A Cooperative Operation Control Method for High-Speed Train Groups Containing Malicious Agents

Abstract

The present invention discloses a cooperative operation control method for a high-speed train group containing malicious agents, comprising the following steps: S1, establishing a dynamic model of each train in the train group; S2, constructing a cooperative control law including a potential function; S3, modeling the malicious agent; S4, using an adaptive control algorithm and a low-pass filter to estimate unknown control parameters contained in the malicious agent; S5, stratifying the trains according to whether the trains in the train group are adjacent to the malicious agent train; S6, constructing a controller for the trains adjacent to the malicious agent; S7, constructing a controller for the trains in the train group that are not adjacent to the malicious agent. The present invention can effectively suppress the destructive influence of the malicious agent on the train formation when the malicious agent deliberately interferes with the system, maintain the normal cooperative operation of the trains, improve the operation efficiency and overall cooperative ability of the trains, and enhance the safety and stability.

Description

Technical Field

[0001] The present invention relates to the technical field of high - speed train braking operation control, and particularly to a cooperative operation control method for a group of high - speed trains with malicious agents. Background Art

[0002] High - speed trains (HSTs), characterized by high speed, low carbon emissions, and environmental sustainability, have become increasingly important in modern transportation. In recent years, with the development of automatic control theory, the progress of train positioning technology, and the continuous improvement of communication links between high - speed trains, the problem of multi - train coordinated control has attracted wide attention. Multi - train coordinated control aims to reduce the running interval, increase the running density, and improve the efficiency of high - speed railways while ensuring the operation quality. Each train dynamically adjusts its speed according to the communication with neighboring trains. However, unexpected situations and disturbances may occur during train operation, which may disrupt the normal operation order, leading to cascading delays and other problems. These situations can significantly affect the railway transportation network and ultimately cause huge economic losses.

[0003] To address potential fault problems, several existing studies on fault - tolerant control of high - speed trains based on the multi - agent system (MAS) model have been explored. Most existing studies focus on the multi - agent system (MAS) model assuming that all agents are healthy and rational. However, in real - world scenarios, agents inevitably face security and safety challenges. Improper behavior in a group may stem from three main factors: physical - layer faults, network - layer attacks, and abnormal or malicious decisions in the supervision layer.

[0004] To cope with the control challenges posed by malicious agents, existing studies have shown that: although malicious agents may transmit misleading information, they still follow collective decisions, which differentiates them from agents with truly malicious intentions. In addition, these studies assume that malicious agents can be removed on the premise of ensuring network - topology connectivity. Regarding malicious agents in the supervision layer, some studies have proposed a hybrid D - silencing method aimed at mitigating the impact of Byzantine agents so that cooperative agents can reach a consensus. However, like most related studies, this method mainly relies on excluding malicious agents. However, maintaining task integrity in a group requires avoiding exclusion by safely restricting malicious agents. Moreover, those exclusion methods that ignore motion dynamics are not applicable to networked agents (such as vehicle fleets, train groups, and drone swarms) subject to dynamic or geometric constraints. Summary of the Invention

[0005] To solve the problem that a train group can still meet cooperative control under the influence of malicious agents, the present invention proposes a cooperative operation control method for a group of high - speed trains with malicious agents to solve the above problems.

[0006] This application discloses a cooperative operation control method for a high - speed train group containing malicious agents, including the following steps:

[0007] S1. Establish the dynamic models of each train in the train group respectively according to the basic running resistance and external disturbances suffered during the train operation;

[0008] S2. Based on the dynamic models obtained in S1, construct a cooperative control law including a potential function;

[0009] S3. Model the malicious agent for the possible impacts it may cause in the train cooperative control;

[0010] S4. Adopt an adaptive control algorithm and a low - pass filter to estimate the unknown control parameters contained in the malicious agent, so as to adjust the control strategy in real - time;

[0011] S5. Stratify the trains according to whether the trains in the train group are adjacent to the malicious - agent train. The first layer is the malicious - agent train, the second layer is the trains adjacent to the malicious - agent train, and the third layer is the trains in the train group that are not adjacent to the malicious agent;

[0012] S6. Construct the controllers of the trains adjacent to the malicious agent, and contain the destructive behaviors that the malicious agent may cause by adjusting the distance and speed between the malicious - agent train and the adjacent trains;

[0013] S7. Construct the controllers of the trains in the train group that are not adjacent to the malicious agent, and adopt adaptive control to ensure the normal cooperative operation of the train group.

[0014] Preferably, the dynamic model of each train in the train group is:

[0015]

[0016] Among them, x i (t) represents the displacement of the i - th train at time t, v i (t) represents the speed of the i - th train at time t, m i is the mass of the i - th train, u i (t) is the control force of the i - th train at time t, is the coefficient obtained through wind - tunnel tests, f ir is the gradient resistance of the i - th train, f ic is the curve resistance of the i - th train, f it is the tunnel resistance of the i - th train. Assume that the operation boundary restricts the speed of each train, satisfying v i (t)≤v max , v max is the boundary of the train speed;

[0017] The goal of train collaborative control is to drive the multi - train system to a unified state and ensure that a given safety spacing is maintained, that is: where \(x\) ij = \(x\) i − \(x\) j represents the difference in distance between train \(i\) and train \(j\),

[0018] \(\mathcal{N}_i\) represents the set composed of all trains that can communicate with train \(i\), \(v\) represents the set of all trains, and \(D\) is the maximum allowable distance between adjacent trains.

[0019] Preferably, the collaborative control law including the potential function is as follows:

[0020]

[0021] where, \(F_i\) represents the sum of the resistances suffered by the train, \(V\) ij represents the potential function, \(\nabla V\) represents the gradient of the potential function with respect to \(x\) i ;

[0022] In formula (2), the first term is used to offset the resistance encountered by the high - speed train, the second term is used to align the speed of the multi - train system with the speed of the \(i\) - th train, and the third term corresponds to the gradient of the potential function \(V\) ij . The potential function \(V\) ij maintains the geometric configuration to prevent collisions and ensure cohesion within the group:

[0023]

[0024] where, \(Z\) represents a positive constant, \(d\leq|x\) ij |\leq D\), and \(d\) is the minimum safe headway;

[0025] Preferably, the potential function \(V\) ij has the following properties:

[0026]

[0027] where, the potential function \(V\) ij can be expressed as the sum of two components: \(V\) aij is the attractive potential between agent \(i\) and agent \(j\), \(V\) rij is the repulsive potential between agent \(i\) and agent \(j\); when \(|x\) ij | = \(\rho\), \(V\) ij reaches the minimum value, and at the unique distance \(\rho\), the condition is satisfied:

[0028] To ensure that the control input u is large enough when |x ij | reaches the critical values d and D, we have:

[0029]

[0030] where N represents the number of elements contained in the set .

[0031] Preferably, the following steps are taken after S3:

[0032] Define to represent a malicious agent train, which may deliberately manipulate the controller parameters. The controller expression of the malicious agent train is:

[0033]

[0034] where

[0035]

[0036] p v < 1, p v , p a and p r are unknown parameters.

[0037] Preferably, the unknown parameters p v , p a and p r have the following physical meanings:

[0038] p v represents the speed consistency strength of the malicious agent train i m . If p v is negative, the speed consistency direction is opposite. If p v = 0, the speed consistency is completely lost. If 0 < p v < 1, the speed consistency effect is partially lost;

[0039] p a represents the attraction strength to the malicious agent train i m . If p a is negative, the attraction direction is opposite. If p a = 0, the attraction completely disappears. If 0 < p a < 1, the attraction is partially weakened. If p a > 1, the attraction is enhanced;

[0040] p r represents the... to the malicious agent train i mThe repulsive force intensity, if p r is negative, the repulsive force direction is opposite, if p r = 0, the repulsive force completely disappears, if 0 < p r < 1, the repulsive force is partially weakened, if p r > 1, the repulsive force increases;

[0041] Compared with the normal controller, when p v = p a = p r = 1, the behavior of the malicious agent train is exactly the same as that of the normal agent train. The malicious agent train has a significant impact on the control of the high-speed train in the following two cases:

[0042] p v ≤ 0, p a ≤ 0, p r >> 1;

[0043] p v ≤ 0, p r ≤ 0, p a >> 1;

[0044] Both of these cases will cause the malicious agent train to be unable to maintain the desired distance from neighboring trains, resulting in the failure of the coordinated control of the high-speed train group and even potentially causing collisions between the malicious agent train and the trains in front and behind.

[0045] Preferably, the S4 includes the following steps:

[0046] For convenience, first rewrite the controller of the malicious agent train i m as:

[0047]

[0048] where P = (p v , p a , p r ) T is a vector of unknown parameters, and

[0049]

[0050] To track the unknown parameters, apply a first-order low-pass filter to and C im :

[0051]

[0052] where a is a scalar filter gain, a > 0, is the filtered is the filtered and Then there is:

[0053]

[0054] Define as the estimated value of p, The adaptive update law of

[0055]

[0056] is as follows: where, Γ p is a positive definite gain matrix.

[0057] Preferably, the controller of the train adjacent to the malicious agent is as follows:

[0058] For the agent Its controller is:

[0059]

[0060] where, k v 、k x are constants, k v > 1, k x > 1, represents the expected displacement difference between train j and train r, ρ jr is a positive constant;

[0061] The non - negative potential function satisfies the following properties:

[0062] Obtains a unique minimum value, and when at this time,

[0063] When |x jr | = d or |x jr | = D,

[0064] Through the potential function make the adjacent train j of the malicious agent train i m and the malicious agent train i m maintain a specified expected value At this distance, the attractive force and repulsive force in the malicious agent controller reach equilibrium. That is to say, no matter how the malicious agent train changes the control parameters, it will not be able to play a role because it is in an equilibrium state, and then the malicious agent train still maintains a uniform speed in the train formation.

[0065] Preferably, the controller of the train in the train group that is not adjacent to the malicious agent is as follows:

[0066] For the agent Construct a distributed adaptive controller as follows:

[0067]

[0068] where sgn(·) represents the sign function, and α kr is a varying gain with an initial value of α kr (0)≥0, and β kr 、 are positive constants, and β kr =β rk .

[0069] Advantages of the present invention:

[0070] (1) Through the identification and suppression mechanism of malicious agents, the present invention can effectively suppress the destructive impact of malicious agents on the train formation when they deliberately interfere with the system, maintain the normal coordinated operation of the trains, improve the robustness of the system, broaden the application scenarios of the intelligent train system in complex environments, and greatly improve the safety and reliability of train group control.

[0071] (2) The present invention improves the update rate of the train adaptive controller, enabling it to respond more quickly to changes in train speed. By optimizing the dynamic adjustment mechanism of the controller, the speed tracking accuracy between trains has been significantly improved, achieving smoother synchronous operation of the trains. Compared with traditional control methods, this improvement can more accurately maintain the speed consistency between trains, thereby improving the operation efficiency and overall coordination ability of the trains.

[0072] (3) The present invention introduces an artificial potential function to control the relative distance between trains. By designing reasonable attractive and repulsive potential functions, the safety of trains during operation is ensured, enabling trains to effectively avoid collision risks while maintaining a tight formation. Even at high speeds, the distance between trains can be ensured to vary within a safe range, thus guaranteeing the stability of the train system and enhancing the safety of the system. Description of the drawings

[0073] Figure 1 is a schematic flow diagram of the cooperative operation control method for a high-speed train group with malicious agents according to an embodiment of the present invention;

[0074] Figure 2 is a schematic diagram of the train communication topology and layering according to an embodiment of the present invention;

[0075] Figure 3 is a schematic diagram of the speed and speed error curves of each train according to an embodiment of the present invention;

[0076] Figure 4Schematic diagram of the absolute value curve of the distances between adjacent trains in the embodiments of the present invention;

[0077] Figure 5 Schematic diagram of the control input curves of the trains in the embodiments of the present invention. Detailed implementation manners

[0078] To make the objectives, technical solutions and advantages of the present application more clear and understandable, the following takes examples with reference to the accompanying drawings and further elaborates on the present application in detail.

[0079] An embodiment of the present application discloses a cooperative operation control method for a high-speed train group containing malicious agents, and its process is as Figure 1 shown, including the following steps:

[0080] S1. According to the basic running resistance and external disturbances suffered during the train operation, respectively establish the dynamic models of the trains in the train group:

[0081]

[0082] where x i (t) represents the displacement of the i-th train at time t, v i (t) represents the speed of the i-th train at time t, m i is the mass of the i-th train, u i (y) is the control force of the i-th train at time y, is a coefficient obtained through wind tunnel tests, f ir is the grade resistance of the i-th train, f ic is the curve resistance of the i-th train, f it is the tunnel resistance of the i-th train. It is assumed that the operation boundary restricts the speed of each train, satisfying v i (t) ≤ v max , v max is the boundary of the train speed.

[0083] The objective of train cooperative control is to drive the multi-vehicle system (MHSTs) to a unified state and ensure that a given safety distance is maintained, that is: where x ij = x i - x j represents the distance difference between train i and train j, represents the set composed of all trains that can communicate with train i, which is also called a neighbor in the multi-agent system, and D is the maximum allowable distance between adjacent trains.

[0084] S2. To achieve the control objective, based on the dynamic model obtained in S1, construct the following cooperative control law including a potential function:

[0085]

[0086] Among them, represents the sum of the resistances acting on the train, V ij represents the potential function, represents the gradient of the potential function with respect to x i ;

[0087] In equation (2), the first term m i f i is used to counteract the resistance encountered by high-speed trains (HSTs), the second term is used to align the speed of the multi-train system with the speed of the i-th train, and the third term corresponds to the gradient of the potential function V ij , and the potential function V ij maintains the geometric configuration to prevent collisions and ensure cohesion within the group:

[0088]

[0089] where Z represents a positive constant, d ≤ |x ij | ≤ D, and d is the minimum safe headway;

[0090] The potential function V ij has the following properties:

[0091]

[0092] Among them, the potential function V ij can be expressed as the sum of two components: V aij is the attractive potential between agent i and agent j, and V rij is the repulsive potential between agent i and agent j. When |x ij | = ρ, V ij reaches its minimum value. At the unique distance ρ, the condition is satisfied:

[0093] To ensure that the control input u is large enough when |x ij | reaches the critical values d and D, then:

[0094]

[0095] Among them, N represents the number of elements contained in the set .

[0096] S3. Model the malicious agent for the possible impacts it may cause in train cooperative control, i.e., collisions, separations, or escapes within the train group.

[0097] Define as a malicious agent train that may deliberately manipulate the controller parameters, and its controller expression is:

[0098]

[0099] where

[0100]

[0101] here \(p\) v <1, \(p\) v , \(p\) a and \(p\) r are unknown parameters with the following physical meanings:

[0102] \(p\) v represents the speed consistency strength of the malicious agent train \(i\) m . If \(p\) v is negative, the speed consistency direction is opposite. If \(p\) v = 0, the speed consistency is completely lost. If \(0 < p\) v <1, the speed consistency effect is partially lost;

[0103] \(p\) a represents the attraction strength for the malicious agent train \(i\) m . If \(p\) a is negative, the attraction direction is opposite. If \(p\) a = 0, the attraction completely disappears. If \(0 < p\) a <1, the attraction is partially weakened. If \(p\) a >1, the attraction is enhanced;

[0104] \(p\) r represents the repulsion strength for the malicious agent train \(i\) m . If \(p\) r is negative, the repulsion direction is opposite. If \(p\) r = 0, the repulsion completely disappears. If \(0 < p\) r <1, the repulsion is partially weakened. If \(p\) r >1, the repulsion is enhanced;

[0105] Compared with the normal controller, when \(p\) v = \(p\) a = \(p\) r = 1, the behavior of the malicious agent train is exactly the same as that of the normal agent train. The malicious agent train has a significant impact on the control of high-speed trains in the following two cases:

[0106] p v ≤0, p a ≤0, p r >> 1;

[0107] p v ≤0, p r ≤0, p a >> 1;

[0108] Both of these situations will cause the malicious agent train to be unable to maintain the desired distance from neighboring trains, resulting in the failure of the coordinated control of the high-speed train group and even potentially causing collisions between the malicious agent train and the trains in front and behind.

[0109] S4. For the type of malicious agent described in S3, an adaptive control algorithm and a low-pass filter are used to estimate the unknown control parameters contained in the malicious agent in order to adjust the control strategy in real time.

[0110] For convenience, first rewrite the controller of the malicious agent train i m as:

[0111]

[0112] where P = (p v , p a , p r ) T is the vector of unknown parameters, and

[0113]

[0114] In order to track the unknown parameters, for and C im apply a first-order low-pass filter:

[0115]

[0116] where a is the scalar filter gain, a > 0, is the filtered is the filtered and Then there is:

[0117]

[0118] Define as the estimated value of p, The adaptive update law of

[0119]

[0120] where Γ pis a positive definite gain matrix.

[0121] S5. Stratify the trains according to whether the trains in the train group are adjacent to the malicious agent train, and construct their controllers respectively. As Figure 2 shown, where the first layer is the malicious agent train, the second layer is the trains adjacent to the malicious agent train, and the third layer is the trains in the train group that are not adjacent to the malicious agent. For convenience, define and to represent the sets of trains in the first, second, and third layers respectively.

[0122] S6. Construct the controller for the trains adjacent to the malicious agent. Its purpose is to curb the destructive behavior that the malicious agent may cause by adjusting the distance and speed between the malicious agent train and the adjacent trains.

[0123] For the agent its controller is:

[0124]

[0125] where k v , k x are constants, k v > 1, k x > 1, represents the expected displacement difference between train j and train r, ρ jr is a positive constant.

[0126] The non - negative potential function satisfies the following properties:

[0127] obtains a unique minimum value, and when it is,

[0128] When |x jr | = d or |x jr | = D,

[0129] Through the potential function make the adjacent train j of the malicious agent train i m and the malicious agent train i m maintain a specified expected value At this distance, the attractive force and repulsive force in the malicious agent controller reach equilibrium. That is to say, no matter how the malicious agent train changes the control parameters, it will not be able to play a role because it is in an equilibrium state, and thus the malicious agent train still maintains a uniform speed in the train fleet.

[0130] S7. Construct the controllers of the trains in the train formation that are not adjacent to the malicious agent. These trains do not directly participate in curbing the behavior of the malicious agent train. Therefore, adaptive control is adopted to ensure the normal coordinated operation of the train formation.

[0131] For the agent Construct a distributed adaptive controller as:

[0132]

[0133] where sgn(·) represents the sign function, and α kr is a varying gain, whose initial value is α kr (0)≥0, and β kr , are positive constants, and β kr =β rk .

[0134] After completing the above steps, verify the above multi-train cooperative control algorithm through the MATLAB simulation program. And load the designed multi-train cooperative control algorithm into the ATO on-vehicle equipment, so as to realize the cooperative operation control of the high-speed train group that can resist the influence of malicious agents.

[0135] In a specific embodiment, verify the method for cooperative operation control of a high-speed train group with malicious agents proposed in this application. Figure 3 Shows the speed of each train and its corresponding speed error curve. The abscissa is time, and the ordinates are the speed and speed error of each train respectively. From Figure 3 it can be seen that the speed errors of all trains quickly converge to zero, indicating that under the action of the cooperative control strategy of this application, the speeds of each train have successfully reached the predetermined synchronization target. The rapid convergence of the speed error shows that the designed control method can effectively eliminate the errors caused by the initial speed difference or external disturbances, and realizes the precise synchronization between the train groups.

[0136] Figure 4 Shows the change of the absolute value of the distance between adjacent trains over time. The abscissa is time, and the ordinates are the distances between each train respectively. The curve shows that under the action of the control strategy, although there are certain changes in the relative speed between the trains, the distances between each train always remain within the safe range and are greater than the minimum safe distance. This result verifies that the control method proposed in this application can effectively prevent collisions or excessive closeness between trains, ensuring the safety of the system.

[0137] Figure 5It shows the variation of the control input (i.e., acceleration or braking force) of each train over time. In the figure, the abscissa is time and the ordinate is the control input of each train. It can be seen that as time goes by, the control input gradually tends to be stable and finally equals the resistance suffered by the train running, which is manifested as the acceleration approaching zero. This indicates that after the system reaches the stable state, each train no longer needs to accelerate or decelerate further, but runs at a constant speed.

[0138] The above has shown and described the basic principle, main features and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification only illustrates the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A cooperative operation control method for a high-speed train group containing malicious agents, characterized in that It includes the following steps: S1. Establish the dynamic models of each train in the train group respectively according to the basic running resistance and external disturbances suffered during the train operation: Among them, x i (t) represents the displacement of the i-th train at time t, v i (t) represents the speed of the i-th train at time t, m i is the mass of the i-th train, u i (t) is the control force of the i-th train at time t, is the coefficient obtained through wind tunnel tests, f ir is the grade resistance of the i-th train, f ic is the curve resistance of the i-th train, f it is the tunnel resistance of the i-th train. Assuming that the operating boundary restricts the speed of each train, satisfying v i (t) ≤ v max , v max is the boundary of the train speed; The goal of train collaborative control is to drive the multi-train system to a unified state and ensure that a given safety distance is maintained, i.e.: where x ij = x i - x j represents the distance difference between train i and train j, represents the set of all trains that can communicate with train i, represents the set of all trains, and D is the maximum allowable distance between adjacent trains; S2. Based on the dynamic models obtained in S1, construct a cooperative control law including a potential function: Among them, represents the sum of the resistances acting on the train, V ij represents the potential function, represents the gradient of the potential function with respect to x i ; The first term in Equation (2) is used to counteract the resistance encountered by the high-speed train, the second term is used to align the speed of the multi-train system with the speed of the i-th train, and the third term corresponds to the gradient of the potential function V ij The potential function V ij maintains the geometric configuration to prevent collisions and ensure cohesion within the group: where Z represents a positive constant, d ≤ |x ij | ≤ D, d is the minimum safe headway distance, S3. Model the malicious agent for the possible impacts caused by the malicious agent in the train cooperative control; it includes the following steps: Definition Represents a malicious agent train that may deliberately manipulate controller parameters. The controller expression of the malicious agent train is as follows: Wherein, p v <1, p v 、p a and p r is an unknown parameter; p v Denotes malicious agent train i m The speed consistency strength, p a Represents the malicious agent train i m The strength of attraction, p r Represents the malicious agent train i m The strength of the repulsive force; S4. Adopt an adaptive control algorithm and a low-pass filter to estimate the unknown control parameters contained in the malicious agent so as to adjust the control strategy in real time; it includes the following steps: Rewrite the controller of malicious agent train i m as follows: where P = (p v , p a , p r ) T is a vector of unknown parameters, and To track the unknown parameters, for and C im apply a first-order low-pass filter: where a is a scalar filtering gain, a > 0, is the filtered is the filtered and then there is: Definition is the estimated value of p, The adaptive update law of is as follows: where Γ p is a positive definite gain matrix; S5. Stratify the trains according to whether the trains in the train group are adjacent to the malicious agent train, where the first layer is the malicious agent train, the second layer is the trains adjacent to the malicious agent train, and the third layer is the trains in the train group that are not adjacent to the malicious agent: S6. Construct the controller of the trains adjacent to the malicious agent, and contain the destructive behavior that may be caused by the malicious agent by adjusting the distance and speed between the malicious agent train and the adjacent trains: S7. Construct the controller of the trains in the train group that are not adjacent to the malicious agent, and adopt adaptive control to ensure the normal cooperative operation of the train group.

2. The collaborative operation control method for high-speed train groups with malicious agents according to claim 1, characterized in that The potential function V ij has the following properties: Among them, The potential function V ij can be expressed as the sum of two components: V aij is the attractive potential between agent i and agent j, and V rij is the repulsive potential between agent i and agent j; when |x ij | = ρ, V ij reaches the minimum value, and at the unique distance ρ, the condition is satisfied: To ensure that when |x ij | reaches the critical values d and D, the control input u is large enough, we have: Among them, N represents the number of elements contained in the set.

3. The collaborative operation control method for high-speed train groups containing malicious agents according to claim 1, characterized in that The unknown parameter p v , p a and p r have the following physical meanings: If p v is negative, the velocity consistency is in the opposite direction. If p v = 0, the velocity consistency is completely lost. If 0 < p v < 1, the velocity consistency effect is partially lost; If p a is negative, the direction of the attractive force is opposite. If p a = 0, the attractive force completely disappears. If 0 < p a < 1, the attractive force is partially weakened. If p a > 1, the attractive force is enhanced; If p r is negative, the direction of the repulsive force is opposite. If p r = 0, the repulsive force completely disappears. If 0 < p r < 1, the repulsive force is partially weakened. If p r > 1, the repulsive force increases; When p v = p a = p r = 1, the behavior of the malicious agent train is exactly the same as that of the normal agent train. The malicious agent train has a significant impact on the control of the high-speed train in the following two cases: p v ≤0, p a ≤0, p r >> 1; p v ≤0, p r ≤0, p a >> 1; Both of these situations will cause the malicious agent train to be unable to maintain the desired distance from the adjacent trains, thus causing the coordinated control of the high-speed train group to fail and even possibly causing the malicious agent train to collide with the trains in front and behind.

4. The collaborative operation control method for high-speed train groups with malicious agents according to claim 1, characterized in that The controller of the trains adjacent to the malicious agent is as follows: For the agent Its controller is: where k v and k x are constants, k v > 1, k x > 1, represents the difference in the expected displacements between train j and train r, ρ jr is a positive constant; Non-negative potential function Satisfies the following properties: obtains a unique minimum value, and when at this time When |x jr | = d or |x jr | = D, Through the potential function Make the adjacent vehicle j of the malicious agent train i m and the malicious agent train i m maintain a specified expected value At this distance, the attractive force and repulsive force in the malicious agent controller reach equilibrium.

5. The collaborative operation control method for high-speed train groups containing malicious agents according to claim 4, characterized in that The controller of the trains in the train group that are not adjacent to the malicious agent is as follows: For the agent Construct a distributed adaptive controller as follows: where sgn(·) represents the sign function, and α kr is a varying gain with its initial value α kr (0) ≥ 0, β kr and are positive constants, and β kr = β rk .

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