a master / slave system? i A state variable in time t The value, The master system and the slave system are in the first i The error of each state variable.

5. The method according to claim 1, characterized in that, During GA optimization, the selection pressure coefficient is dynamically adjusted based on population diversity. pressure The calculation formula is as follows: (11) (12) in diversity It is population diversity. It is the variance of each individual's genetic variables. n It refers to the size of the population; Equation (11) indicates that as diversity increases, selection pressure decreases, thus maintaining population diversity; next, a roulette wheel selection is performed, with a probability... This represents the probability that each individual is selected: (13) in It is the first i The fitness function value of each individual; Assuming there are two parent-child pairs and Where l is the length of the individual; select multiple intersection points, assuming two intersection points and satisfy The generated offspring It can be represented as: (14) The mutation method was chosen to be Gaussian mutation; in addition, the crossover rate was also considered. and variability It is dynamically adjusted, through population diversity. diversity To perform adaptive adjustment; (15) (16) in The initial crossover rate is 0.

4. The initial mutation rate is 0.

4.

6. The method according to claim 1, characterized in that, Dynamically adjust the inertia weight during PSO optimization. ; Adjust the inertia weights using an exponential decay method: (17) in and These are the minimum and maximum values ​​of the inertia weight, respectively. This is the current iteration number.

7. The method according to claim 1, characterized in that, Dynamically adjust the acceleration coefficient during PSO optimization. and acceleration coefficient and These factors determine the degree to which a particle depends on its individual optimal position and the global optimal position when updating its position; the acceleration coefficient is dynamically adjusted using an exponential function, expressed by the following formula: (18) (19) in and They are acceleration The initial maximum and minimum values, It is the current iteration number. It is the total number of iterations. and They are acceleration The initial maximum and minimum values; The PSO algorithm iteratively optimizes the process by updating the velocity and position of each particle; the formulas for updating velocity and position are as follows: (20) (21) in It is a particle i In the k The speed of each iteration It is a particle i In the k The position of the next iteration. It is a particle i The optimal position of an individual g It is the optimal position for the particle swarm.

8. A secure communication method, characterized in that, The secure communication method is implemented based on the controller described in claim 1; the secure communication method uses a linear combination of the state variables of the master system as a synchronization signal, and the slave system does the same, specifically: during communication, the synchronization signal sent by the sender is... , The expression is as follows: The receiver generates it in the same way. In this method, the sender linearly combines the state variables of the main system and then sends the combined data... This signal is sent to the receiver as a synchronization signal; the receiver's response system also uses a linear combination method to obtain the response. Finally As input to the memristor neural controller.

9. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it implements the steps of the method according to any one of claims 1-8.

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

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