A method, apparatus, and computer system for fixed-time sliding mode control of vehicle queuing based on an event-triggered mechanism.

Abstract

This invention discloses a fixed-time sliding mode control method for vehicle platooning based on an event-triggered mechanism, comprising: S1, establishing longitudinal dynamic models of following and lead vehicles, and defining the spacing error between adjacent vehicles; S2, designing fixed-time integral adaptive sliding mode control, and introducing an event-triggered mechanism to obtain an event-triggered fixed-time sliding mode controller; S3, using the Lyapunov stability method to ensure the stability of the spacing error of the vehicle platoon at a fixed time, and ensuring the fixed-time stability of the vehicle platoon based on the fixed-time stability of the spacing error; S4, ensuring the fixed-time series stability of the vehicle platoon based on the fixed-time stability of the vehicle platoon. This invention also discloses a fixed-time sliding mode control device and computer system for vehicle platooning based on an event-triggered mechanism. This invention ensures the stability and series stability of the vehicle longitudinal dynamic system and provides a key path for the development of vehicle platooning control technology.

Description

Technical Field

[0001] This invention relates to the field of vehicle control technology, and in particular to a vehicle queuing fixed-time sliding mode control method, device, and computer system based on an event-triggered mechanism. Background Technology

[0002] Most existing control methods for the stability of vehicle longitudinal dynamics systems employ linear sliding mode control or nonlinear terminal sliding mode control. This means that the system state asymptotically converges to an equilibrium point or converges to an equilibrium point within a finite time. It is worth noting that although the system can stabilize within a finite time, the convergence time changes depending on the initial state. Furthermore, vehicle platooning control strategies typically assume unlimited network bandwidth. However, such ideal transmission conditions do not exist. Especially for vehicle platooning systems, each vehicle must exchange information with neighboring vehicles through the vehicle-to-everything (V2X) communication network. Without appropriate transmission mechanisms, a large amount of redundant data may occupy limited network bandwidth, leading to untimely data transmission and reception and increased computational burden on the controller. This inevitably and severely impacts the safety and stability of the vehicle platoon.

[0003] Therefore, how to effectively reduce the data transmission frequency in the vehicle platooning system and ensure the stability of the system's convergence time upper bound is independent of the initial state is a technical problem that urgently needs to be solved. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the above-mentioned background technology and provide a vehicle queuing fixed-time sliding mode control method, device and computer system based on an event-triggered mechanism, so as to ensure the stability and series stability of the vehicle longitudinal dynamics system.

[0005] This invention provides a fixed-time sliding mode control method for vehicle platoons based on an event-triggered mechanism, comprising the following steps: S1, establishing longitudinal dynamic models of the following and lead vehicles. Under a constant headway strategy, defining the spacing error between adjacent vehicles; S2, designing a fixed-time integral adaptive sliding mode control, further introducing an event-triggered mechanism to obtain an event-triggered fixed-time sliding mode controller; S3, using the Lyapunov stability method to ensure the stability of the spacing error of the vehicle platoon at a fixed time. Based on the fixed-time stability of the spacing error and some lemmas, ensuring the fixed-time stability of the vehicle platoon; S4, based on the fixed-time stability of the vehicle platoon, ensuring the fixed-time series stability of the vehicle platoon.

[0006] Furthermore, the specific process of step S1 is as follows: S11. Assuming a convoy consisting of one lead car and N follower cars is traveling on a straight road, establish a longitudinal dynamics model for the follower cars:

[0007] in, , , and They represent the first The position, external disturbances, speed, and control input of the following vehicle. Indicates vehicle mass; S12. Based on the constant headway strategy, define the spacing error between adjacent vehicles:

[0008] in, , , , These represent the spacing error, actual spacing, stationary distance, and expected distance between two adjacent vehicles, respectively.

[0009] Furthermore, the specific process of step S2 is as follows: S21. Design a fixed-time integral sliding surface to ensure spacing error. Convergence:

[0010] in, , , , , and , Based on the bidirectional communication topology, the following coupled sliding mode surface is constructed:

[0011] in ; S22, in order to make The following fixed-time adaptive sliding mode reaching law is given:

[0012] in, , , , . The switching gain in the adaptive scheme has the following form:

[0013] in , , .in addition, It can inhibit The infinite growth of the universe therefore always has an upper bound. , making ; S23. To eliminate the impact of external disturbances on the stability of the vehicle platoon, it is assumed that the external disturbances experienced by the vehicles during platooning are bounded and that there exists an unknown positive parameter. Make the following inequality hold

[0014] S24. The adaptive law for external disturbance parameters is designed as follows:

[0015] in, , , It is a positive parameter. ; In addition, estimation error and satisfy , yes The estimated value; S25. Combining the coupled sliding surface, the adaptive sliding mode reaching law, and the parameter adaptive law of external disturbances, the following fixed-time sliding mode controller is obtained. :

[0016] in,

[0017] S26. To conserve resources and reduce redundant transmissions, an event-triggered controller is introduced:

[0018] The trigger condition is selected as follows: ; in, , For the next trigger time, and .

[0019] Furthermore, the specific process of step S3 is as follows: S31. The following definition is given: For a given constant-time vehicle spacing strategy and a designed fixed-time integral sliding mode control, when the spacing error satisfies... Then the following vehicle and lead vehicle platooning system is stable within a fixed time period; S32. Given the following lemmas 1, 2, 3, 4, 5 and theorem 1: Lemma 1, specifically: For platooning systems of following vehicles and lead vehicles, if there exists , , , Make the Lyapunov function satisfy So, in the vehicle platooning system It is stable over a fixed period of time, among which ; Lemma 2, specifically: For platooning systems of following and lead vehicles, if scalar , , , and If it exists, then it can be obtained. ,in ; Therefore, the following vehicle and lead vehicle platooning system meets the requirement of fixed-time stability, and when The minimal convergence region satisfies Fixed-time convergence upper bound ; Lemma 3 is as follows: If it exists and Then there is ,in ; Lemma 4 is as follows: if Then the following inequality holds:

[0020] ; Lemma 5 is as follows: if If it is stable for a fixed time in the minimal region of convergence, then... At a fixed time A minimal neighborhood that converges to zero. in ; Theorem 1, specifically: Considering the following and lead vehicle platooning system, coupled sliding surface and event-triggered fixed-time integral sliding mode controller, spacing error Can be done at a fixed time A minimal neighborhood that converges to zero, where , As given in Lemma 5, ; S33. Based on the proposed longitudinal dynamics system of vehicle platooning, establish the Lyapunov function, and use the inequality scaling technique and fixed-time stability theory to ensure that the vehicle platoon is stable at a fixed time.

[0021] Furthermore, the specific process of step S32 is as follows: S321. Construct the Lyapunov function for spacing error:

[0022] S322, regarding the Lyapunov function Differentiate, and by Lemma 3, we get

[0023] in , and .

[0024] S323, By means of Lemma 2, when , In the minimal convergence region It is stable over a fixed period of time, among which

[0025] S324, according to Spacing error can be obtained The convergence time for a fixed-time stable condition is .

[0026] Furthermore, the specific process of step S33 is as follows: S331. Construct a Lyapunov function:

[0027] S332, regarding the Lyapunov function Taking the derivative and combining it with Lemmas 3 and 4, we can obtain...

[0028] in , , , ,

[0029] S333, According to Lemma 2 In the minimal convergence region It is stable over a fixed period of time, among which

[0030] S334, according to It can be seen that the convergence time of the system at a fixed time is ; S335. According to Lemma 5, a total fixed time can be obtained. Therefore, the vehicle queue is at a fixed time. It is stable.

[0031] Furthermore, the specific process of step S4 is as follows: S41. Theorem 2 is given, specifically: Considering a platooning system of following and lead vehicles, coupled with a sliding surface and an event-triggered fixed-time integral sliding controller, if... Then the entire longitudinal vehicle queue is stable; S42. According to Theorem 1, for a fixed-time integral sliding surface... and coupling sliding surface We perform a case-by-case discussion, and then use proof by contradiction and Laplace transform to obtain the results. .

[0032] Furthermore, the specific process of step S42 is as follows: S421: According to Theorem 1, the coupled sliding surface can be expressed as...

[0033] in: , ; S422: Yes , and , By classifying and discussing, we can obtain...

[0034] because It is not infinite. There must exist one , making

[0035] in ; S423: respectively for , Discussion yields Then, by proof by contradiction, we obtain: ; S424: Yes Using the Laplace transform, we can obtain ,Right now Therefore, it is necessary to ensure the stability of the fixed time series of the vehicle queue.

[0036] The present invention also provides a vehicle queue fixed-time sliding mode control device based on an event-triggered mechanism, which has a computer program that can execute a vehicle queue fixed-time sliding mode control method based on an event-triggered mechanism.

[0037] The present invention also provides a computer system having a processor and a memory, wherein the processor is capable of processing a computer program stored in the memory, the computer program being capable of executing a vehicle queue fixed-time sliding mode control method based on an event-triggered mechanism.

[0038] The present invention provides a vehicle queuing fixed-time sliding mode control method, apparatus, and computer system based on an event-triggered mechanism, which has the following beneficial effects: 1. The present invention provides a fixed-time sliding mode control method for vehicle queuing based on an event-triggered mechanism, which ensures the stability of the vehicle longitudinal dynamics system through Lyapunov stability theory; considering that the upper bound of the convergence time of the fixed time is independent of the initial state of the system, a fixed-time integral terminal sliding mode is constructed; furthermore, in order to solve the chattering problem caused by discontinuous control, an adaptive law and a continuous hyperbolic tangent function are introduced. 2. The present invention uses a vehicle queue fixed-time sliding mode control device based on an event-triggered mechanism, which can effectively reduce the update frequency of the controller, thereby reducing the consumption of communication resources.

[0039] 3. This invention ensures the fixed-time stability and string stability of the vehicle queue by using the Lyapunov function method, fixed-time and sliding mode control theory. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the overall process of Embodiment 1 of the vehicle queue fixed-time sliding mode control method based on event triggering mechanism of the present invention; Figure 2 This is a schematic diagram of the position and speed curves of the vehicle queue in Embodiment 2 of the vehicle queue fixed-time sliding mode control method based on the event triggering mechanism of the present invention; Figure 3 This is a schematic diagram of the actual spacing and spacing error of the vehicle queue in Embodiment 2 of the vehicle queue fixed-time sliding mode control method based on the event triggering mechanism of the present invention; Figure 4 This is a schematic diagram of the control input and fixed-time integral sliding mode curves of the vehicle queue in Embodiment 2 of the vehicle queue fixed-time sliding mode control method based on the event triggering mechanism of the present invention. Figure 5This is a schematic diagram of event triggering in the vehicle queue in Embodiment 2 of the vehicle queue fixed-time sliding mode control method based on event triggering mechanism of the present invention; Figure 6 This is a schematic diagram of the architecture of the vehicle queue fixed-time sliding mode control device based on the event triggering mechanism of the present invention; Figure 7 This is a schematic diagram of the architecture of the computer system of the present invention. Detailed Implementation

[0041] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments, but these embodiments should not be construed as limiting the present invention.

[0042] The flowchart of the fixed-time sliding mode control method for vehicle queuing based on the event-triggered mechanism of this invention is as follows: Figure 1 As shown. Based on the constant headway strategy, the distance error between adjacent vehicles is defined. A coupled sliding surface is constructed by combining an integral sliding surface with a bidirectional communication topology. A fixed-time adaptive sliding mode merging law is designed to reduce chattering. Furthermore, an event-triggered mechanism is introduced to reduce the controller update frequency, ultimately forming a fixed-time convergent sliding mode control closed-loop system. Embodiments of this invention include the following steps: Example 1 See Figure 1 The embodiments of the present invention include the following steps: S1. Establish longitudinal dynamics models for the following and leading vehicles. Under a constant headway strategy, define the spacing error between adjacent vehicles.

[0043] S11. Assuming a convoy consisting of one lead car and N follower cars is traveling on a straight road, establish a longitudinal dynamics model for the follower cars:

[0044] in , , and They represent the first The position, external disturbances, speed, and control input of the following vehicle. Indicates vehicle mass.

[0045] S12. Based on the constant headway strategy, define the spacing error between adjacent vehicles:

[0046] in , , , These represent the spacing error, actual spacing, stationary distance, and expected distance between two adjacent vehicles, respectively.

[0047] S2. Design a fixed-time integral adaptive sliding mode control. Further, introduce an event-triggered mechanism to obtain an event-triggered fixed-time sliding mode controller.

[0048] S21. Design a fixed-time integral sliding surface to ensure spacing error. Convergence:

[0049] in , , , , and .

[0050] Based on the bidirectional communication topology, the following coupled sliding mode surface is constructed:

[0051] in .

[0052] S22, in order to make The following fixed-time adaptive sliding mode reaching law is given:

[0053] in , , , . The switching gain in the adaptive scheme has the following form:

[0054] in , , .in addition, It can inhibit The infinite growth of the universe therefore always has an upper bound. , making .

[0055] S23. To eliminate the impact of external disturbances on the stability of the vehicle platoon, it is assumed that the external disturbances experienced by the vehicles during platooning are bounded and that there exists an unknown positive parameter. Make the following inequality hold .

[0056] S24. The adaptive law for external disturbance parameters is designed as follows:

[0057] in , , It is a positive parameter. In addition, estimation error and satisfy , yes The estimated value.

[0058] S25. Combining the coupled sliding surface, the adaptive sliding mode reaching law, and the parameter adaptive law of external disturbances, the following fixed-time sliding mode controller is obtained. :

[0059] in

[0060] S26. To conserve resources and reduce redundant transmissions, an event-triggered controller is introduced:

[0061] The trigger condition is selected as follows:

[0062] in , For the next trigger time, and .

[0063] S3. Using the Lyapunov stability method, ensure the stability of the vehicle queue spacing error over a fixed time. Based on the fixed-time stability of the spacing error and some lemmas, ensure the fixed-time stability of the vehicle queue.

[0064] S31. The following definition is given: For a given constant-time vehicle spacing strategy and a designed fixed-time integral sliding mode control, when the spacing error satisfies... Then the following vehicle and lead vehicle platooning system is stable within a fixed time period.

[0065] S32. Given the following lemmas 1, 2, 3, 4, 5 and theorem 1: Lemma 1, specifically: For platooning systems of following vehicles and lead vehicles, if there exists , , , Make the Lyapunov function satisfy So, in the vehicle platooning system It is stable over a fixed period of time, among which .

[0066] Lemma 2, specifically: For platooning systems of following and lead vehicles, if scalar , , , and If it exists, then it can be obtained. ,in Therefore, the following and lead vehicle platooning system meets the requirement of fixed-time stability, and when... The minimal convergence region satisfies Fixed-time convergence upper bound .

[0067] Lemma 3 is as follows: If it exists and Then there is ,in .

[0068] Lemma 4 is as follows: if Then the following inequality holds:

[0069]

[0070] Lemma 5 is as follows: if If it is stable for a fixed time in the minimal region of convergence, then... At a fixed time A minimal neighborhood that converges to zero. in .

[0071] Theorem 1, specifically: Considering the following and lead vehicle platooning system, coupled sliding surface and event-triggered fixed-time integral sliding mode controller, spacing error Can be done at a fixed time A minimal neighborhood that converges to zero, where , As given in Lemma 5, .

[0072] Furthermore, in step S32, the specific steps are as follows: S321. Construct the Lyapunov function for spacing error:

[0073] S322, regarding the Lyapunov function Differentiate, and by Lemma 3, we get

[0074] in , and .

[0075] S323, By means of Lemma 2, when , In the minimal convergence region It is stable over a fixed period of time, among which

[0076] S324, according to Spacing error can be obtained The convergence time for a fixed-time stable condition is .

[0077] S33. Based on the proposed longitudinal dynamics system of vehicle platooning, establish the Lyapunov function, and use the inequality scaling technique and fixed-time stability theory to ensure that the vehicle platoon is stable at a fixed time.

[0078] Furthermore, in step S33, the specific steps are as follows: S331. Construct a Lyapunov function:

[0079] S332, regarding the Lyapunov function Taking the derivative and combining it with Lemmas 3 and 4, we can obtain...

[0080] in , , , ,

[0081] S333, According to Lemma 2 In the minimal convergence region It is stable over a fixed period of time, among which

[0082] S334, according to It can be seen that the convergence time of the system at a fixed time is .

[0083] S335. According to Lemma 5, a total fixed time can be obtained. Therefore, the vehicle queue is at a fixed time. It is stable.

[0084] S4. Based on the fixed-time stability of the vehicle queue, ensure the stability of the fixed-time sequence of the vehicle queue.

[0085] S41. Theorem 2 is given, specifically: Considering a platooning system of following and lead vehicles, coupled with a sliding surface and an event-triggered fixed-time integral sliding controller, if... If so, the entire longitudinal vehicle queue is stable.

[0086] S42. According to Theorem 1, for a fixed-time integral sliding surface... and coupling sliding surface We perform a case-by-case discussion, and then use proof by contradiction and Laplace transform to obtain the results. .

[0087] Furthermore, in step S42, the specific steps are as follows: S421. According to Theorem 1, the coupled sliding surface can be expressed as:

[0088] in: , .

[0089] S422, to , and , By classifying and discussing, we can obtain...

[0090] because It is not infinite. There must exist one , making

[0091] in .

[0092] S423, respectively for , Discussion yields Then, by proof by contradiction, we obtain... .

[0093] S424, Yes Using the Laplace transform, we can obtain ,Right now Therefore, it is necessary to ensure the stability of the fixed time series of the vehicle queue.

[0094] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this application.

[0095] Example 2 This embodiment is basically the same as Embodiment 1, except that: See Figures 2 to 5 In conjunction with MATLAB simulation experiments, the technical features of the embodiments of the present invention will be described in further detail and in a complete manner to verify the effectiveness of the design method proposed in the present invention.

[0096] This section provides a numerical simulation to verify the feasibility of an event-triggered fixed-time integral sliding strategy. Let... One vehicle is a follower, and one vehicle is the leader. The vehicle's mass is [missing information]. ,in The initial positions and speeds of the leader and followers are: , , , The stationary distance is Other parameters are , , , , , , , , , , , , .

[0097] Depend on Figure 2 It is evident that the vehicle positions do not intersect or overlap, indicating no collisions within the convoy and ensuring vehicle safety during operation. From Figure 2 In (b), the speed curve is relatively flat, which indicates that passenger comfort is not affected, while ensuring the performance of the system.

[0098] Depend on Figure 3 Actual vehicle distance is visible Distance error The simulation results show that... Figure 3 In (a), the distance between adjacent vehicles can achieve the expected value through a constant-time vehicle spacing strategy, and Figure 3 The vehicle distance error in (b) converges to a neighborhood close to zero within a fixed time.

[0099] like Figure 4 The event triggers the control input shown. and fixed-time integral terminal sliding mode The curve, in which the adaptive scheme and the continuous hyperbolic tangent function solve the problem. Figure 4 (a) chattering problem caused by discontinuous control, and as Figure 4 As shown in (b), It converges to a neighborhood close to zero within a fixed time.

[0100] like Figure 5 The data shows the number of triggered events, the average event interval, and the reduction in communication. It can be seen that event-triggered control can effectively reduce the update frequency of the controller, thereby reducing the consumption of communication resources.

[0101] Example 3 See Figure 6 The present invention provides a vehicle queue fixed-time sliding mode control device based on an event-triggered mechanism, comprising the following components: Longitudinal Dynamics Module: Establish longitudinal dynamics models for the following and leading vehicles, and define the spacing error between adjacent vehicles based on a constant headway strategy; Sliding mode control module: Design a fixed-time integral adaptive sliding mode control and introduce an event-triggered mechanism to obtain an event-triggered fixed-time sliding mode controller; Spacing error stabilization module: Using the Lyapunov stability method, the spacing error of the vehicle queue is guaranteed to be stable over a fixed time. Based on the fixed-time stability of the spacing error and several lemmas, the stability of the vehicle queue over a fixed time is also guaranteed. Time series stabilization module: Based on the fixed time stability of the vehicle queue, ensure the stability of the fixed time series of the vehicle queue.

[0102] Example 4 See Figure 7 The computer system of the present invention has a processor and a memory. The processor is capable of processing a computer program stored in the memory, which is capable of executing a vehicle queue fixed-time sliding mode control method based on an event-triggered mechanism.

[0103] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

[0104] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A vehicle platoon fixed-time sliding mode control method based on event-triggered mechanism, characterized in that: Includes the following steps: S1. Establish longitudinal dynamic models for the following and leading vehicles, and define the spacing error between adjacent vehicles based on a constant headway strategy; S2. Design a fixed-time integral adaptive sliding mode control and introduce an event-triggered mechanism to obtain an event-triggered fixed-time sliding mode controller; S3. Using the Lyapunov stability method, the stability of the spacing error of the vehicle queue at a fixed time is guaranteed, and based on the fixed-time stability of the spacing error and several lemmas, the stability of the vehicle queue at a fixed time is guaranteed. S4. Based on the fixed-time stability of the vehicle queue, ensure the stability of the fixed-time sequence of the vehicle queue.

2. The event-triggered mechanism based vehicle platoon fixed-time sliding mode control method according to claim 1, wherein: The specific process of step S1 is as follows: S11. Assuming a convoy consisting of one lead car and N follower cars is traveling on a straight road, establish a longitudinal dynamics model for the follower cars: ， in, , , and They represent the first The position, external disturbances, speed, and control input of the following vehicle. Indicates vehicle mass; S12. Based on the constant headway strategy, define the spacing error between adjacent vehicles: ， wherein, , , , respectively represent a spacing error, an actual spacing, a standstill distance and a desired distance between two adjacent vehicles.

3. The event-triggered mechanism based vehicle platoon fixed-time sliding mode control method according to claim 2, wherein: The specific process of step S2 is as follows: S21. Design a fixed-time integral sliding surface to ensure spacing error. Convergence: ， in, , , , , and , Based on the bidirectional communication topology, the following coupled sliding mode surface is constructed: in, , S22, in order to make The following fixed-time adaptive sliding mode reaching law is given: ， in, , , , , The switching gain in the adaptive scheme has the following form: in, , , .in addition, It can inhibit The infinite growth of the universe therefore always has an upper bound. , making ; S23. To eliminate the impact of external disturbances on the stability of the vehicle platoon, it is assumed that the external disturbances experienced by the vehicles during platooning are bounded and that there exists an unknown positive parameter. Makes the following inequality true: S24. The adaptive law for external disturbance parameters is designed as follows: ， in, , , It is a positive parameter. ;in, estimation error and satisfy , yes The estimated value; S25. Combining the coupled sliding surface, the adaptive sliding mode reaching law, and the parameter adaptive law of external disturbances, the following fixed-time sliding mode controller is obtained. : in, S26. To conserve resources and reduce redundant transmissions, an event-triggered controller is introduced: The trigger condition is selected as follows: in , For the next trigger time, and .

4. The vehicle queue fixed-time sliding mode control method based on event triggering mechanism according to claim 3, characterized in that: The specific process of step S3 is as follows: S31. The following definition is given: For a given constant-time vehicle spacing strategy and a designed fixed-time integral sliding mode control, when the spacing error satisfies... Then the following vehicle and lead vehicle platooning system is stable within a fixed time period; S32. The following lemmas 1, 2, 3, 4, 5 and theorem 1 are given; Lemma 1, specifically: For platooning systems of following vehicles and lead vehicles, if there exists , , , Make the Lyapunov function satisfy So, in the vehicle platooning system It is stable over a fixed period of time, among which ; Lemma 2, specifically: For platooning systems of following and lead vehicles, if scalar , , , and If it exists, then it can be obtained. ,in Therefore, the following vehicle and lead vehicle platooning system meets the requirement of fixed-time stability, and when The minimal convergence region satisfies Fixed-time convergence upper bound ; Lemma 3 is as follows: If it exists and Then there is ,in ; Lemma 4 is as follows: if Then the following inequality holds: ； Lemma 5 is as follows: if If it is stable for a fixed time in the minimal region of convergence, then... At a fixed time A minimal neighborhood that converges to zero. in ; Theorem 1, specifically: Considering the following and lead vehicle platooning system, coupled sliding surface and event-triggered fixed-time integral sliding mode controller, spacing error Can be done at a fixed time A minimal neighborhood that converges to zero, where , As given in Lemma 5, ; S33. Based on the proposed longitudinal dynamics system of vehicle platooning, establish the Lyapunov function, and use the inequality scaling technique and fixed-time stability theory to ensure that the vehicle platoon is stable at a fixed time.

5. The vehicle queue fixed-time sliding mode control method based on event triggering mechanism according to claim 4, characterized in that: The specific process of step S32 is as follows: S321. Construct the Lyapunov function for spacing error: ； S322, regarding the Lyapunov function Differentiate, and by Lemma 3, we get in, , and ; S323, By means of Lemma 2, when , In the minimal convergence region It is stable over a fixed period of time, among which S324, according to Spacing error can be obtained The convergence time for a fixed-time stable condition is .

6. The vehicle queue fixed-time sliding mode control method based on event triggering mechanism according to claim 5, characterized in that: The specific process of step S33 is as follows: S331. Construct a Lyapunov function: ； S332, regarding the Lyapunov function Taking the derivative and combining it with Lemmas 3 and 4, we can obtain... in , , , , S333, According to Lemma 2 In the minimal convergence region It is stable over a fixed period of time, among which, S334, according to It can be seen that the convergence time of the system at a fixed time is... ; S335. According to Lemma 5, a total fixed time can be obtained. Therefore, the vehicle queue is at a fixed time. It is stable.

7. The vehicle queue fixed-time sliding mode control method based on event triggering mechanism according to claim 6, characterized in that: The specific process of step S4 is as follows: S41. Theorem 2 is given, specifically: Considering a platooning system of following and lead vehicles, coupled with a sliding surface and an event-triggered fixed-time integral sliding controller, if... Then the entire longitudinal vehicle queue is stable; S42. According to Theorem 1, for a fixed-time integral sliding surface... and coupling sliding surface We perform a case-by-case discussion, and then use proof by contradiction and Laplace transform to obtain the results. .

8. The vehicle queue fixed-time sliding mode control method based on event triggering mechanism according to claim 7, characterized in that: The specific process of step S42 is as follows: S421. According to Theorem 1, the coupled sliding surface can be expressed as: in: , ; S422, to , and , By classifying and discussing, we can obtain... because It is not infinite. There must exist one , making ， S423, respectively for , Discussion yields Then, by proof by contradiction, we obtain... ; S424, Yes Using the Laplace transform, we can obtain... ,Right now This ensures the stability of the fixed time series of the vehicle queue.

9. A vehicle queue fixed-time sliding mode control device based on an event-triggered mechanism, comprising a computer program, characterized in that: The computer program is capable of executing the vehicle queue fixed-time sliding mode control method based on the event-triggered mechanism as described in any one of claims 1 to 8.

10. A computer system having a processor and a memory, the processor being capable of processing a computer program stored in the memory, characterized in that: The computer program is capable of executing the vehicle queue fixed-time sliding mode control method based on the event-triggered mechanism as described in any one of claims 1 to 8.

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