Network control system time delay compensation method based on neural network sliding mode control

Abstract

The present application relates to a kind of network control system time delay compensation method based on neural network sliding mode control, steps are as follows: establishing echo state network;Echo state network training update;Introduce myxomycete algorithm to optimize echo state network model, form the combination prediction model of echo state network based on myxomycete algorithm optimization Prediction network time delay value;According to network time delay value, sliding mode function is designed, the state equation when system is in sliding surface is obtained, and system control quantity is solved.The present application solves the control problem of linear system with input delay, effectively improves the prediction accuracy, uses the predicted result to combine sliding mode control algorithm to output future control quantity, compensates network control system time-varying time delay, improves the tracking ability of network control system signal.

Description

Technical Field

[0001] This invention belongs to the field of network control system technology, specifically relating to a time delay compensation method for network control systems based on SMA (slimemold algorithm, SMA)-ESN (echo state network, ESN) neural network sliding mode control in a network environment. Background Technology

[0002] Networked control systems (NCS) are a new type of control system that integrates network communication technology, computer information technology, and automatic control technology. They offer advantages such as good real-time performance, ease of expansion and maintenance, and high reliability. However, the design of networked control systems involves numerous information sources. During data transmission, network communication lines are used, resulting in network latency. This latency can cause data packet loss and timing discrepancies, severely hindering the use and widespread adoption of networked control systems.

[0003] Sliding mode control (SMC) is robust to system model structural uncertainties and external disturbances, making it an ideal choice for NCS design. NIZARA et al. proposed applying predictive sliding mode control (PSMC) to time-delay systems. For linear systems with state delays, they proposed an enhanced predictive discrete-time sliding mode control with sliding functionality, demonstrating that PSMC performs well for systems with time delays. However, in some practical applications, system chattering can occur when implementing the SMC method due to input delays. Furthermore, data loss and out-of-order delivery can exacerbate the chattering problem.

[0004] In summary, existing algorithms have been studied comprehensively for linear systems with state delays, but relatively little research has been done on input delays. This method can effectively compensate for input delay problems in the system. Summary of the Invention

[0005] This invention provides a time delay compensation method for a networked control system (NCS) based on neural network sliding mode control. Its purpose is to solve the control problem of linear systems with input delay, so as to achieve accurate prediction and effective compensation of the time delay of the networked control system, which has good development prospects.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows:

[0007] A time delay compensation method for a network control system based on neural network sliding mode control, comprising the following steps:

[0008] Step 1: Establish the echo state network;

[0009] Step 2: Echo State Network Training and Update;

[0010] Step 3: Introduce the slime mold algorithm to optimize the echo state network model, and form a combined prediction model based on the echo state network optimized by the slime mold algorithm to predict the network delay value τ(t);

[0011] Step 4: Design the sliding mode function based on the network delay value τ(t), obtain the state equation of the system when it is on the sliding surface, and solve for the system control quantity.

[0012] Furthermore, in step one, the input unit u(t) of the echo state network contains the time delay data from previous time steps, and the input layer has K nodes; the reservoir x(t) represents the current state, and contains N neural nodes; the output unit y(t) represents the network time delay value output at the next time step, and the network has L output nodes; the states of the input unit, reservoir, and output unit are as follows:

[0013] u(t) = [u1(t), u2(t), ... u K (t)] T

[0014] x(t) = [x1(t), x2(t), ... x N (t)] T

[0015] y(t)=[y1(t),y2(t),...y L (t)] T .

[0016] Furthermore, the output state equation of the echo state network in step one is:

[0017] y(t+1)=f out ·(W out ·(u(t+1),x(t+1)),

[0018] In the formula, fout is the activation function of the output layer neuron, and W out It represents the connection weights from the reservoir to the output layer, y(t+1) is the output at the next time step, u(t+1) is the control input at the next time step, and x(t+1) is the input at the next time step.

[0019] Furthermore, the optimization process of the echo state network based on the slime mold algorithm in step three is as follows:

[0020] (1) Initialize the parameters involved in the slime mold algorithm, including the population size parameter N, the maximum number of iterations maxT, and the parameter Z in the population position update formula;

[0021] (2) Calculate the fitness value of each population using the fitness function;

[0022] (3) Applying the slime mold individual location update model to the population location, optimal fitness value and optimal population location information X b Update the fitness value; if the global optimal fitness value is higher than the optimal fitness value during the iteration process, replace the global optimal fitness value with the fitness value obtained from the iteration, and update the optimal position information of the population with the currently obtained position information.

[0023] (4) After updating the location information, calculate the fitness of each population and update the global optimal position of the population;

[0024] (5) Determine whether the maximum number of iterations has been reached. If maxT is reached, output the reserve pool parameters corresponding to the optimal individual location information, and apply the optimal parameter combination of the two to establish the echo state network prediction model based on the slime mold algorithm. Then, predict the test set data and output y(t). The output y(t) is also the network delay value τ(t). If maxT is not reached, repeat steps (2)-(4) to continue the parameter optimization operation.

[0025] Furthermore, step (3) involves seeking the optimal fitness value:

[0026] First, the approach behavior of slime molds was mathematically modeled, and the following rules were proposed to simulate the contraction pattern of slime molds:

[0027]

[0028] In the formula, vb is a random number between [-a, a], W represents the weighting coefficient of slime mold, and X A (t) and X B (t) represents the positions of two random individuals, vc is a parameter that oscillates between [-1, 1] and eventually tends to zero, and X b X(t) represents the current position of the slime mold individual with the best fitness, and X(t) represents the current position of the slime mold individual.

[0029] Secondly, the update formulas for the control parameters p, vb, a, and weight coefficient W are as follows:

[0030] p = tanh|S(i) - DF|

[0031] Where i∈1,2,…,n,S(i) represents the fitness value of the i-th slime mold individual, and DF is the currently obtained optimal fitness value;

[0032] vb = [-a, a]

[0033]

[0034]

[0035] SmellIndex = sort(S)

[0036] Where, condition represents the top half of the individuals in the population with the highest fitness, others represent the remaining individuals, r represents a random number between [0,1], bF represents the best fitness value obtained in the current iteration, wF represents the worst fitness value in the current iteration, T is the current iteration number, maxT is the maximum iteration number, and SmellIndex is the sorting of the fitness sequence. Thus, SmellIndex, bF, and wF are obtained, and finally W is calculated.

[0037] Finally, to find the optimal fitness value, i.e., when the evaluation index approaches 0, we consider using the root mean square error (RMSE) evaluation index to evaluate the performance of the proposed prediction model, setting the RMSE to 0.

[0038]

[0039] m represents the total length of the time series, i represents the number of iterations, and y k and These represent the actual value of the time series at time k and the output prediction value of the ESN model, respectively.

[0040] Furthermore, the position update model for slime mold individuals in step (3) is as follows:

[0041]

[0042] Where UB and LB are the upper and lower bounds, rand is a random number uniformly distributed between 0 and 1, z is a user-defined parameter, the value of vb oscillates randomly between [-a, a] and gradually approaches zero as the number of iterations increases, and the value of vc oscillates between [-1, 1] and eventually tends to zero. The calculation formula is as follows:

[0043] vc = [-b, b]

[0044] b = 1 - T / maxT

[0045] The synergistic effect between vb and vc simulates the selective behavior of slime molds.

[0046] Furthermore, the sliding mode function in step four is as follows:

[0047] S(t)=Cx(t)-∫C(A-BK)x(t)dt+∫CB[u(t)-u(t-τ(t))]dt

[0048] Where C is a constant matrix of appropriate dimension, and CB is guaranteed to be a non-singular matrix, K is the parameter to be designed, t is time, A is an m×m matrix, B is an m×n full-rank matrix, τ(t) is the network delay value, and u(t) is the control input.

[0049] Furthermore, the system control quantity in step four is:

[0050] u(t)=-Kx(t)-(CB) -1 (ηS+εsgnS)

[0051] In the formula, η = 1, ε = 0.005, and S is the sliding mode function;

[0052] The state equation of the system when it is on the sliding surface can be described as follows:

[0053]

[0054] By adopting the above technical solution, the present invention can produce the following technical effects:

[0055] A time-varying delay prediction model for NCS (Network Control System) is established. The SMA-ESN algorithm solves the control problem of linear systems with input delay, effectively improving prediction accuracy. The prediction results are combined with a sliding mode control algorithm to output future control quantities, compensating for the time-varying delay of the network control system and improving the signal tracking capability of the network control system. This invention is simple, highly stable, easy to operate, highly portable, and inexpensive, making it applicable to engineering practice. Attached Figure Description

[0056] Figure 1 A comparison chart of time delay predictions between the SMA-ESN neural network prediction algorithm and the ESN prediction algorithm;

[0057] Figure 2 The experimental results of the conventional sliding mode controller method are shown in the figure.

[0058] Figure 3 Experimental results designed for this method;

[0059] Figure 4 The control law obtained by a conventional sliding mode controller;

[0060] Figure 5 The control law obtained by the controller designed for this method;

[0061] Figure 6 The evolution of the sliding surface in a conventional sliding mode controller;

[0062] Figure 7 The evolution of the sliding surface of the controller in this method;

[0063] Figure 8 This is a structural diagram of the network control system based on this method;

[0064] Figure 9 This is a schematic diagram of the NCS network delay compensation scheme based on neural network sliding mode control according to the present invention.

[0065] Figure 10 This is a schematic diagram of an echo state network. Detailed Implementation

[0066] The technical solutions of the present invention will now be clearly and completely described with reference to the accompanying drawings in the embodiments of the present invention.

[0067] This invention establishes an Echo State Network (SMA-ESN) optimization algorithm based on the actual measured raw network latency data. The SMA algorithm iterates over the pool parameters of the Echo State Network, assigning the optimal solution obtained from the iteration to the Echo State Network. Here, SMA updates the population position. Fitness values ​​are calculated, and the global optimal position is updated. The termination condition is checked; if met, the optimal result is output; otherwise, the above steps are repeated. After optimizing the weights of the Echo State Network, the SMA algorithm is trained using the previously measured network latency dataset. The trained model is then used for latency prediction. The network latency prediction model predicts the time-varying network latency at the next moment based on the SMA-ESN algorithm.

[0068] like Figure 9 As shown, this invention proposes a time delay compensation method for NCS networks based on neural network sliding mode control. The method includes the following steps:

[0069] Step 1: Establish an Echo State Network (ESN);

[0070] Figure 10 The diagram shows the structure of an echo state network. The network input u(t) represents the time delay data from previous time steps, and the output y(t) represents the time delay data for the next time step. In the diagram, u(t) represents the input at time t, with K nodes in the input layer; x(t) represents the current state of the buffer pool, which contains N neural nodes; and y(t) represents the output of the echo state network, which has L output nodes. When the system has K input units, N internal processing units, and L output units, the states of the input units, the buffer pool, and the output units are as follows:

[0071] u(t) = [u1(t), u2(t), ... u K (t)] T

[0072] x(t) = [x1(t), x2(t), ... x N (t)] T

[0073] y(t)=[y1(t),y2(t),...y L (t)] T

[0074] The reservoir in the diagram represents the hidden layer structure in a conventional neural network, and the connection weights from the input layer to the reservoir are W. in W is an (N*K) matrix, where W is the internal connection weight from the reservoir to the reservoir state at the next time step. W is an (N*N) matrix, where W is the connection weight from the reservoir to the output layer. out It is an L*(K+N+L) order matrix, and there is also a connection W from the output layer of the previous time step to the reservoir of the next time step. back It is an (N*L) order matrix, but this connection is not required.

[0075] At each input u(t), the reservoir needs to update its state. Its state update equation is:

[0076] x(t+1)=f(W in ·u(t+1)+W·x(t)+W back ·y(t))

[0077] In the formula, W in and W back They are all randomly initialized when the network is initially established, and remain fixed.

[0078] u(t+1) is the input at this time step, x(t+1) is the state of the reservoir at this time step, and x(t) is the state of the reservoir at the previous time step. f is the activation function of the neuron inside DR.

[0079] The output state equation of the ESN is: y(t+1)=f out ·(W out ·(u(t+1),x(t+1)), where fout is the activation function of the output layer neuron, W out It outputs the weight matrix.

[0080] The final performance of an ESN is determined by various parameters of the reservoir, including: the radius of the internal connection weight spectrum SR, the reservoir size N, the reservoir input cell scale IS, and the reservoir sparsity SD.

[0081] The spectral radius SR of the reservoir is the absolute value of the largest eigenvalue of the internal connection weight matrix W of the reservoir. The spectral radius of the echo state network reservoir affects the memory ability of the echo state network. This value can determine the memory ability of the reservoir. Therefore, the selection of the spectral radius of the reservoir is very crucial. Generally, it is considered that when 0 < SR < 1, the ESN has stable echo state properties. When the spectral radius is selected too small, the memory ability of the ESN is poor and the ability to handle non-linearity is weak. However, when the spectral radius is selected too large, it will affect the stability of the reservoir state and thus affect the prediction ability of the echo state network.

[0082] The reservoir size N is the number of neurons in the reservoir. The selection of the reservoir size is related to the number of samples and has a great impact on the network performance. The larger the reservoir size, the more accurate the ESN describes the given dynamic system, but it will bring the problem of overfitting.

[0083] The input unit scale IS of the reservoir is a scale factor that needs to be multiplied before the input signal of the reservoir is connected to the internal neurons of the reservoir, that is, the input signal is scaled. Generally, the stronger the non-linearity of the object to be processed, the larger the IS.

[0084] The sparsity degree SD of the reservoir represents the connection situation between neurons in the reservoir. Not all neurons in the reservoir are connected. SD represents the percentage of the total number of interconnected neurons in the reservoir to the total number of neurons N. The larger its value, the stronger the non-linear approximation ability. n is the number of interconnected neurons, and N is the total number of neurons.

[0085] Step 2: Training and updating of the echo state network;

[0086] Based on the parameters of the ESN network described above, the training process of the ESN is given.

[0087] 1. Initialize the ESN network

[0088] First, initialize W in the ESN in 、W、W back and the initial state x(0) of the reservoir. Among them, W in ,W back is a randomly generated connection matrix, W is a randomly generated sparse matrix with a spectral radius less than 1. Before network training, the reservoir has no initial state.

[0089] 2. Update the reservoir state matrix

[0090] Input the network training samples (u(1), yt(1)), … (u(n), yt(n)), and the internal state information of the system is updated according to the state update equation of the reservoir x(t + 1) = f(Win ·u(t+1)+W·x(t)+W back The network is updated using y(t). Each update represents the current state of the reservoir and the network output x(t+1), while u(t+1) corresponds to the next state of the network reservoir and the next input to the network. During network learning, W... in W, W back All remain unchanged.

[0091] 3. Collect each state vector

[0092] During the state update process in the reservoir, in order to remove the influence of the initial state of the reservoir, some early data is discarded. Starting from time M0, the internal state x(i) of the reservoir and the input sample u(i) are recorded to form a state vector. At this time, the system output did not perform the ESN output equation.

[0093] y(t+1)=f out ·(W out In the operation of ·(u(t+1),x(t+1)), at this stage, the information in the output node is merely a cover of the training data, and the corresponding training samples form the state vector as the output matrix. When 1, then the state matrix S is T×(N+K) and D is a state vector with dimension T×L.

[0094] 4. Calculate and output the weight matrix Wout

[0095] To calculate the weights of the output matrix, we need to use the internal state matrix x(n) of the system and the sample data ((u(1),yt(1)),…(u(n),yt(n)))) to calculate the output connection weight matrix Wout. After obtaining the output weight matrix Wout, we approximate the desired output yt(n) using the actual output y(n) in the network, that is: That is, the expected weight matrix W out To achieve the minimum system mean square error E(y,yt):

[0096] Where |||| represents the Euclidean distance, and thus W is derived. out =(M -1 ×T) T M is the input and T is the output.

[0097] Step 3: Introduce the slime mold algorithm to optimize the echo state network model, and form a combined prediction model of the echo state network (SMA-ESN) optimized by the slime mold algorithm to predict the time delay τ(t);

[0098] Figure 8This is a block diagram of a networked control system, where sensors and controllers, as well as controllers and actuators, are interconnected via a network. There is a time delay τ between the sensors and controllers. sc (t), and there is a time delay τ between the controller and the actuator. ca (t). The total input delay in the network is here To compensate for the impact of network latency on the system, a slime mold (SMA)-echo state network (ESN) predictor is set up. The designed SMA-ESN neural network is trained using past latency data to predict the latency value τ(t) at the next moment, and τ(t) is used to design the corresponding sliding mode controller. Due to the existence of latency, the actuator may not receive the control signal in time. A latency compensator is set up by adding a buffer before the actuator to save the previous sliding mode controller control signal sequence u(t). In this way, if the actuator does not receive the control signal, it can select the control signal from the previous control sequence based on the time stamp and transmit it to the controlled object.

[0099] The core of the ESN training process is to use a dynamic reservoir to replace the hidden layers of the traditional neural network. The performance of ESN is mainly determined by the various parameters of the reservoir. Due to the black-box nature of the reservoir, the optimal parameters of the reservoir cannot be directly derived through mathematical formulas. Furthermore, it is difficult for a randomly initialized reservoir to achieve the best prediction performance of ESN. Therefore, the slime mold algorithm is introduced to optimize the echo state network model, forming a combined prediction model based on SMA-ESN.

[0100] The weights of the echo state network are initialized, and the neurons in the reserve pool of the echo state network are mapped to slime mold individuals. The weights of the echo state network are mapped to the positions of slime mold individuals, and the positions of slime mold individuals are updated through the slime mold algorithm. The updated optimal solution is assigned to the echo state network to form the echo state network SMA-ESN optimized based on the slime mold algorithm.

[0101] The four reservoir parameters of the echo state network (reservoir size N, spectral radius SR, input shrinkage factor IS, and reservoir sparsity SD) are considered as objects to be optimized. It is assumed that there exists a point in space whose coordinates conform to the four optimal parameters of the reservoir. Then, the slime mold algorithm iteratively searches to make the position of the slime mold individual infinitely close to the optimal value point, which is the optimal parameter of the reservoir. The optimized parameters are then brought back to the echo state network for weight training to obtain the output weight matrix, and finally the prediction result of the echo state network is obtained.

[0102] The optimization process of applying SMA to the four parameters of the ESN reserve pool is as follows:

[0103] (1) Initialize the parameters involved in the SMA algorithm, including the population size parameter N, the maximum number of iterations maxT, and the parameter Z in the population position update formula.

[0104] (2) The fitness value of each population is calculated using the fitness function.

[0105] First, the approach behavior of slime molds was mathematically modeled, and the following rules were proposed to simulate the contraction pattern of slime molds:

[0106]

[0107] Where vb is a random number between [-a, a], vc is a parameter that oscillates between [-1, 1] and eventually tends to zero, t is the current iteration number, and X b X(t) represents the current position of the slime mold individual with optimal fitness, and X(t) represents the current position of the slime mold individual. A (t) and X B (t) represents the positions of two random individuals, and W represents the weighting coefficient of the slime mold.

[0108] The update formulas for control parameters p, vb, a, and weight coefficient W are as follows:

[0109] p = tanh|S(i) - DF|

[0110] In the formula, i∈1,2,…,n,S(i) represents the fitness value of the i-th slime mold individual, and DF is the currently obtained optimal fitness value.

[0111] vb = [-a, a]

[0112]

[0113]

[0114] SmellIndex = sort(S)

[0115] In the formula, condition represents the top half of the individuals in the population with the highest fitness, others represent the remaining individuals, r represents a random number between [0,1], bF represents the best fitness value obtained in the current iteration, wF represents the worst fitness value in the current iteration, T represents the current iteration, maxT is the maximum number of iterations, and SmellIndex is the sorting of the fitness sequence. SmellIndex, bF, and wF are obtained, and finally W is calculated.

[0116] To find the optimal fitness value, i.e., when the evaluation index approaches 0, we consider using the root mean square error (RMSE) evaluation index to assess the performance of the proposed prediction model. We set the RMSE to be...

[0117]

[0118] m represents the total length of the time series, i represents the number of iterations, and y k and These represent the actual value of the time series at time k and the output prediction value of the ESN model, respectively.

[0119] (3) Applying the slime mold individual location update model to analyze population location, optimal fitness value, and optimal population location information X. b Update the fitness value; if the global optimal fitness value is higher than the optimal fitness value during the iteration process, replace the global optimal fitness value with the fitness value obtained from the iteration, and update the best position information of the population with the currently obtained position information.

[0120] The position update model for slime mold individuals is as follows:

[0121]

[0122] Where UB and LB are the upper and lower bounds, rand is a random number uniformly distributed between 0 and 1, z is a user-defined parameter (value 0.03), and X... b (t) represents the coordinates of the location corresponding to the highest concentration of food odor, X A (t) and X B (t) represents the coordinates of two randomly defined slime mold locations. The value of vb oscillates randomly between [-a, a] and gradually approaches zero as the number of iterations increases. The value of vc oscillates between [-1, 1] and eventually tends to zero. The calculation formula is as follows:

[0123] vc = [-b, b]

[0124] b = 1 - T / maxT

[0125] The synergistic effect between vb and vc simulates the selective behavior of slime molds.

[0126] (4) Calculate fitness and update the global optimal position of the population.

[0127] Use the formula in step three The parameters a and b are updated and calculated in relation to b = 1 - T / maxT, and then the global optimal position information is updated.

[0128] (5) Determine if the maximum number of iterations has been reached. If maxT is reached, output the reserve pool parameters corresponding to the optimal individual location information, and apply the best parameter combination of the two to establish the SMA-ESN prediction model. Then, predict the test set data and output y(t). The output y(t) is also the network delay value τ(t). If maxT has not been reached, repeat step (2)-

[0129] (4) Continue to optimize the parameters.

[0130] Step 4: Design the sliding mode function based on the network delay value τ(t), obtain the state equation of the system when it is on the sliding surface, and solve for the system control quantity.

[0131] Based on the predicted time delay τ(t) obtained in the previous step, consider a multi-input multi-output continuous system. The SMA-ESN neural network designed in the previous step predicts the time delay value of the next moment using past time delay data and transmits it to the sliding mode controller to be designed. Due to the existence of time delay, the actuator may not receive the control signal in time. A time delay compensator is designed, which involves adding a buffer before the actuator to store the control signal sequence u(t). This way, if no control signal is received during execution, the control signal can be selected from the previous control sequence based on the time stamp. The continuous state model from the controller to the actuator to the object can be described as follows:

[0132] Where τ(t) is the time delay value predicted by the SMA-ESN neural network in the previous step. It is a state vector. The input is the control input, A is an m×m matrix, B is an m×n full-rank matrix, i.e., rank(B) = n, and τ(t) is the network delay value.

[0133] The sliding mode function is designed based on the network delay value τ(y) as follows:

[0134] S(t)=Cx(t)-∫C(A-BK)x(t)dt+∫CB[u(t)-u(t-τ(t))]dt

[0135] Where C is a constant matrix of appropriate dimension, and it is guaranteed that CB is a non-singular matrix, and K is the parameter to be designed.

[0136] Then set the following exponential reaching law: Let Therefore, we can know

[0137]

[0138] Therefore, satisfying the accessibility condition of the sliding surface, we can obtain:

[0139]

[0140] It can be seen that the sliding mode function eliminates the content of u(t-τ(t)) after differentiation, taking... The equivalent control term can be obtained as u. eq =-Kx(t),

[0141] Based on the equivalent control term u obtained above eq From the exponential approach law, we can obtain the final control law as follows:

[0142] u(t)=-Kx(t)-(CB) -1 (ηS+εsgnS). The state equation of the system when it is on the sliding surface can be described as: Therefore, the original continuous state model The input delay τ(t) is compensated.

[0143] In summary, this invention improves the algorithm for predicting time delay models by combining an echo state network based on the slime mold algorithm with a sliding mode controller. This allows for the rapid establishment of a predictive model for random time delays in the NCS (Network Control System). The SMA-ESN algorithm effectively reduces the training time of the predictive model and maintains good prediction accuracy. The predicted results are then combined with the sliding mode control algorithm to output future control variables, compensating for random time delays in the network control system and improving its signal tracking capability. This invention features a simple structure, high stability, easy operation, strong portability, and low cost, making it suitable for engineering applications.

[0144] In this invention, we provide an example to illustrate the effectiveness of the proposed control measure, and compare the results with those of a conventional sliding mode controller. The continuous state-space model parameters of the controlled object are given below:

[0145] Pick

[0146] The system's initial state is [0.20], with C = [1.5 1], η = 1, ε = 0.005, and K =

[11] . The sliding mode controller designed using this method is used to control this networked control system with variable input time delay. The experimental results are shown below.

[0147] First, we will focus on the time delay prediction of network control. We will then use Matlab to simulate it. Figure 1 This indicates that the SMA-ESN neural network prediction algorithm has higher prediction accuracy and better control effect than the ESN prediction algorithm, and is more conducive to predicting time delay.

[0148] To compensate for the time delay caused by data transmission in the system, a neural network sliding mode controller is designed to ensure the stability of the network control system. Figure 2The experimental results are for the conventional sliding mode controller method. Figure 3 Based on the experimental results designed for this method, compared with ordinary sliding mode controllers, this method has smaller oscillations and faster convergence speed. Figure 4 The output of the control signal for a typical sliding mode controller is given. Figure 5 Compared with the former, the control law u(t) obtained by the controller designed for this method shows that the control output of this method has a smaller overshoot and a faster control speed. Figure 6 and Figure 7 The evolution of the sliding surface for both the conventional sliding mode controller and the controller proposed in this method is plotted. Figure 7 This indicates that the proposed method has a faster convergence speed on the sliding surface, smaller overshoot, and stronger system robustness.

[0149] In summary, the method of this invention converges faster than the ordinary sliding mode method for all variables, and exhibits less oscillation and better robustness.

Claims

1. A time delay compensation method for a network control system based on neural network sliding mode control, characterized in that: The steps are as follows: Step 1: Establish the echo state network; Step 2: Echo State Network Training and Update; Step 3: Introduce the slime mold algorithm to optimize the echo state network model, forming a combined prediction model based on the echo state network optimized by the slime mold algorithm to predict the network delay value. ; Step 4: Based on network latency values Design the sliding mode function, obtain the state equation of the system when it is on the sliding surface, and solve for the system control variables; The output state equation of the echo state network in step one is: ， In the formula, fout It is the activation function of the output layer neurons. W out These are the connection weights from the reservoir to the output layer. y(t+1) The output at the next moment, u(t+1) The control quantity in the next moment, x(t+1) The input at the next moment; The sliding mode function in step four is as follows: ； in, It is a constant matrix of appropriate dimension, and it can guarantee that... It is a non-singular matrix. For the parameters to be designed, For time, for 1-th order matrix B for A full-rank matrix of order and column. It is the network latency value. For controlling input.

2. The time delay compensation method for a network control system based on neural network sliding mode control according to claim 1, characterized in that: Input unit of the echo state network in step one The input layer has K nodes, containing latency data from previous time points; a reserve pool... Given the current state, the reservoir contains N neural nodes; the output unit... The network delay value is the output value at the next time step. There are L output nodes in the network. The states of the input unit, the storage pool, and the output unit are: 。 3. The time delay compensation method for a network control system based on neural network sliding mode control according to claim 1, characterized in that: The optimization process of the echo state network based on the slime mold algorithm in step three is as follows: (1) Initialize the parameters involved in the slime mold algorithm, including the population size parameter. N The maximum number of iterations (max) T and the parameters in the population position update formula Z ; (2) Calculate the fitness value of each population using the fitness function; (3) Apply the slime mold individual location update model to the population location, optimal fitness value and optimal population location information. X b Update; If, during the iteration process, the global optimal fitness value is higher than the optimal fitness value, then the global optimal fitness value is replaced with the fitness value obtained through iteration, and the optimal position information of the population is updated to the currently obtained position information. (4) After updating the location information, calculate the fitness of each population and update the global optimal position of the population; (5) Determine if the maximum number of iterations has been reached. If it has, then... T Then, the optimal individual location information is output as the corresponding reservoir parameters. The optimal parameter combination is then used to establish an echo state network prediction model based on the slime mold algorithm. Finally, predictions are generated from the test set data. Output That is, network latency value If the maximum value is not reached. T Then repeat steps (2)-(4) to continue the parameter optimization operation.

4. The time delay compensation method for a network control system based on neural network sliding mode control according to claim 3, characterized in that: Step (3) involves finding the optimal fitness value: First, the approach behavior of slime molds was mathematically modeled, and the following rules were proposed to simulate the contraction pattern of slime molds: ； In the formula, vb for[- a , a Random numbers between ] W The weighting coefficients represent slime molds. and Given the positions of two random individuals, vc It is a parameter that oscillates between [-1, 1] and eventually tends to zero. This indicates the location of the individual with the best current fitness. Indicates the current location of the slime mold individual; Secondly, control parameters ,parameter ,parameter a With weighting coefficients W The update formula is as follows: ； in, Indicates the first Fitness value of an individual slime mold. This is the currently obtained optimal fitness value; ； in, This refers to the top half of the individuals in the population in terms of fitness. Indicates the remaining individuals, Represents a random number between [0, 1]. This represents the best fitness value obtained in the current iteration. This represents the worst-case fitness value in the current iteration. T max is the current iteration number. T is The maximum number of iterations, and SmellIndex representing the sorting of the fitness sequence, are used to obtain SmellIndex. bF , wF Finally, for W Perform calculations; Finally, to find the optimal fitness value, i.e., when the evaluation index approaches 0, we consider using the root mean square error (RMSE) evaluation index to evaluate the performance of the proposed prediction model, setting the RMSE to 0. ； Represents the total length of the time series. Represented as the number of iterations, and They represent The actual values ​​of the time series at each time point and the output predicted values ​​of the ESN model.

5. The time delay compensation method for a network control system based on neural network sliding mode control according to claim 3, characterized in that: The position update model for slime mold individuals in step (3) is as follows: ； in, and For upper and lower boundaries, A random number that is uniformly distributed between 0 and 1. For custom parameters, vb The value in [- a , a It oscillates randomly between [a certain value] and gradually approaches zero as the number of iterations increases. vc The value in It oscillates between these values ​​and eventually tends to zero. The calculation formula is as follows: ； vb and vc The synergistic effect between them simulated the selective behavior of slime molds.

6. The time delay compensation method for a network control system based on neural network sliding mode control according to claim 1, characterized in that: The system control variables in step four are: ； In the formula, take It is a sliding mode function; The state equation of the system when it is on the sliding surface can be described as follows: 。

Images