Cooperative operation control method for high-speed train group containing malicious agent

Abstract

The invention discloses a cooperative operation control method for a high-speed train group containing malicious agents. The cooperative operation control method comprises the following steps: S1, establishing a dynamic model of each train in the train group; s2, constructing a cooperative control law containing a potential function; s3, modeling is carried out on a malicious agent; s4, estimating unknown control parameters contained in the malicious agent by adopting a self-adaptive control algorithm and a low-pass filter; s5, the trains are layered according to whether the trains in the train group are adjacent to the malicious agent train or not; s6, constructing a controller of a train adjacent to the malicious agent; and S7, constructing a controller of a train which is not adjacent to the malicious agent in the train group. According to the method, the destructive influence of a malicious agent on the train formation can be effectively inhibited when the malicious agent deliberately disturbs the system, the normal cooperative operation of the trains is kept, the operation efficiency and the overall cooperative capability of the trains are improved, and the safety and the stability are enhanced.

Description

Technical Field

[0001] The present invention relates to the technical field of high-speed train braking operation control, and in particular to a method for controlling the coordinated operation of a high-speed train group containing malicious intelligent agents. Background Art

[0002] High-speed trains (HSTs) are becoming increasingly important in modern transportation due to their high speed, low carbon emissions, and environmental sustainability. In recent years, with the development of automatic control theory, the advancement of train positioning technology, and the continuous improvement of communication links between high-speed trains, the issue of multi-train coordinated control has attracted widespread attention. Multi-train coordinated control aims to reduce running intervals, increase running density, and improve the efficiency of high-speed railways while ensuring operational quality. Each train dynamically adjusts its speed based on communication with neighboring trains. However, trains may encounter unexpected situations and interference during operation, which may disrupt the normal operation order, leading to chain reaction delays and other problems. These situations may significantly affect railway traffic and transportation networks, ultimately causing huge economic losses.

[0003] In order to solve the potential failure problem, several 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, which assumes that all agents are healthy and rational. However, in practical scenarios, agents inevitably face safety and security challenges. Misbehavior in the group may come from three main factors: physical layer failures, network layer attacks, and abnormal or malicious decisions in the supervisory layer.

[0004] To address the control challenges posed by malicious agents, existing studies have shown that although malicious agents may convey misleading information, they still follow collective decisions, which distinguishes them from agents with truly malicious intentions. In addition, these studies assume that malicious agents can be removed while ensuring network topology connectivity. As for malicious agents in the supervision layer, some studies have proposed hybrid D-silencing methods that aim to mitigate the influence of Byzantine agents so that cooperative agents can reach consensus. However, like most related studies, this method mainly relies on excluding malicious agents. However, maintaining task integrity in the group requires avoiding the exclusion of malicious agents by safely restricting them. In addition, those exclusion methods that ignore motion dynamics are not applicable to networked agents that are subject to dynamic or geometric constraints, such as vehicle convoys, train groups, and drone swarms. Summary of the invention

[0005] In order to solve the problem that a train group can still meet cooperative control under the influence of a malicious intelligent agent, the present invention proposes a cooperative operation control method for a high-speed train group containing a malicious intelligent agent to solve the above problem.

[0006] The present application discloses a method for controlling the coordinated operation of a high-speed train group containing a malicious agent, comprising the following steps:

[0007] S1. According to the basic running resistance and external disturbances encountered by the train during operation, a dynamic model of each train in the train set is established respectively;

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

[0009] S3. Model the malicious agent based on the possible impact it may have on train cooperative control;

[0010] S4, using adaptive control algorithm and low-pass filter to estimate unknown control parameters contained in the malicious agent to adjust the control strategy in real time;

[0011] S5. According to whether the train in the train set is adjacent to the malicious agent train, the trains are layered, wherein the first layer is the malicious agent train, the second layer is the train adjacent to the malicious agent train, and the third layer is the train in the train set that is not adjacent to the malicious agent;

[0012] S6. Construct a controller for the trains adjacent to the malicious agent, and curb 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;

[0013] S7. Construct a controller for the trains in the train set that are not adjacent to the malicious agent, and use adaptive control to ensure the normal coordinated operation of the train set.

[0014] Preferably, the dynamic model of each train in the train set 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 test, f ir is the slope 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 running boundary limits the speed of each train to satisfy v i (t)≤v max , v max is the boundary of train speed;

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

[0018] represents the set of all trains that can communicate with train i, v represents the set of all trains, and D is the maximum allowed distance between adjacent trains.

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

[0020]

[0021] in, Represents the total resistance of the train, V ij represents the potential function, represents the potential function with respect to x i The gradient of

[0022] The first term in equation (2) is used to offset the resistance encountered by the high-speed train, the second term is used to align the speed of the multi-vehicle system with the speed of the i-th train, and the third term corresponds to the potential function V ij The gradient of the potential function V ij Maintain geometry configuration to place collisions and ensure cohesion within groups:

[0023]

[0024] Where Z represents a positive constant, d≤|x ij |≤D, d is the minimum safe headway;

[0025] Preferably, the potential function V ij Features include:

[0026]

[0027] in, Potential function V ij can be expressed as the sum of two components: V aij is the attraction between agent i and agent j, V rij is the repulsive potential between agent i and agent j; when |x ij |=ρ,V ij To reach the minimum value, at the unique distance ρ, the condition is satisfied:

[0028] To ensure that when |x ij When the critical values ​​d and D are reached, the control input u is large enough, then:

[0029]

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

[0031] Preferably, the S3 steps include:

[0032] definition represents a malicious agent train, which may intentionally manipulate controller parameters. The controller expression of the malicious agent train is:

[0033]

[0034] in,

[0035]

[0036] p v <1, p v 、p a and p r is an unknown parameter.

[0037] Preferably, the unknown parameter p v 、p a and p r It has the following physical meanings:

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

[0039] p a Represents the malicious agent train i m The strength of attraction, if p a is negative, the attraction direction is opposite, if p a =0, the attraction disappears completely, if 0 <p a <1, the attraction is partially weakened, if p a >1, attractiveness increases;

[0040] p r Represents the malicious agent train i mThe repulsive force strength, if p r is negative, the repulsive force is in the opposite direction. r = 0, the repulsive force disappears completely. <p r <1, the repulsive force is partially weakened, if p r >1, repulsion is enhanced;

[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 situations:

[0042] p v ≤0, p a ≤0, p r >>1;

[0043] p v ≤0, p r ≤0, p a >>1;

[0044] Both situations will cause the malicious intelligent train to be unable to maintain the desired distance from the adjacent trains, thereby making the coordinated control of the high-speed train group invalid, and may even cause the malicious intelligent train to collide with the trains in front and behind.

[0045] Preferably, S4 comprises the following steps:

[0046] For convenience, firstly, the malicious agent train i m The controller is rewritten as:

[0047]

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

[0049]

[0050] In order to track unknown parameters, and C im Apply a first-order low-pass filter:

[0051]

[0052] Where a is the scalar filter gain, a>0, After filtering After filtering and Then we have:

[0053]

[0054] definition is the estimated value of p, The adaptive update law is as follows:

[0055]

[0056] Among them, 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 intelligent agent Its controller is:

[0059]

[0060] Among them, k v , k x is a constant, k v >1,k x >1, represents the difference in expected displacement between train j and train r, ρ jr is a positive constant;

[0061] Non-negative potential function Satisfy the following properties:

[0062] Get the only minimum value, and when hour,

[0063] When |x jr |=dor|x jr |=D,

[0064] Through the potential function Make the malicious agent train i m The neighboring car j and the malicious agent train i m Maintain to a specified expected value At this distance, the attraction and repulsion in the malicious agent controller are balanced. That is, no matter how the malicious agent train changes the control parameters, it will not work because it is in a balanced state, so that the malicious agent train still maintains a constant speed in the convoy.

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

[0066] For the intelligent agent Constructing a distributed adaptive controller is:

[0067]

[0068] Among them, sgn(·) represents the sign function, α kr is a variable gain, whose initial value is α kr (0)≥0, β kr , is a positive constant, and β kr =β rk .

[0069] Beneficial effects of the present invention:

[0070] (1) Through the identification and suppression mechanism of malicious intelligent agents, the present invention can effectively suppress the destructive impact of malicious intelligent 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 so that it can respond more quickly to changes in train speed. By optimizing the dynamic adjustment mechanism of the controller, the speed tracking accuracy between trains is significantly improved, and smoother synchronous operation of trains is achieved. Compared with traditional control methods, this improvement can more accurately maintain speed consistency between trains, thereby improving the operating 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 attraction and repulsion potential functions, the safety of trains during operation is ensured, so that trains can effectively avoid collision risks while maintaining a tight formation. Even when traveling at high speeds, the distance between trains can be ensured to change within a safe range, thereby ensuring the stability of the train system and enhancing the safety of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is a flow chart of a method for controlling the coordinated operation of a high-speed train group containing a malicious agent according to an embodiment of the present invention;

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

[0075] Figure 3 Schematic diagram of the speed and speed error curves of each train in an embodiment of the present invention;

[0076] Figure 4Schematic diagram of absolute value curves of distances between adjacent trains according to an embodiment of the present invention;

[0077] Figure 5 Schematic diagram of each train control input curve according to an embodiment of the present invention. DETAILED DESCRIPTION

[0078] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below with reference to the accompanying drawings and examples.

[0079] The present application embodiment discloses a method for controlling the coordinated operation of a high-speed train group containing a malicious agent, and the process is as follows: Figure 1 As shown, the following steps are included:

[0080] S1. According to the basic running resistance and external disturbances encountered by the train during operation, the dynamic model of each train in the train group is established respectively:

[0081]

[0082] 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 (y) is the control force of the i-th train at time y, is the coefficient obtained through wind tunnel test, f ir is the slope 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 running boundary limits the speed of each train to satisfy v i (t)≤v max , v max is the boundary of train speed.

[0083] The goal of coordinated train control is to drive the multi-car 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 difference in distance between train i and train j, represents the set of all trains that can communicate with train i, also called neighbors in the multi-agent system, and D is the maximum allowed distance between adjacent trains.

[0084] S2. In order to achieve the control target, based on the dynamic model obtained in S1, the following collaborative control law including potential function is constructed:

[0085]

[0086] in, Represents the total resistance of the train, V ij represents the potential function, represents the potential function with respect to x i The gradient of

[0087] The first term m in formula (2) i f i To counteract the drag encountered by high-speed trains (HSTs), the second The third term is used to align the speed of the multi-car system with the speed of the i-th train. Corresponding to the potential function V ij The gradient of the potential function V ij Maintain geometry configuration to place collisions and ensure cohesion within groups:

[0088]

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

[0090] Potential function V ij Features include:

[0091]

[0092] in, Potential function V ij can be expressed as the sum of two components: V aij is the attraction between agent i and agent j, V rij is the repulsive potential between agent i and agent j. ij |=ρ,V ij Reach the minimum value. Under the unique distance ρ, the condition is satisfied:

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

[0094]

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

[0096] S3. Model the malicious agent based on the possible impact it may cause in the coordinated control of the train, i.e. collision, separation or escape within the train set.

[0097] definition represents a malicious agent train that may intentionally manipulate controller parameters. Its controller expression is:

[0098]

[0099] in,

[0100]

[0101] Here p v <1, p v 、p a and p r is an unknown parameter with the following physical meaning:

[0102] p v Denotes malicious agent train i m The speed consistency strength is, if p v is negative, the direction of velocity consistency is opposite. If p v = 0, the speed consistency is completely lost. <p v <1, the speed consistency effect is partially lost;

[0103] p a Represents the malicious agent train i m The strength of attraction, if p a is negative, the attraction direction is opposite, if p a =0, the attraction disappears completely, if 0 <p a <1, the attraction is partially weakened, if p a >1, attractiveness increases;

[0104] p r Represents the malicious agent train i m The repulsive force strength, if p r is negative, the repulsive force is in the opposite direction. r = 0, the repulsive force disappears completely. <p r <1, the repulsive force is partially weakened, if p r >1, 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 the high-speed train in the following two situations:

[0106] p v ≤0, p a ≤0, p r >>1;

[0107] p v ≤0, p r ≤0, p a >>1;

[0108] Both situations will cause the malicious intelligent train to be unable to maintain the desired distance from the adjacent trains, thereby making the coordinated control of the high-speed train group invalid, and may even cause the malicious intelligent train to collide with 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 to adjust the control strategy in real time.

[0110] For convenience, firstly, the malicious agent train i m The controller is rewritten as:

[0111]

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

[0113]

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

[0115]

[0116] Where a is the scalar filter gain, a>0, After filtering After filtering and Then we have:

[0117]

[0118] definition is the estimated value of p, The adaptive update law is as follows:

[0119]

[0120] Among them, Γ pis a positive definite gain matrix.

[0121] S5. According to whether the trains in the train group are adjacent to the malicious agent train, the trains are layered and their controllers are constructed respectively, such as Figure 2 As shown in the figure, 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 set that are not adjacent to the malicious agent. For convenience, we define and represents the set of trains in the first, second, and third layers.

[0122] S6. Construct a controller for the trains adjacent to the malicious agent, the purpose of which is to curb 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.

[0123] For the intelligent agent Its controller is:

[0124]

[0125] Among them, k v , k x is a constant, k v >1,k x >1, represents the difference in expected displacement between train j and train r, ρ jr Is a normal number.

[0126] Non-negative potential function Satisfy the following properties:

[0127] Get the only minimum value, and when hour,

[0128] When |x jr |=dor|x jr |=D,

[0129] Through the potential function Make the malicious agent train i m The neighboring car j and the malicious agent train i m Maintain to a specified expected value At this distance, the attraction and repulsion in the malicious agent controller are balanced. That is, no matter how the malicious agent train changes the control parameters, it will not work because it is in a balanced state, so that the malicious agent train still maintains a constant speed in the convoy.

[0130] S7. Construct controllers for the trains in the train set that are not adjacent to the malicious agent. These trains do not directly participate in the containment of the malicious agent's train behavior, so adaptive control is used to ensure the normal coordinated operation of the train set.

[0131] For the intelligent agent Constructing a distributed adaptive controller is:

[0132]

[0133] Among them, sgn(·) represents the sign function, α kr is a variable gain, whose initial value is α kr (0)≥0, β kr , is a positive constant, and β kr =β rk .

[0134] After completing the above steps, the multi-train cooperative control algorithm is verified through the MATLAB simulation program. The designed multi-train cooperative control algorithm is loaded into the ATO on-board equipment to achieve the cooperative operation control of high-speed train groups that can resist the influence of malicious intelligent agents.

[0135] In a specific embodiment, the method for controlling the coordinated operation of a high-speed train group containing malicious intelligent agents proposed in this application is verified. Figure 3 The speed error curves of each train speed and its corresponding speed are shown, with the horizontal axis representing time and the vertical axis representing the speed and speed error of each train. Figure 3 It can be seen that the speed errors of all trains converge to zero quickly, indicating that under the action of the collaborative control strategy of this application, the speed of each train successfully reaches the predetermined synchronization target. The rapid convergence of the speed error indicates that the designed control method can effectively eliminate the error caused by the initial speed difference or external disturbance, and achieve accurate synchronization between the train groups.

[0136] Figure 4 The curve shows how the absolute value of the distance between adjacent trains changes over time, with the horizontal axis being time and the vertical axis being the distance between each train. The curve shows that under the control strategy, although the relative speed between trains varies to a certain extent, the distance between each train is always kept within a safe range and greater than the minimum safe distance. This result verifies that the control method proposed in this application can effectively prevent collisions or excessive proximity between trains, ensuring the safety of the system.

[0137] Figure 5The figure shows the change of control input (i.e. acceleration or braking force) of each train over time. The horizontal axis of the figure is time, and the vertical axis is the control input of each train. It can be seen that as time goes by, the control input gradually stabilizes and eventually equals the resistance encountered by the train, which is manifested as acceleration close to zero. This shows that after the system reaches a stable state, each train no longer needs to accelerate or decelerate further, but maintains a constant speed.

[0138] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A method for controlling the coordinated operation of a high-speed train group containing malicious agents, characterized in that: The following steps are involved: S1. According to the basic running resistance and external disturbances encountered by the train during operation, a dynamic model of each train in the train set is established respectively; S2, based on the dynamic model obtained in S1, construct a cooperative control law including potential function; S3. Model the malicious agent based on the possible impact it may have on train cooperative control; S4, using adaptive control algorithm and low-pass filter to estimate unknown control parameters contained in the malicious agent to adjust the control strategy in real time; S5. According to whether the trains in the train set are adjacent to the malicious agent train, the trains are layered, wherein the first layer is the malicious agent trains, the second layer is the trains adjacent to the malicious agent trains, and the third layer is the trains in the train set that are not adjacent to the malicious agent trains; S6. Construct a controller for the trains adjacent to the malicious agent, and curb 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 a controller for the trains in the train set that are not adjacent to the malicious agent, and use adaptive control to ensure the normal coordinated operation of the train set.

2. The method for controlling the coordinated operation of a high-speed train group containing malicious agents according to claim 1 is characterized in that: The dynamic model of each train in the train set is: 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 test, f ir is the slope resistance of the i-th train, f ic is the curve resistance of the f-th train, f it is the tunnel resistance of the i-th train, assuming that the running boundary limits the speed of each train to satisfy v i (t)≤v max , v max is the boundary of train speed; The goal of train coordinated control is to drive the multi-car system to a unified state and ensure that a given safety distance is maintained, namely: 0<|x ik | <D, where x ij =x i -x j , represents the difference in distance between train i and train j, represents the set of all trains that can communicate with train i, V represents the set of all trains, and D is the maximum allowed distance between adjacent trains.

3. The method for controlling the coordinated operation of a high-speed train group containing malicious agents according to claim 2 is characterized in that: The cooperative control law including the potential function is as follows: in, Represents the total resistance of the train, V ij represents the potential function, represents the potential function with respect to x i The gradient of The first term in equation (2) is used to offset the resistance encountered by the high-speed train, the second term is used to align the speed of the multi-vehicle system with the speed of the i-th train, and the third term corresponds to the potential function V ij The gradient of the potential function V ij Maintain geometry configuration to place collisions and ensure cohesion within groups: Where Z represents a positive constant, d≤|x ij |≤D, d is the minimum safe headway between vehicles.

4. The method for controlling the coordinated operation of a high-speed train group containing malicious agents according to claim 3 is characterized in that: The potential function V ij Features include: in, Potential function V ij can be expressed as the sum of two components: V aij is the attraction between agent i and agent j, V rij is the repulsive potential between agent i and agent j; when |x ij |=ρ,V ij To reach the minimum value, at the unique distance ρ, the condition is satisfied: To ensure that when \x ij When the critical values ​​d and D are reached, the control input u is large enough, then: in, N represents the number of elements contained in the set v.

5. The method for controlling the coordinated operation of a high-speed train group containing malicious agents according to claim 4 is characterized in that: The S3 steps are as follows: Definition m ∈v represents a malicious agent train, which may intentionally manipulate the controller parameters. The controller expression of the malicious agent train is: in, p v <1, p v 、p a and p r is an unknown parameter.

6. The method for controlling the coordinated operation of a high-speed train group containing malicious agents according to claim 5 is characterized in that: The unknown parameter p v 、p a and p r It has the following physical meanings: p v Denotes malicious agent train i m The speed consistency strength is, if p v is negative, the direction of velocity consistency is opposite. If p v = 0, the speed consistency is completely lost. <p v <1, the speed consistency effect is partially lost; p a Represents the malicious agent train i m The strength of attraction, if p a is negative, the attraction direction is opposite, if p a =0, the attraction disappears completely, if 0 <p a <1, the attraction is partially weakened, if p a >1, attractiveness increases; p r Represents the malicious agent train i m The repulsive force strength, if p r is negative, the repulsive force is in the opposite direction. r = 0, the repulsive force disappears completely. <p r <1, the repulsive force is partially weakened, if p r >1, repulsion is enhanced; 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 situations: p v ≤0,p a ≤0,p r >>1; p v ≤0,p r ≤0,p a >>1; Both situations will cause the malicious intelligent train to be unable to maintain the desired distance from the adjacent trains, thereby making the coordinated control of the high-speed train group invalid, and may even cause the malicious intelligent train to collide with the trains in front and behind.

7. The method for controlling the coordinated operation of a high-speed train group containing malicious agents according to claim 6 is characterized in that: The S4 comprises the following steps: The malicious agent train i m The controller is rewritten as: Where P = (p v ,p a ,p r ) T is a vector of unknown parameters, and In order to track unknown parameters, and C im Apply a first-order low-pass filter: Where a is the scalar filter gain, a>0, After filtering After filtering and Then we have: definition is the estimated value of p, The adaptive update law is as follows: Among them, Γ p is a positive definite gain matrix.

8. The method for controlling the coordinated operation of a high-speed train group containing malicious agents according to claim 7 is characterized in that: The controller of the train adjacent to the malicious agent is as follows: For the intelligent agent Its controller is: Among them, k v , k x is a constant, k v >1,k x >1, represents the difference in expected displacement between train j and train r, ρ jr is a positive constant; Non-negative potential function Satisfy the following properties: Get the only minimum value, and when hour, When |x jr |=dor|x jr |=D, Through the potential function Make the malicious agent train i m The neighboring car j and the malicious agent train i m Maintain to a specified expected value At this distance, the attractive and repulsive forces in the malicious agent controller are balanced.

9. The method for controlling the coordinated operation of a high-speed train group containing malicious agents according to claim 8, characterized in that: The controllers of the trains in the train set that are not adjacent to the malicious agent are as follows: For an agent k∈v f , construct a distributed adaptive controller as: Among them, sgn(·) represents the sign function, α kr is a variable gain, whose initial value is α kr (0)≥0, β kr , is a positive constant, and β kr =β rk .

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