Control method and system for keeping safe driving of high-speed train under DoS attack

Abstract

The invention relates to a control method and system for keeping safe driving of a high-speed train under DoS attack. The method comprises the following steps: setting a pseudo partial derivative step length, a pseudo partial derivative weight, a control law step length, a control law weight, a regulation factor and a control input linearization length; setting an expected track of a leader compartment, a train speed initial value output by a following compartment and a train traction / braking force initial value input by the following compartment; updating the predicted value of the pseudo partial derivative; resetting the predicted value of the pseudo partial derivative; updating the control input; updating and outputting the mathematical expectation of successful data transmission based on the DoS attack; calculating the train speed; judging whether the running time of the train reaches the termination time or not, and if yes, stopping control; otherwise, repeating the steps. The invention provides a control law updating method for expanding model-free control and introducing an input criterion function of an error regulation factor, so that the convergence time for high-speed train control to reach stability can be effectively shortened, and the tracking effect of the system can be improved.

Description

Technical Field

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

[0002] With the rapid development of the global high-speed railway network, high-speed trains have become a key component of the modern transportation system. Their high efficiency, comfort and environmental protection are deeply loved by people. However, with the widespread application of information technology, the high-speed railway system is also facing increasingly serious network security threats. If a high-speed train is attacked by Denial-of-Service (DoS), the train control system may be maliciously manipulated, resulting in other unpredictable behaviors such as overspeeding and emergency stops, which seriously affects the operation safety of the train. In addition, DoS attacks may cause the functions of signal systems and communication systems to fail, which may lead to serious consequences such as train delays, suspension of operation or emergency evacuation of passengers. Under network attacks, the equipment loss and system maintenance caused will cause a lot of economic losses to the railway department. Traditional security protection measures often rely on pre-defined models and rules, and have limited ability to identify and defend against new attacks and unknown threats. Therefore, exploring a control strategy that can adapt to unknown attack modes and has adaptive capabilities is of great significance to ensure the safe operation of high-speed trains when they are attacked by DoS.

[0003] Most of the current tracking control methods for high-speed trains are centralized control. For electric multiple units, especially variable multiple units, more emphasis is placed on the autonomy of each car. Variable multiple units adopt a modular design. On the one hand, each car is required to be able to operate autonomously, and on the other hand, multiple cars can be freely assembled to form the train body. Each car of a high-speed train can operate autonomously, so the operation of a high-speed train is regarded as a collaborative behavior of a multi-agent system, and the entire train is described as a multi-agent system in the form of a longitudinal formation.

[0004] Traditional control system design often relies on accurate mathematical models, but in high-speed railway systems, it is very difficult to establish accurate mathematical models due to the complexity of the system and the variability of the environment. Therefore, the model-free adaptive control (MFAC) method has gradually attracted the attention of researchers. Model-free adaptive control does not rely on accurate mathematical models, but instead establishes a dynamic linear data model equivalent to the nonlinear system at each operating point, and uses the I / O data of the controlled system to estimate the system parameters online, thereby realizing model-free adaptive control of unknown nonlinear systems. The advantage of this method lies in its flexibility and adaptability, which enables it to maintain the stability and performance of the system in an uncertain and changing environment. In the context of DoS attacks, the high-speed train safety driving strategy based on model-free adaptive control is particularly important. By real-time monitoring and analysis of the input and output data of the system, the model-free control method can promptly detect potential DoS attack threats and adaptively adjust the control strategy to deal with the attack. This adaptive capability enables the system to maintain stable operation when attacked by DoS, ensuring the safe driving of the train. 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 an input criterion function of an 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 solution:

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

[0008] S1, control parameter setting step;

[0009] Set controller parameters, including 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 car 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 time k i 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 traction / braking force of trains at adjacent moments, L represents the linearization length of 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)];

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

[0017] ResetΦ i (k) Prediction 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, updating 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 Φ i (k) The first pseudo partial derivative in the vector; y d (k+1) represents the expected speed of the high-speed train; ypi(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, controlling the received train speed update step;

[0025] If P αi (k)=1, then y pi (k) = y i (k); otherwise, y pi (k) = y i (k-1); where P αi (k) 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, a 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 reaches the end time, if so, stop 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-S8; otherwise, execute S8.

[0035] Preferably, the y pi (k), which is expressed 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, and the high-speed train control system uses the control method to control each follower car.

[0038] It can be seen from the above description of the present invention 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 regards each carriage of the high-speed train as a separate intelligent entity, takes into account the interaction force between the carriages and the length of the train, and can more accurately reflect the dynamic model of the train and the actual operation of the train, so that the train can adapt to complex operating environments;

[0040] (2) The partial format dynamic linearization (PFDL) method adopted by the present invention considers the influence of all input changes in 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 also 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 and a control law updating method that introduces an input criterion function of an error adjustment factor, which can effectively shorten the convergence time of a 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 It is a high-speed train speed expected trajectory diagram according to an embodiment of the present invention;

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

[0047] Figure 5 This is a train traction force / braking force input diagram 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 It is the speed tracking curve of different algorithms under DoS attack of the 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 implementation modes.

[0052] As follows, we will first establish the PFDL data model, the extended EMFAC framework of the high-speed train and the DoS attack model, and then design a control method for the high-speed train to maintain safe driving under DoS attacks based on the PFDL data model, the extended EMFAC framework of the high-speed train and the DoS attack model.

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

[0054] Consider the dynamic model of a high-speed train, where k represents the travel time of the train (i.e., the sampling time), m i represents the mass of the i-th carriage, s i and v i Represent 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 carriage. 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 represents the mechanical resistance and air resistance of the carriage, c k (s i-1 -s i ) represents the traction or damping force generated by the preceding car, i.e. the i-1th car, on the i-th car through the action of the coupler force coupler; c k (s i -s i+1 ) represents the coupling force generated by the rear car, that is, 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 deadweight of the carriage and its weight when fully loaded.

[0058] Since the basic resistance and additional resistance of high-speed trains are difficult to obtain accurately, and some unknown parameters are difficult to measure, the train system model is unknown and uncertain, and it is difficult to establish an accurate dynamic model. Then, during the operation of the train, a large amount of input and output data will be generated. According to the input and output data of the train, the system model of the i-carriage 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 )) (0.2)

[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 composed of the train traction / braking forces within the 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||, we have

[0065] ||Δy i (k+1)||≤b||ΔU i (k)|| (0.3)

[0066] Where: b>0 is a constant Δyi (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 are all known numbers, representing the deadweight of the carriage and the weight when fully loaded, which is reasonable. Assumption 2 is a typical constraint for train controller design. Assumption 3 is a necessary assumption for the high-speed train communication network system. Assumption 4 is a restriction on the upper bound of the rate of change of the train system output, that is, the bounded input of the system can only produce bounded output.

[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 DoS, the attacker's main goal is to control the information of the current car to affect the communication with the attacked car and the effectiveness of 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 the high-speed train system, maintaining the distance and speed between the cars 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 DoS.

[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 MFAC algorithm only considers the impact of the output error on the control law when calculating the control law, but does not consider the problem that when the output error is large, the fluctuation of the control law at adjacent moments caused by the large range of output error fluctuations, which in turn leads to a long system convergence time. The present invention introduces an error adjustment factor β>0 to optimize the calculation of the control law, designs the following control input update law, and an improved control protocol for longitudinal formation control:

[0076] J(u i (k)) = β|y d (k+1)-y i (k+1)| 2 +λ||ΔU i (k)|| 2 (0.6)

[0077] Among them, β is the error adjustment factor, the purpose of which is to accelerate the convergence time of the system. λ is a penalty factor, which is mainly used to limit the change of the control input, thereby limiting the range of nonlinear systems replaced by dynamic linearization, and then indirectly limiting the rate of change of the partial derivative value. Secondly, it can avoid the singular situation where the denominator may 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)) Find the extreme value and 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] Wherein, 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 safety and stability of the high-speed train system during the transmission 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 to 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 successfully transmitted,

[0095]

[0096] Where P(·) represents the mathematical expectation. 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

[0097] When a high-speed train system is attacked by DoS, it is easy to cause data packet loss and fail to generate control input in time, thus affecting the stability of the system. When a DoS attack occurs on the transmission network, the information received by the controller will be converted into the following form.

[0098]

[0099] In order 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 driving under DoS attacks is designed 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 expected 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 = 1 to 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 driving 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] Table 1 High-speed train parameters

[0120]

[0121]

[0122] During the simulation, three running conditions of the train were considered, including the train's start-up acceleration, the train's uniform speed, and the train's deceleration. These three running conditions basically cover the running conditions that may occur in various time periods during the high-speed train's running. The running conditions of the train can be summarized as accelerating to a uniform speed state within a period of time in the initial stage and running for a period of time. After a period of running, the train gradually decelerates until the speed is 0. The high-speed train includes two acceleration stages, three uniform speed stages, and three deceleration stages.

[0123] According to the requirements for control system stability, 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, η2η3) = [0.9, 0.9, 0.7], pseudo partial derivative weight (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 weight (λ1, λ2, λ3) = [1, 4, 4], adjustment factor β = 2, pseudo partial derivative reset threshold ε = 1e-5.

[0124] 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.

[0125] 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.

[0126] like Figure 7 and Figure 8It shows that different model-free adaptive control methods can quickly approach the desired trajectory. Then, by observing the curve graph, it can be seen that the fluctuation range and tracking error observed using the PFDL linearized data model are significantly smaller than those observed by the CFDL model, which also reflects the superiority of the invented method.

[0127] The above embodiments are only used to illustrate the present invention, and are not used to limit the present invention. As long as they are based on the technical essence of the present invention, changes and 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 driving under DoS attacks, characterized in that: include: S1, control parameter setting step; Set controller parameters, including 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 car 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 time 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 traction / braking force of trains at adjacent moments, L represents the linearization length of 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; ResetΦ i (k) Prediction 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, updating 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; ypi(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, controlling the received train speed update step; If P αi (k)=1, then y pi (k) = y i (k); otherwise, y pi (k) = y i (k-1); where P αi (k) 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, a 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 reaches the end time, if so, stop control; otherwise, set k=k+1 and repeat S3~S8.

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

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

4. A high-speed train control system, comprising a leader car and a plurality of follower cars, all of which 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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