Control method and system for high-speed trains to maintain safe driving under DoS attacks

Abstract

The present invention relates to a control method and system for maintaining safe driving of high-speed trains under DoS attacks. The method comprises: setting pseudo-partial derivative step size, pseudo-partial derivative weight, control law step size, control law weight, adjustment factor, and control input linearization length; setting the expected trajectory of the leader car, the initial value of the train speed output by the following car, and the initial value of the train traction / braking force input by the following car; updating the predicted value of the pseudo-partial derivative; resetting the predicted value of the pseudo-partial derivative; updating the control input; updating the output based on the mathematical expectation of successful data transmission under DoS attacks; calculating the train speed; judging whether the train's travel time has reached the termination time, and if so, stopping the control; otherwise, repeating the above steps. The present invention proposes an extended model-free control, which introduces a control law update method with an input criterion function of an error adjustment factor, which can effectively shorten the convergence time of high-speed train control to achieve stability and improve the tracking effect of the system.

Description

Technical Field

[0001] The present invention relates to the field of train control technology, and more particularly to a control method and system for ensuring safe running of a high-speed train under a DoS attack. Background Art

[0002] With the rapid development of high-speed rail networks worldwide, high-speed trains have become a key component of modern transportation systems, enjoying widespread popularity for their efficiency, comfort, and environmental friendliness. However, with the widespread application of information technology, high-speed rail systems are also facing increasingly severe cybersecurity threats. If a high-speed train is subjected to a denial-of-service (DoS) attack, the train control system may be maliciously manipulated, causing unpredictable train behavior such as overspeeding and sudden stops, seriously impacting operational safety. Furthermore, DoS attacks can disable signaling and communication systems, potentially leading to serious consequences such as train delays, suspensions, or the need for emergency passenger evacuations. The resulting equipment damage and system maintenance costs associated with cyberattacks can incur significant economic losses for railway authorities. Traditional security measures often rely on predefined models and rules, limiting their ability to identify and defend against new attacks and unknown threats. Therefore, developing adaptive control strategies that can adapt to unknown attack patterns is crucial for ensuring the safe operation of high-speed trains under DoS attacks.

[0003] Currently, most high-speed train tracking control methods rely on centralized control. However, for electric multiple units (EMUs), especially those with variable train formations, greater emphasis is placed on the autonomy of each car. These modular designs require that each car operate autonomously while also allowing for the flexible arrangement of multiple cars to form the train body. Because each car on a high-speed train can operate autonomously, its operation can be viewed as the collaborative behavior of a multi-agent system, with the entire train being described as a multi-agent system in a longitudinal formation.

[0004] Traditional control system design often relies on precise mathematical models. However, in high-speed railway systems, establishing precise mathematical models is extremely difficult due to system complexity and environmental variability. Consequently, model-free adaptive control (MFAC) methods have gradually attracted research attention. Model-free adaptive control does not rely on precise mathematical models. Instead, it establishes a dynamic linear data model equivalent to the nonlinear system at each operating point and uses the controlled system's I / O data to online estimate system parameters, thereby achieving model-free adaptive control of unknown nonlinear systems. The advantages of this method lie in its flexibility and adaptability, enabling it to maintain system stability and performance in uncertain and changing environments. In the context of DoS attacks, safe operation strategies for high-speed trains based on model-free adaptive control are particularly important. By monitoring and analyzing the system's input and output data in real time, model-free control methods can promptly detect potential DoS attack threats and adaptively adjust the control strategy to address them. This adaptive capability enables the system to maintain stable operation under DoS attacks, ensuring safe train operation. Summary of the Invention

[0005] The present invention aims to overcome the problems of the prior art and provide a control method for high-speed trains to maintain safe driving under DoS attacks. Based on the strategy of extended model-free high-speed train system control, a control law update method of the input criterion function of the error adjustment factor is introduced, which can effectively shorten the convergence time of high-speed train control to achieve stability and improve the tracking effect of the system.

[0006] The present invention adopts the following technical solutions:

[0007] In one aspect, a control method for a high-speed train to maintain safe running under a DoS attack includes:

[0008] S1, control parameter setting step;

[0009] Set the controller parameters, including the pseudo partial derivative step size η i , pseudo partial derivative weight μ i , control law step length ρ i , control law weight λ i , adjustment factor β and control input linearization length L; where i∈[1,N], N represents the number of following carriages;

[0010] S2, initialization step;

[0011] Set the desired velocity trajectory of the leader car and the initial value y of the train velocity output by the follower car i (0) and the initial value u of the train traction / braking force input by the following carriage i (0), initialize the train's travel time k = 1;

[0012] S3, the predicted value update step of the pseudo partial derivative;

[0013] Update the pseudo partial derivative Φ at the current driving moment k i The predicted value of (k) as follows:

[0014]

[0015] in, Represents the predicted value The transpose of represents the transpose of the predicted value of the pseudo partial derivative at the driving time k-1; ΔU i (k-1)=[Δu i (k-1),...,Δu i (kL)] represents a vector of train traction / braking force differences within a sliding time window [k-L+1,k], Δu i (·) represents the difference in train traction / braking force at adjacent moments, L represents the linearization length of the control input; Δy i (k) represents the difference in train speed between time k and time k-1; Φ i (k)=[φ i,1 (k),φ i,2 (k),...,φ i,L (k)];

[0016] S4, the step of resetting the predicted value of the pseudo partial derivative;

[0017] Reset Φ i (k) Predicted value of pseudo partial derivative as follows:

[0018] like but

[0019] Among them, ε represents the pseudo partial derivative reset threshold; represents the pseudo partial derivative value at the initial moment; sign(·) represents the sign function; ||·|| represents the 2-norm;

[0020] S5, update control input step;

[0021] Update the control input u at time k i (k) as follows:

[0022]

[0023] Among them, u i (k-1) represents the control input at time k-1; φ i,1 (k) represents Φi (k) The first pseudo partial derivative in the vector; y d (k+1) represents the expected speed of the high-speed train; y pi (k) represents the train speed received by the control at time k; φ i,j (k) represents Φ i (k) the jth pseudo partial derivative in the vector;

[0024] S6, control the received train speed update step;

[0025] like Then y pi (k) = y i (k); otherwise, y pi (k) = y i (k-1); where represents the mathematical expectation of successful data transmission under DoS attack; y i (k) represents the train speed output by the sensor at time k; y i (k-1) represents the train speed output by the sensor at time k-1;

[0026] S7, step of calculating the train speed output by the sensor;

[0027] Calculate y i (k+1), as follows:

[0028]

[0029] y i (k+1)=y i (k)+Δy i (k+1)

[0030] in, ΔU i (k)=[Δu i (k),...,Δu i (k+1-L)];

[0031] S8, control stop judgment step;

[0032] Determine whether the train's travel time k has reached the end time. If so, stop the control; otherwise, set k=k+1 and repeat S3~S8.

[0033] Preferably, before the control stop determination step, the method further includes:

[0034] Determine whether all following carriages have completed the execution. If not, set i=i+1 and repeat S3 to S8; otherwise, execute S8.

[0035] Preferably, the ypi (k), which is represented as follows:

[0036]

[0037] On the other hand, a high-speed train control system includes a leader car and several follower cars, all of which can directly or indirectly receive signals from the leader car. The high-speed train control system uses the control method to control each follower car.

[0038] From the above description of the present invention, it can be seen that compared with the prior art, the present invention has the following beneficial effects:

[0039] (1) Compared with the single-mass model used in traditional research, the present invention adopts a multi-mass model, which treats each carriage of the high-speed train as a separate intelligent entity. The interaction force between the carriages and the length of the train are taken into account, which can more accurately reflect the dynamic model of the train and the actual operation of the train, allowing the train to adapt to complex operating environments.

[0040] (2) The partial format dynamic linearization (PFDL) method adopted by the present invention considers the impact of all input changes within a fixed-length sliding time window at the current moment on the output changes at the next moment, which can more accurately reflect the dynamic characteristics of high-speed trains and improve the accuracy of the model;

[0041] (3) The present invention considers the impact of DoS attacks on the input and output changes of high-speed trains and proposes a new attack compensation mechanism to mitigate the impact of DoS attacks;

[0042] (4) The present invention proposes an extended model-free control method that introduces a control law update method of an input criterion function of an error adjustment factor, which can effectively shorten the convergence time of the high-speed train control system to achieve stability and improve the tracking effect of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 A schematic diagram of a DoS attack strategy according to an embodiment of the present invention;

[0044] Figure 2 This is a schematic diagram of an application of a control method for maintaining safe running of a high-speed train under a DoS attack according to an embodiment of the present invention;

[0045] Figure 3 This is a diagram of the expected speed trajectory of a high-speed train according to an embodiment of the present invention;

[0046] Figure 4 This is a high-speed train speed tracking diagram under a DoS attack according to an embodiment of the present invention;

[0047] Figure 5 This is a diagram of the train traction / braking force input under a DoS attack according to an embodiment of the present invention;

[0048] Figure 6 This is a speed tracking error diagram under a DoS attack according to an embodiment of the present invention;

[0049] Figure 7 The speed tracking curves of different algorithms under DoS attack in an embodiment of the present invention;

[0050] Figure 8 1 is a speed tracking error curve of different algorithms according to an embodiment of the present invention. DETAILED DESCRIPTION

[0051] The present invention is further described below through specific embodiments.

[0052] The following will first establish the PFDL data model, the extended EMFAC framework of high-speed trains, and the DoS attack model. Then, based on the PFDL data model, the extended EMFAC framework of high-speed trains, and the DoS attack model, a control method for high-speed trains to maintain safe operation under DoS attacks will be designed.

[0053] (1) Constructing a PFDL-based MFAC framework

[0054] Consider the dynamic model of a high-speed train, where k represents the train's travel time (i.e., sampling time), m i represents the mass of the i-th carriage, s i and v i Represents the displacement and velocity of the i-th carriage, u i represents the traction or braking force provided by the power unit of the i-th car. According to Newton's laws of motion, the force balance equation of the high-speed train can be expressed as follows:

[0055]

[0056] Among them, m i (c0+c v v i )and Indicates the mechanical resistance and air resistance of the carriage, c k (s i-1 -s i ) represents the leading car, i.e. the traction or damping force generated by the i-1th car on the i-th car through the coupler force coupling; c k (s i -s i+1 ) represents the coupler force generated by the rear car, i.e. the i+1th car.

[0057] Assumption 1: For the mass m of the i-th carriagei , there is an inequality in m i and These are all known numbers, representing the weight of the carriage and its weight when fully loaded.

[0058] Because the basic resistance and additional resistance of high-speed trains are difficult to accurately obtain, and some unknown parameters are also difficult to measure, the train system model is unknown and uncertain, making it difficult to establish an accurate dynamic model. During the operation of the train, a large amount of input and output data is generated. Based on the train's input and output data, the system model of carriage i can be expressed as follows:

[0059] y i (k+1)=f(y i (k),...,y i (kn y ),u i (k),...,u i (kn u )) (1.2)

[0060] Among them, y i (·) represents the train speed, u i (·) is the system traction / braking force, f(·) is an unknown nonlinear function, n y and n u are two unknown positive integers.

[0061] Definition U i (k)=[u i (k),...,u i (k-L+1)] is a vector of train traction / braking forces within a sliding time window [k-L+1, k].

[0062] Assumption 2: The function f(·) is i The partial derivative of (k) is continuous.

[0063] Assumption 3: All cars can directly or indirectly obtain information about the leader.

[0064] Assumption 4: The system satisfies the generalized Lipschitz condition, that is, for any t ≥ 0, when ||ΔU i When (k)≠0||, there is

[0065] ||Δy i (k+1)||≤b||ΔU i (k)|| (1.3)

[0066] Where: b>0 is a constant Δy i(k+1)=y i (k+1)-y i (k),Δu i (k)=u i (k)-u i (k-1)ΔU i (k)=[Δu i (k),...,Δu i (k+1-L)].

[0067] Note 1: Assumption 1 m j and These are all known numbers, representing the deadweight and fully loaded weight of the carriage, and are reasonable. Assumption 2 is a typical constraint in train controller design. Assumption 3 is a necessary assumption for high-speed train communication network systems. Assumption 4 places an upper bound on the rate of change of the train system's output, meaning that bounded inputs to the system can only produce bounded outputs.

[0068] Lemma 1: The train system satisfies Assumptions 1 to 4. When ||ΔU(k)≠0||, there exists a system time-varying parameter Φ(k) such that Equation (1.2) can be transformed into the following PFDL data model:

[0069]

[0070] |Φ i (k)|≤b, b is a positive number

[0071] When a high-speed train is attacked by a DoS attack, the attacker's main goal is to control the information of the current car, in order to affect the communication with the attacked car and the effectiveness of the formation control of other cars. When the leading car is attacked, the other cars in the formation are too dependent on the leading car. Once the leading car is attacked and exceeds the speed limit, the entire high-speed train system will be paralyzed. In a high-speed train system, maintaining the distance and speed between each car is a necessary condition for the safety of the train. The control goal of the high-speed train longitudinal formation control is to ensure that the speed of all cars is consistent with that of the leading car when it is attacked by a DoS attack.

[0072]

[0073] Among them, y r (k) represents the ideal leading car speed.

[0074] (2) Proposed Extended Model-Free Control (EMFAC) method

[0075] In the actual train system, the parameter Φ i(k) is difficult to measure. To overcome this problem, an observer is designed to obtain Φ i Estimated value of (k) The traditional model-free control method, the MFAC algorithm, only considers the impact of output error on the control law when calculating the control law. It does not consider the problem that when the output error is large, the fluctuation of the control law at adjacent moments due to the large range of output error fluctuations, which in turn leads to long system convergence time. This paper introduces an error adjustment factor β>0 to optimize the calculation of the control law. The following control input update law and an improved control protocol for longitudinal formation control are designed:

[0076] J(u i (k)) = β | y d (k+1)-y i (k+1)| 2 +λ||ΔU i (k)|| 2 (1.6)

[0077] Here, β is the error adjustment factor, whose purpose is to accelerate the system's convergence time. λ is a penalty factor, primarily used to limit the change in the control input, thereby limiting the range of nonlinear systems that can be replaced by dynamic linearization, and indirectly limiting the rate of change of the partial derivatives. Secondly, it can avoid singular cases where the denominator could be zero.

[0078] Taking the derivative of the above formula, we get

[0079]

[0080] make have to

[0081]

[0082] In order to make the control method more general, the step size factor ρ is introduced i ∈(0,1)(i=1,2,...,N).

[0083] Pseudo partial derivative Φ i (k) Parameter estimation algorithm:

[0084]

[0085] Same, for J(Φ i (k)) to find the extreme value, we can get the pseudo partial derivative Φ i (k) The estimation algorithm is:

[0086]

[0087] In order to improve the tracking ability of the algorithm, a reset algorithm was added:

[0088] if but

[0089] Where sign(·) represents the sign function.

[0090] (3) Propose a DOS attack model

[0091] Due to the instability of the network transmission channel, the information transmission process may be subject to DoS attacks. Consider a type of DoS attacker that mainly destroys the information transmission channel between carriages, which will cause data packet loss during the data transmission process, thereby affecting the security and stability of the high-speed train system during the similar process. The present invention assumes that DoS attacks have the characteristics of randomness and limited energy. The attacker can destroy the transmission channel of system information during the attack, and then enter a dormant period to store energy and prepare for the next attack. DoS attacks such as Figure 1 shown.

[0092] The tth attack interval can be expressed as: D t ={d t}∪[d t ,d t +θ t ), where D t is the time of transmission interruption, d t is the starting time when the system is attacked by DoS, θ t is the duration of the attack. For the i-th carriage, use α i (k) = 1 means the attacker is in sleep mode at this moment, α i (k)=0 means that the attacker is attacking the information transmission system of the high-speed train at this time.

[0093]

[0094] Considering that the high-speed train system may still successfully transmit information when it is attacked by DoS, assuming that the success rate of information transmission under DoS attack follows Bernoulli distribution, we use To indicate whether the information is successfully transmitted under DoS attack. If the information is transmitted successfully,

[0095]

[0096] Where P(·) represents the mathematical expectation, and the data transmission success rate when the attacker is sleeping is higher than the success rate at the attack time, that is, definition The mathematical expectation is α i ={0,1}.

[0097] When a high-speed train system is attacked by a DoS attack, it can easily cause packet loss and prevent timely control input, thus affecting system stability. When a DoS attack occurs on the transmission network, the information received by the controller is converted into the following form.

[0098]

[0099] To mitigate the impact of DoS attacks, the following attack compensation mechanism is adopted:

[0100]

[0101] (4) Control method for high-speed trains to maintain safe operation under DoS attacks

[0102] Combining (1.5) to (1.11) and considering the impact of DoS attacks, the following complete control method for high-speed trains to maintain safe operation under DoS attacks is designed. Its structure is as follows: Figure 2 shown.

[0103]

[0104] like but

[0105] From equation (1.13), we can see that due to the possibility of data transmission failure, the controller may not receive the output value of the sensor at time k. pi (k) represents the train speed received by the control, y i (k) represents the train speed output by the sensor. pi (k) is set for the controller designed based on the control method of the present invention. αi (k) = 1, then the train speed received by the controller at time k is the same as the train speed output by the sensor. If P αi (k)=0, then the train speed received by the controller at time k is set to the train speed output by the sensor at time k-1.

[0106] In summary, the execution process of the control method for maintaining safe running of a high-speed train under a DoS attack of the present invention is as follows.

[0107] 1: Choose appropriate controller parameters, pseudo-partial derivative step size η i , pseudo partial derivative weight μ i , control law step length ρ i , control law weight λ i , adjustment factor β and control input linearization length L.

[0108] 2: Set the desired velocity trajectory of the leader car and the pseudo partial derivative Φ i (k) and the initial value of the output of the following car.

[0109] 3: for k=1to end

[0110] Step 1: Update the predicted value of the pseudo partial derivative through formula (1.15)

[0111] Step 2: Reset the predicted value of the pseudo partial derivative through formula (1.16)

[0112] Step 3: Update the control input u through equation (1.14) i (k);

[0113] Step 4: If P αi (k)=1,y pi (k) = y i (k), P αi (k) is the mathematical expectation of successful data transmission under DoS attack, y pi (k) is the actual output at time k. Otherwise y pi (k) = y i (k-1);

[0114] Step 5: Pass Calculate y i (k+1);

[0115] Step 6:

[0116]

[0117] The following simulation verifies the effectiveness of the control method and system for high-speed trains to maintain safe operation under DoS attacks.

[0118] During the simulation, it is assumed that the simulated train consists of four carriages, one of which is the leader carriage and the other three are follower carriages. The simulation environment parameters are set as shown in the following table.

[0119] The simulation considered three train operating conditions: initial acceleration, constant speed, and deceleration. These three operating states essentially encompass the various possible operating conditions of a high-speed train during its operation. The train's operating conditions can be summarized as: an initial phase in which the train accelerates to a constant speed over a period of time and then continues to operate for a period of time. After this period of operation, the train gradually decelerates until its speed reaches zero. A high-speed train consists of two acceleration phases, three constant speed phases, and three deceleration phases.

[0120] Table 1 High-speed train parameters

[0121] parameter value unit Physical meaning <![CDATA[m1]]> <![CDATA[6×10 4 ]]> kg Leading car quality <![CDATA[m2,m3,m4]]> <![CDATA[3×10 4 ]]> kg Following car mass <![CDATA[c0]]> 5.2 N / kg Mechanical resistance coefficient <![CDATA[c v ]]> 0.0015 <![CDATA[N·s 2 / (m 2 ·kg)]]> Basic drag coefficient <![CDATA[c t ]]> <![CDATA[4×10 5 ]]> N / m Coupler damping coefficient <![CDATA[c a ]]> 0.032 N·s / (m·kg) Air resistance coefficient

[0122] According to the requirements for the stability of the control system, the initial values ​​of the train are set to y1(0) = 0, y2(0) = 0.5 m / s, y3(0) = 1 m / s, u1(0) ​​= 0.4 N / kg, u2(0) = 0.2 N / kg, u3(0) = 0.7 N / kg, y i and u i Represent the train speed and system traction / braking force, respectively. The controller parameters are pseudo-partial derivative step size (η1, η2, η3) = [0.9, 0.9, 0.7], pseudo-partial derivative weights (μ1, μ2, μ3) = [1.5, 3, 3], control law step size (ρ1, ρ2, ρ3) = [0.6, 0.15, 0.3], control input linearization length L = 2, sampling time K = 2500, control law weights (λ1, λ2, λ3) = [1, 4, 4], adjustment factor β = 2, and pseudo-partial derivative reset threshold ε = 1e-5.

[0123] like Figure 3 The figure shows the expected speed trajectory of the high-speed train. Figure 4 The figure shows the speed tracking effect of a high-speed train, where the black solid line is the expected speed curve, and the red, blue and green dashed lines are the actual speed curves of the three following carriages. Figure 4 It can be seen that even in the case of DoS attacks, the train speed can still achieve good tracking effect by combining the MFAC and attack compensation mechanism algorithms. Figure 5 The following is the system input diagram under DoS attack. Figure 6 In the figure, the three solid lines of different colors represent the tracking errors of different carriages. When the speed changes, the curve oscillates obviously and the burrs increase.

[0124] Finally, the control method of the invention is compared with the method of the CFDL data model. The following controller parameters are selected: η = 0.9, μ = 3, ρ = 0.3, λ = 4, β = 2, and sampling time K = 2500.

[0125] like Figure 7 and Figure 8 It shows that different model-free adaptive control methods can quickly approach the desired trajectory. Then, by observing the curve graph, we can see that the fluctuation range and tracking error observed using the PFDL linearized data model are significantly smaller than those observed using the CFDL model, which also reflects the superiority of the invented method.

[0126] The above embodiments are merely for illustrating the present invention and are not intended to limit the present invention. As long as they are based on the technical essence of the present invention, any changes or modifications to the above embodiments will fall within the scope of the claims of the present invention.

Claims

1. A control method for high-speed trains to maintain safe running under DoS attacks, characterized in that: include: S1, control parameter setting step; Set the controller parameters, including the pseudo partial derivative step size η i , pseudo partial derivative weight μ i , control law step length ρ i , control law weight λ i , adjustment factor β and control input linearization length L; where i∈[1,N], N represents the number of following carriages; S2, initialization step; Set the desired velocity trajectory of the leader car and the initial value y of the train velocity output by the follower car i (0) and the initial value u of the train traction / braking force input by the following carriage i (0), initialize the train's travel time k = 1; S3, the predicted value update step of the pseudo partial derivative; Update the pseudo partial derivative Φ at the current driving moment k i Predicted value of (k) as follows: in, Represents the predicted value The transpose of represents the transpose of the predicted value of the pseudo partial derivative at the driving time k-1; ΔU i (k-1)=[Δu i (k-1),...,Δu i (kL)] represents a vector of train traction / braking force differences within a sliding time window [k-L+1,k], Δu i (·) represents the difference in train traction / braking force at adjacent moments, L represents the linearization length of the control input; Δy i (k) represents the difference between the train speed at time k and time k-1; Φ i (k)=[φ i,1 (k),φ i,2 (k),...,φ i,L (k)]; S4, the step of resetting the predicted value of the pseudo partial derivative; Reset Φ i (k) Predicted value of pseudo partial derivative as follows: like but Among them, ε represents the pseudo partial derivative reset threshold; represents the pseudo partial derivative value at the initial moment; sign(·) represents the sign function; ||·|| represents the 2-norm; S5, update control input step; Update the control input u at time k i (k) as follows: Among them, u i (k-1) represents the control input at time k-1; φ i,1 (k) represents Φ i (k) The first pseudo partial derivative in the vector; y d (k+1) represents the expected speed of the high-speed train; y pi (k) represents the train speed received by the control at time k; φ i,j (k) represents Φ i (k) the jth pseudo partial derivative in the vector; S6, control the received train speed update step; like Then y pi (k) = y i (k); otherwise, y pi (k) = y i (k-1); where represents the mathematical expectation of successful data transmission under DoS attack; y i (k) represents the train speed output by the sensor at time k; y i (k-1) represents the train speed output by the sensor at time k-1; S7, step of calculating the train speed output by the sensor; Calculate y i (k+1), as follows: y i (k+1)=y i (k)+Δy i (k+1) Among them, D.U. i (k)=[Δu i (k),...,Du i (k+1-L)]; S8, control stop judgment step; Determine whether the train's travel time k has reached the end time. If so, stop the control; otherwise, set k=k+1 and repeat S3~S8.

2. The control method for maintaining safe running of a high-speed train under a DoS attack according to claim 1 is characterized in that: Before the control stop determination step, the method further includes: Determine whether all following carriages have completed the execution. If not, set i=i+1 and repeat S3 to S8; otherwise, execute S8.

3. The control method for maintaining safe running of a high-speed train under a DoS attack according to claim 1 is characterized in that: The y pi (k), which is represented as follows:

4. A high-speed train control system comprising a leader car and several follower cars, wherein all follower cars can directly or indirectly receive signals from the leader car, characterized in that: Each follower carriage is controlled using the control method as claimed in claim 1.

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