CN106707765A - Running-tracking, real-time optimization control method for high speed train - Google Patents

Abstract

The invention discloses a real-time optimization control method for high-speed EMU tracking operation. By collecting actual operation data of the high-speed EMU, an offline ANFIS model of the high-speed EMU is first established, and a predictive controller based on the offline ANFIS model is designed. When the object characteristics or environmental changes lead to poor tracking performance, causing the absolute value of the feedback velocity error | _er | to exceed the set error threshold χ, start the online adjustment strategy of the model, return the actual operating data, and use Kalman filtering and BP gradient descent The algorithm optimizes the ANFIS model in real time to adjust the parameters of the predictive controller online, eliminate the impact of characteristic changes on the operation of the EMU, and realize the real-time optimal control of the operation process of the high-speed EMU. The invention guarantees the running performance of the high-speed EMU and provides favorable technical support for the automatic driving system of the high-speed EMU. The invention is applicable to the technical field of real-time optimization control of high-speed EMU tracking operation.

Description

Real-time optimization control method for high-speed EMU tracking operation

technical field

The invention relates to a multiple working condition modeling and operation optimization control method in the operation process of a high-speed train set, and belongs to the technical field of real-time optimization control for tracking operation of a high-speed train set.

Background technique

High-speed EMUs are valued by many countries for their advantages of large passenger capacity, safety and comfort, punctual speed, energy saving and environmental protection, and all-weather transportation, and have become the first choice for many countries to develop advanced transportation systems. With the development of my country's economy and society, there is an urgent need for large-scale, rapid development of high-speed railways, and the construction of train operation control systems marked by safety, punctuality, and energy saving. In the rail transit system, the train operation control system is the core system to ensure the safe operation of the train and improve the operation efficiency. The quality of its control strategy directly affects the ability of railway transportation. The high-speed EMU runs at a high speed and has a long distance. Its operation process is highly sensitive to relevant influencing factors, and it is affected more and more complicated than traditional railways. The existing high-speed EMU operation control is a manual control mode based on the actual operating conditions of the driver under the guidance of the automatic train protection system (ATP). The operation performance of the EMU is closely related to the driver's operating experience and response to faults . Therefore, in order to ensure the high-speed and safe operation of EMUs in real time, we need to establish a model of the high-speed EMUs' operating process and perform real-time optimal control of the operation process.

The traditional modeling of the running process of high-speed EMUs usually adopts the description method based on traction calculation and running resistance empirical model, but it cannot completely describe the complex and changeable dynamic behavior of EMUs. In order to restore the dynamic operation process of high-speed EMUs more accurately, data-driven modeling has gradually become a research hotspot in modeling high-speed EMUs. For the tracking control of the train running process, the more classic one is the PID control method. Relevant scholars have designed a fuzzy PID method to control the track speed trajectory of MRT trains. Since PID control does not have adaptive ability, it is only suitable for subway systems with relatively stable environment and low speed. In order to solve this problem, some scholars adopt the robust adaptive control method to realize the speed and position tracking control of high-speed EMUs; however, the parameter decomposition and control law design of adaptive robust control require a lot of calculations, which cannot solve the problem of actual high-speed EMUs well. Operating environment. Considering that the generalized predictive control method can effectively overcome the uncertainty and nonlinearity of the process, and can easily deal with various constraints of the controlled variables in the process, it is suitable for complex uncertain systems. At present, many scholars study the generalized prediction of high-speed EMUs. control, realizing the high-precision control of the speed and displacement of the high-speed EMU during operation. However, none of the above control methods has real-time optimal control performance, and it is difficult to eliminate the influence of some uncertain factors in the operation of high-speed EMUs in time.

Contents of the invention

The purpose of the present invention is to design a high-speed EMU tracking operation real-time Optimize the control system, adjust model parameters online, and improve the safety and punctuality of the high-speed EMU operation process.

Technical scheme of the present invention is:

A real-time optimal control method for high-speed EMUs. The method establishes an ANFIS model for high-speed EMUs by collecting actual operating data for high-speed EMUs, and designs a corresponding predictive controller based on the model, collects predicted output speed and expected speed in real time, and analyzes the operation Speed error; when the high-speed EMU is affected by uncertain factors such as unknown environment or EMU characteristics change on the tracking control, the Kalman filter algorithm and BP gradient descent method are combined to adjust the model parameters in real time to adapt to the next high-speed EMU high-precision tracking Control and eliminate the impact of characteristic changes on the operation of EMUs, so as to ensure the operating performance of high-speed EMUs.

Described high-speed EMU real-time optimal control method, described high-speed EMU off-line ANFIS model is:

Suppose there are m data points {X ₁ ,…,X _i ,…,X _m } of the running process of high-speed EMUs, where X _i =[v _i (k-1),u _i (k-1),v _i ( _k )], the density index at the data point Xi is defined as

In the formula, δ _a is the effective neighborhood radius of the set cluster center, which is a positive number; select the highest value of the density index get the first cluster center

Then the density index of each data point Xi is _corrected by the following formula

where δ _b is a positive number greater than δ _a ; obviously, the density index of data points close to the first cluster center c ₁ will be significantly reduced, which makes these points less likely to be selected as the next cluster center; correction After obtaining the density index of each data point, select the next cluster center c ₂ , correct all the density indexes of the data point again, and repeat this process until Get the last cluster center c _n , so the number of cluster centers of high-speed EMU running process data is n;

The minimum variance estimation is used to obtain n linear models for n rule consequents; the n linear models are fused to obtain the following offline ANFIS model:

in, is the normalized value of all rule fitness.

In the real-time optimization control method of the high-speed EMU, the predictive controller based on the off-line ANFIS model is:

The described high-speed EMU operation process model (7) can be described as the following form

In the formula, with is a polynomial of z ^-1 , Δ=1-z ^-1 ;

where parameters with Obtained by the modeling process.

In order to obtain the optimal control scalar, the performance index function can be designed as

Among them, L, H, G and is the parameter matrix of the introduced Diophantine equation, is the weighting coefficient matrix;

Minimize performance metrics (i.e. ) to get the optimal control increment as

According to the real-time optimization control method for high-speed EMUs, when the high-speed EMUs are affected by uncertain factors such as unknown environment or EMU characteristics change on the tracking control, the online adjustment model strategy is started to adapt to the high-precision tracking control of the next high-speed EMUs , the real-time optimization control strategy adjusts the model parameters in real time by combining the Kalman filter algorithm and the BP gradient descent method. The specific optimization steps can be expressed as:

Step 1. Design a generalized predictive controller based on the ANFIS model of the high-speed EMU, and calculate the speed feedback error e _r (t)=y(t)-y _r (t) at time t;

Step 2. Perform high-speed EMU tracking operation control;

Step 3. Determine whether the time t has reached the total time T _t , and if so, end the process; otherwise, enter the next time t+1 and go to Step 4;

Step 4. At time t+1, compare the feedback error e _r (t) at the previous time with the set error threshold χ, if |e _r (t)|≥χ, it indicates that the model does not match and is not suitable for current control In this case, Step 5 is required to adjust the model parameters online; if the feedback error |e _r (t)|<χ, it indicates that the tracking accuracy is high, and there is no need to optimize the model parameters for the time being, and return to Step 1 directly;

Step 5. Combining the Kalman filter algorithm and BP gradient descent method, adjust the parameters of the anterior part and subsequent part of the ANFIS model online, and substitute the optimized model into the generalized predictive controller, and return to Step 1.

Described high-speed EMU real-time optimization control method, described Step 5. in conjunction with Kalman filter algorithm and BP gradient descent method, online adjustment ANFIS model front piece, the method of back piece parameter is:

On the basis of the established model (8), first use the following Kalman filter algorithm to adjust the parameters of the after parts

In the formula, For the consequent parameters obtained in the modeling process, the forgetting factor 0<λ _KF ≤1 usually selects a positive number close to 1 (in this paper, λ _KF =0.9995); P _KF (k)=q _KF I∈R ^2n×2n , q _KF is a large positive number, usually 10 ⁴ to 10 ¹⁰ (q _KF = 10 ⁶ in the present invention);

Secondly, the BP gradient descent method is used to optimize the antecedent parameters c _ij and σ _ij in real time;

The calculation error index function is

In the formula, the k-th data points y(k) and yr(k) respectively represent the actual output speed and expected output speed at the time _t of the model mismatch transmitted from the control part, and so on; the optimization algorithm of the antecedent parameters is as follows:

After the ANFIS model parameters are corrected, they are substituted into the generalized predictive controller for recalculation, and the corresponding control force is obtained to implement real-time optimal control for the tracking operation of the high-speed EMU.

The beneficial effect of the present invention compared with the prior art is that the high-speed EMU is a complex nonlinear system operating in a variable environment. In order to improve the running performance of high-speed EMUs, it is necessary to design an effective operating process controller to precisely control high-speed EMUs. The control methods of high-speed EMUs designed by existing researchers do not have real-time optimization functions, and it is difficult to deal with the degraded tracking performance caused by the characteristics of EMUs or environmental changes, which makes the operation performance of high-speed EMUs unguaranteed. The present invention proposes a novel real-time optimization control method for tracking operation based on the characteristics of complex operating environment, frequent changes in operating conditions, and many factors affecting operating performance of high-speed EMUs. Firstly, an off-line ANFIS model of high-speed EMU operation process is established, and a corresponding generalized predictive controller is designed. When the EMU characteristics or environmental changes lead to poor tracking performance, start the online adjustment strategy, and use the Kalman filter and BP gradient descent method to adjust the high-speed EMU running ANFIS model online, thereby adjusting the parameters of the predictive controller to achieve EMU tracking The real-time optimization control of operation improves the safety and punctuality of its operation.

The invention is suitable for real-time optimization control of high-speed EMU tracking operation.

Description of drawings

Figure 1 is a structural block diagram of the real-time optimal control system for high-speed EMUs;

Figure 2 is the stress situation during the operation of the high-speed EMU;

Fig. 3 is the real-time optimization control process of the high-speed EMU operation process;

Fig. 4 is the output error distribution curve of test data;

Fig. 5 is characteristic change speed tracking curve;

Fig. 6 is characteristic change speed tracking error curve;

Fig. 7 is characteristic change traction/braking force curve;

Fig. 8 is characteristic change acceleration curve;

Fig. 9 is the parameter optimization process of characteristic change ANFIS model;

detailed description

The present invention will be described in detail below in conjunction with specific embodiments.

The invention collects the actual operation data of the high-speed EMU, analyzes the tracking operation control mechanism of the EMU, combines its traction/braking characteristic curve and the actual operation data, establishes the offline ANFIS model of the high-speed EMU operation process, and designs the generalized predictive control based on the ANFIS model The algorithm realizes the control of the EMU tracking operation process; when the object characteristics or environmental changes cause the tracking performance to deteriorate, the online adjustment strategy of the model is started, and the Kalman filter and BP gradient descent algorithm are used to optimize the ANFIS model in real time to adjust the parameters of the predictive controller online , to realize the real-time optimal control of the running process of high-speed EMUs.

The present invention is based on the high-speed train operation process modeling step of ANFIS as:

1. Analysis of the principle of real-time optimal control of high-speed EMUs:

Figure 1 illustrates the structure of the real-time optimal control system for EMU operation based on the ANFIS model and generalized predictive control. Based on the data-driven ANFIS modeling method, an accurate model of the EMU operation process is established and transmitted to the generalized predictive controller. After specific calculations, the control variable u is obtained and output, and the EMU is controlled to track the given inter-station operation mode curve (the operation mode curve It is composed of the actual ATP speed limit curve and the optimal expected speed curve. The optimal expected speed curve is combined with the excellent driver's EMU handling experience, based on the operating indicators such as safety, punctuality and energy saving, from the actual operating speed curve of a large number of high-speed EMUs filter OK) to run. Collect the predicted output speed y and the expected speed y _r in real time, and analyze the running speed error. When the high-speed EMU is affected by uncertain factors such as unknown environment or EMU characteristic change, etc. to the tracking control, causing the absolute value of the feedback speed error |e _r | to exceed the set error threshold χ (in order to ensure the punctuality and To optimize the real-time performance of control, the threshold χ is selected in combination with the permissible error range of CTCS-3 train control system and the sampling cycle requirements of real-time control), return the actual operating data, and adjust the model in real time by combining the Kalman filter algorithm and BP gradient descent method parameters, and adjust the generalized predictive controller of the high-speed EMU based on the adjusted ANFIS model to adapt to the next high-precision tracking control of the high-speed EMU and eliminate the impact of characteristic changes on the operation of the EMU.

2. Offline ANFIS modeling of high-speed EMU operation process:

The force of the high-speed EMU during operation is shown in Figure 2. The train is simplified to a single rigid mass point, and all the forces during the operation of the EMU are applied to this mass point for analysis and calculation. In the figure, y is the high-speed train running The speed is obtained by the speed measuring and distance measuring unit, and u is the unit control force (traction force/braking force), which is obtained by the driver operating the handle under the guidance of the ATP vehicle equipment, so as to achieve the effects of traction, constant speed, coasting and braking. r _b is unit basic resistance, r _b =A _r +B _ry +C _ry ² . The force situation of the high-speed EMU in the figure can be described by the following mathematical model.

In the formula, ε is the acceleration coefficient, A _r , B _r , and C _r are the drag coefficients, and C _ry ² represents the air resistance. With the increase of the train speed, the larger the proportion of C _y ² is, the nonlinearity of the system more obvious features. The differential transformation of formula (1) can be described as a relational expression:

y(k)=f{y(k-1), u(k-1)} (2)

In view of the fact that ANFIS combines the adaptive learning characteristics of the neural network and the nonlinear modeling characteristics of the T-S fuzzy model, the conclusion part of the model replaces the fuzzy numbers in the general Mamdani fuzzy system with linear equations, so that the system can describe a complex system with fewer rules. nonlinear system. For the EMU running process described by formula (2), the following fuzzy reasoning rules are used to describe

R _i represents the i-th fuzzy inference rule; y(k-1), u(k-1) are input quantities, and y(k) is output quantity; is the i-th fuzzy set of the input quantity; is the consequent parameter, n is the number of rules; ξ _i is a constant term.

Suppose there are m data points {X ₁ ,…,X _i ,…,X _m } of the running process of high-speed EMUs, where X _i =[v _i (k-1),u _i (k-1),v _i ( _k )], the density index at the data point Xi is defined as

In the formula, δ _a is the effective neighborhood radius of the set cluster center, which is a positive number. Select the highest value of the density index get the first cluster center

Then the density index of each data point Xi is _corrected by the following formula

Where δ _b is a positive number greater than δ _a . Obviously, the density index of data points close to the _first cluster center c1 will be significantly reduced, which makes these points less likely to be selected as the next cluster center. After correcting the density index of each data point, select the next cluster center c ₂ , correct all the density indexes of the data point again, and repeat this process until Get the last cluster center c _n , so the number of cluster centers of the high-speed EMU running process data is n.

n linear models are obtained by minimum variance estimation for n rule consequents. The n linear models are fused to obtain the following ANFIS model:

in, is the normalized value of all rule fitness.

3. Real-time optimization control of high-speed EMU tracking operation

Based on the high-speed EMU ANFIS model established above, the corresponding generalized predictive controller is designed as follows:

The high-speed EMU operation process model (7) obtained above can be described as the following form

In the formula, with is a polynomial of z ^-1 , Δ=1-z ^-1 .

where parameters with Obtained by the modeling process, it can be expressed as

with is the model order of the controlled object.

In order to obtain the optimal control scalar, the performance index function can be designed as

Among them, L, H, G and is the parameter matrix of the introduced Diophantine equation, is the weighting coefficient matrix.

Minimize performance metrics (i.e. ) to get the optimal control increment as

In order to eliminate the impact of the unmodeled part, the change of EMU operating characteristics caused by unknown environment and faults on the tracking control, and the feedback control error, the online adjustment strategy of the ANFIS model is implemented:

Step 1. Design a generalized predictive controller based on the high-speed EMU ANFIS model (as shown above), and calculate the speed feedback error e _r (t)=y(t)-y _r (t) at time t.

Step 2. Execute high-speed EMU tracking operation control.

Step 3. Determine whether the time t has reached the total time T _t , and if so, end the process; otherwise, enter the next time t+1 and go to Step 4.

Step 4. At time t+1, compare the feedback error e _r (t) at the previous time with the set error threshold χ, if |e _r (t)|≥χ, it indicates that the model does not match and is not suitable for current control In this case, Step 5 is required to adjust the model parameters online; if the feedback error |er ( _t )|<χ, it indicates that the tracking accuracy is high, and there is no need to optimize the model parameters for the time being, and return to Step 1 directly.

Step 5. Combining the Kalman filter algorithm and the BP gradient descent method, adjust the parameters of the anterior and posterior components of the ANFIS model online (as shown below). The optimized model is substituted into the generalized predictive controller and returns to Step 1.

On the basis of the established model (8), first use the following Kalman filter algorithm to adjust the parameters of the after parts

In the formula, For the consequent parameters obtained in the modeling process, the forgetting factor 0<λ _KF ≤1 usually chooses a positive number close to 1 (in this paper, λ _KF =0.9995); P _KF (k)=q _KF I∈R ^2n×2n , q _KF is a large positive number, usually 10 ⁴ -10 ¹⁰ (q _KF =10 ⁶ in the present invention).

Secondly, the antecedent parameters c _ij and σ _ij are optimized in real time by using BP gradient descent method.

The calculation error index function is

In the formula, the k-th data points y(k) and y _r (k) represent the actual output speed and expected output speed at time t of the model mismatch transmitted from the control part, and so on. The optimization algorithm of the antecedent parameters is as follows:

After the ANFIS model parameters are corrected, they are substituted into the generalized predictive controller for recalculation, and the corresponding control force is obtained to implement real-time optimal control for the tracking operation of the high-speed EMU. The specific process is shown in Figure 3.

To sum up, in view of the complex operating environment of high-speed EMUs, frequent changes in operating conditions, and many factors affecting operating performance, the ANFIS model of the operation process is established, and a real-time optimization control method for tracking and running of high-speed EMUs is proposed. When the EMU characteristics or environmental changes lead to poor tracking performance, the online adjustment strategy is activated to optimize the control performance in real time and improve the safety and punctuality of the EMU.

The implementation of the present invention selects the CRH380AL type high-speed EMU as the experimental verification object. First of all, collect the 10-day full-run speed and control data of the EMU on the Beijing-Shanghai high-speed railway from Jinan West to Xuzhou East, select 2000 sets of valid data representing all working conditions of traction, coasting, and braking, and take the global average Among them, 1400 sets of data are used as modeling data samples, and the remaining 600 sets of data are used as data to test the accuracy of the model. First, based on 1400 sets of modeling sample data, the ANFIS modeling method is used to obtain 4 optimal fuzzy rules (n = 4 in formula (3)). The off-line ANFIS model parameters are shown in Table 1. In order to verify the effectiveness of the model, the remaining 600 sets of operating data are used to test the established model, and the model output error distribution curve is shown in Figure 4. :

Table 1 ANFIS model parameters

The speed limit curve in Figure 4 is drawn according to the positioning and speed measurement requirements of the CTCS-3 train control system. Observe the model verification process in Figure 4. When the speed is less than 30km/h, the model output error range: -0.5876～0.5234km/h; when the speed is greater than 30km/h, the error range: -2.1421～1.6899km/h, which meets CTCS- 3 The positioning and speed measurement requirements of the train control system show that the established ANFIS model has high precision, strong generalization ability, and good prediction effect.

Based on the established ANFIS model, using generalized predictive control, combined with Kalman filter algorithm and BP gradient descent method to design a real-time optimal control strategy for the tracking operation of high-speed EMUs in the Jinan West Station-Xuzhou East Station section of the Beijing-Shanghai high-speed railway line Implement real-time optimization control. During the actual operation of the EMU, if an unknown environment causes changes in the characteristics of the EMU, the tracking performance of the high-speed EMU will deteriorate, making it difficult to track the upper target curve, and the speed tracking error exceeds the set threshold (the threshold χ=2km/ h). In this case, the real-time optimization control strategy of the present invention optimizes the running process model of the EMU in time, so that the high-speed EMU quickly tracks the upper target curve again. In this paper, when the EMU runs to mileage railmileage = 500km and rail mileage = 600km, uncertain disturbance factors are added, resulting in changes in the operating characteristics of the EMU. The control simulation results are shown in Figures 5 to 8, and Figure 9 lists the real-time Optimization process curves for the parameters of the ANFIS model.

Figures 5 to 8 show that when the characteristics of the EMU change, the speed changes suddenly, and the target curve cannot be tracked. The real-time optimization control strategy based on ANFIS can optimize the operation model in real time according to the existing EMU data, adjust the control force, and make the high-speed EMU quickly correct the operating speed and track the target curve again with high precision. Fig. 9 shows that after a fault occurs, the present invention's method to the front and rear parameters of the ANFIS model c _ij , σ _ij (i=1,2,3,4; j=1,2) are precisely adjusted in real time until the optimal ANFIS model is obtained again, and the high-speed EMU operation model is optimized in real time. Table 2 lists the velocity and acceleration tracking errors of the method of the present invention after an unknown fault occurs.

Table 2 Velocity and acceleration tracking error

feature change Speed (km/h) Acceleration (m/s²) maximum negative error -1.6502 -0.4649 maximum positive error 2.3763 0.7095 root mean square error 0.7793 0.0203

It can be seen intuitively from Table 2 that in the case of changes in the operating characteristics of the EMU, the maximum positive and negative tracking errors and the root mean square error of the method of the present invention are controlled within a certain range, which meets the positioning of the CTCS-3 train control system The requirement of speed measurement further quantitatively shows the validity of the method in this paper.

It should be understood that those skilled in the art can make improvements or changes based on the above description, and all these improvements and changes should fall within the protection scope of the appended claims of the present invention.

Claims (5)

1. A high-speed EMU real-time optimization control method is characterized in that, the method is by collecting the actual operation data of the high-speed EMU, setting up the ANFIS model of the high-speed EMU, and designing a corresponding predictive controller based on this model, and collecting and predicting output speed in real time and the expected speed, and analyze the operating speed error; when the high-speed EMU is affected by uncertain factors such as unknown environment or EMU characteristics change on the tracking control, combine the Kalman filter algorithm and BP gradient descent method to adjust the model parameters in real time to adapt to the following The high-precision tracking control of high-speed EMUs eliminates the impact of characteristic changes on the operation of EMUs, thereby ensuring the operating performance of high-speed EMUs. 2. the real-time optimization control method of high-speed multiple train set according to claim 1, is characterized in that, described high-speed multiple train set off-line ANFIS model is: Suppose there are m data points {X ₁ ,…,X _i ,…,X _m } of the running process of high-speed EMUs, where X _i =[v _i (k-1),u _i (k-1),v _i ( _k )], the density index at the data point Xi is defined as ${\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; m</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; ,</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; ,</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; )</span>$ In the formula, δ _a is the effective neighborhood radius of the set cluster center, which is a positive number; select the highest value of the density index get the first cluster center ${\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; |</span>}_{{\mathrm{<span\; class="notranslate">\; maxD</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}$ Then the density index of each data point Xi is _corrected by the following formula ${\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; \&lsqb;</span><span\; class="notranslate">\; -</span>\frac{<span\; class="notranslate">\; |</span><span\; class="notranslate">\; |</span>{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; |</span>{<span\; class="notranslate">\; |</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}<span\; class="notranslate">\; \&rsqb;</span>$ where δ _b is a positive number greater than δ _a ; obviously, the density index of data points close to the first cluster center c ₁ will be significantly reduced, which makes these points less likely to be selected as the next cluster center; correction After obtaining the density index of each data point, select the next cluster center c ₂ , correct all the density indexes of the data point again, and repeat this process until Get the last cluster center c _n , so the number of cluster centers of high-speed EMU running process data is n; The minimum variance estimation is used to obtain n linear models for n rule consequents; the n linear models are fused to obtain the following offline ANFIS model: $\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&CenterDot;</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&lsqb;</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&xi;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$ in, is the normalized value of all rule fitness. 3. the real-time optimization control method of high-speed train set according to claim 2, is characterized in that, the predictive controller based on off-line ANFIS model is: The described high-speed EMU operation process model (7) can be described as the following form $\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>$ In the formula, with is a polynomial of z ^-1 , Δ=1-z ^-1 ; $\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; a</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}}}<span\; class="notranslate">\; ,</span>$ $\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span>\mathrm{<span\; class="notranslate">\; b</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; +</span>{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}}_{{\mathrm{<span\; class="notranslate">\; no</span>}}_{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}}}{\mathrm{<span\; class="notranslate">\; z</span>}}^{<span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; no</span>}}_{\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; b</span>}}}}<span\; class="notranslate">\; ,</span>$ where parameters with Obtained by the modeling process. In order to obtain the optimal control scalar, the performance index function can be designed as $\begin{array}{c}\mathrm{<span\; class="notranslate">\; J</span>}<span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>}^{\mathrm{<span\; class="notranslate">\; T</span>}}\\ \stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}<span\; class="notranslate">\; \&lsqb;</span>\mathrm{<span\; class="notranslate">\; L</span>}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span>\\ <span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; u</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; r</span>}\mathrm{<span\; class="notranslate">\; u</span>}\end{array}$ Among them, L, H, G and is the parameter matrix of the introduced Diophantine equation, is the weighting coefficient matrix; Minimize performance metrics (i.e. ) to get the optimal control increment as $\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}\mathrm{<span\; class="notranslate">\; L</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; R</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; L</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&mu;</span>}}<span\; class="notranslate">\; \&lsqb;</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; W</span>}}{\mathrm{<span\; class="notranslate">\; Y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; G</span>}\mathrm{<span\; class="notranslate">\; Y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}\mathrm{<span\; class="notranslate">\; \&Delta;</span>}\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; j</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&rsqb;</span><span\; class="notranslate">\; .</span>$ 4. The real-time optimal control method for high-speed multiple units according to claim 3, characterized in that, when the high-speed multiple units are affected by uncertain factors such as unknown environment or changes in the characteristics of high-speed multiple units, the online adjustment model strategy is started to adapt to The following high-speed EMU high-precision tracking control, the real-time optimization control strategy adjusts the model parameters in real time by combining the Kalman filter algorithm and the BP gradient descent method. The specific optimization steps can be expressed as: Step 1. Design a generalized predictive controller based on the ANFIS model of the high-speed EMU, and calculate the speed feedback error e _r (t)=y(t)-y _r (t) at time t; Step 2. Perform high-speed EMU tracking operation control; Step 3. Determine whether the time t has reached the total time T _t , and if so, end the process; otherwise, enter the next time t+1 and go to Step 4; Step 4. At time t+1, compare the feedback error e _r (t) at the previous time with the set error threshold χ, if |e _r (t)|≥χ, it indicates that the model does not match and is not suitable for current control In this case, Step 5 is required to adjust the model parameters online; if the feedback error |e _r (t)|<χ, it indicates that the tracking accuracy is high, and there is no need to optimize the model parameters for the time being, and return to Step 1 directly; Step 5. Combining the Kalman filter algorithm and BP gradient descent method, adjust the parameters of the anterior part and the subsequent part of the ANFIS model online, and substitute the optimized model into the generalized predictive controller, and return to Step 1. 5. high-speed EMU real-time optimization control method according to claim 4, it is characterized in that, described Step5 combines Kalman filtering algorithm and BP gradient descent method, on-line adjustment ANFIS model preceding part, the method for following part parameter is: On the basis of the established model (8), first use the following Kalman filter algorithm to adjust the parameters of the after parts In the formula, For the consequent parameters obtained in the modeling process, the forgetting factor 0<λ _KF ≤1 usually chooses a positive number close to 1 (in this paper, λ _KF =0.9995); P _KF (k)=q _KF I∈R ^2n×2n , q _KF is a large positive number, usually 10 ⁴ ~ 10 ¹⁰ , preferably q _KF = 10 ⁶ ; Secondly, the BP gradient descent method is used to optimize the antecedent parameters c _ij and σ _ij in real time; The calculation error index function is $\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}{<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; e</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}$ In the formula, the k-th data points y(k) and yr(k) respectively represent the actual output speed and expected output speed at the time _t of the model mismatch transmitted from the control part, and so on; the optimization algorithm of the antecedent parameters is as follows: ${\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}\frac{<span\; class="notranslate">\; \&part;</span>\mathrm{<span\; class="notranslate">\; E.</span>}}{<span\; class="notranslate">\; \&part;</span>{\mathrm{<span\; class="notranslate">\; c</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}}$ ${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&alpha;</span>}}_{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}\frac{<span\; class="notranslate">\; \&part;</span>\mathrm{<span\; class="notranslate">\; E.</span>}}{<span\; class="notranslate">\; \&part;</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}}$ After the ANFIS model parameters are corrected, they are substituted into the generalized predictive controller for recalculation, and the corresponding control force is obtained to implement real-time optimal control for the tracking operation of the high-speed EMU.