Vehicle platoon control method and system with time-varying gain extended state observer

Abstract

The application belongs to the technical field of distributed vehicle platoon control, and provides a vehicle platoon control method and system with a time-varying gain extended state observer, which comprises establishing a vehicle dynamics model; external disturbances are estimated in real time based on the time-varying gain extended state observer, and the initial differential peak value phenomenon is effectively inhibited; the stability analysis of the observer system is discussed in different cases, and it is verified that the time-varying gain extended state observer has a more rigorous and simple stability proof process; an extended state observer for compensating external disturbances and unknown nonlinear terms of the model is designed, a virtual controller and an actual controller are constructed by using the backstepping method based on the extended state observer and the fixed-time stability theory; by designing a fast fixed-time backstepping control method, the system state converges to the expected signal in a fixed time, and the system obtains good tracking performance.

Description

Technical Field

[0001] This invention belongs to the field of distributed vehicle queue control technology, specifically relating to a fast fixed-time queue tracking control method and system for interconnected vehicles based on a time-varying gain extended state observer. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Vehicle platooning control originated from automated highway systems within the field of intelligent transportation. Throughout the development of urban transportation, it plays a crucial role in ensuring travel safety, reducing pollution emissions, and conserving energy. Therefore, it has become a key technology for transportation development, initially targeting single-vehicle systems and gradually evolving into vehicle platooning systems.

[0004] Over the past few decades, the control community has maintained a high level of enthusiasm for studying the convergence speed of various systems. Among these, finite-time stability and fixed-time stability have attracted widespread attention due to their unique fast convergence characteristics. However, due to unmodeled dynamics, unknown parameters, and external disturbances, achieving finite-time or fixed-time stability in practice is difficult. To address this, the concept of practical finite-time / fixed-time stability has been proposed. In this context, it is noteworthy that fast fixed-time queue tracking control improves convergence speed and performance. Therefore, current research focuses on accelerating convergence speed in practical engineering by constructing fast fixed-time strategies.

[0005] For vehicle platooning systems, disturbance suppression / attenuation is an unavoidable problem due to environmental influences on vehicles and interference caused by non-ideal characteristics within the vehicle system. The estimation of total disturbance obtained from an extended state observer can compensate for the controller design, reducing the impact of total disturbance on the feedback loop and significantly improving disturbance suppression, enabling the system to achieve the desired control performance under uncertain disturbances. From the perspective of its observation gain, extended state observers can be divided into linear extended state observers and nonlinear extended state observers. Nonlinear extended state observers have high estimation accuracy and fast response speed, but their application in engineering is hindered by the large number of parameters required and the complexity of stability analysis. Linear extended state observers are easy to tune and have advantages in stability analysis, but in the initial stage, due to the large deviation between the estimated initial values ​​of each state variable and the corresponding actual values, the so-called "initial differential peak" phenomenon occurs. Therefore, designing a time-varying gain extended state observer that possesses both high observation accuracy and fast response speed while effectively suppressing the "initial differential peak" phenomenon is a significant problem. Summary of the Invention

[0006] The present invention aims to overcome the shortcomings of the prior art and provide a vehicle queuing control method and system with a time-varying gain extended state observer, which has ideal transient performance, wide applicability, high observation accuracy, strong robustness, fast convergence speed when the system state is close to the equilibrium point, and can realize external disturbance estimation.

[0007] To solve the above-mentioned technical problems, the present invention is implemented as follows:

[0008] The first aspect of this invention provides a vehicle queue control method with a time-varying gain extended state observer, comprising the following steps:

[0009] (1) Establish a vehicle dynamics model under external disturbances and unknown nonlinear terms;

[0010] (2) Design a time-varying gain extended state observer to compensate for external disturbances and unknown nonlinear terms, and combine it with the output signal of the tracking differentiator to construct a virtual controller and an actual controller using the backstepping method.

[0011] (3) Distributed fast fixed-time anti-interference queue tracking control is realized in the backstepping method by using a time-varying gain extended state observer and Lyapunov stability analysis.

[0012] Furthermore, before establishing the vehicle dynamics model, the present invention also includes acquiring the state information and parameter information of each vehicle. Through information transmission between the leader vehicle and multiple follower vehicles, each follower vehicle can acquire the state information and parameter information of other vehicles in real time.

[0013] Furthermore, the state information described in this invention includes the vehicle's position information, speed information, and acceleration information.

[0014] Furthermore, the time-varying gain in the time-varying gain extended state observer of the present invention is as follows:

[0015]

[0016] Here, η0 is a constant, η(t) is a time-varying gain, and ρ is a constant controlling the growth rate of η(t). Because the estimated initial state value deviates significantly from the actual value in the initial stage, the "initial difference peak" phenomenon adversely affects the transient performance of the system. In the designed time-varying gain extended state observer, the initial value of η(t) is small, and its convergence speed can be adjusted according to different ρ values. Using different ρ values ​​controls its rate, allowing η(t) to rapidly increase from a small initial value to a large constant value η0. This avoids the peak phenomenon, thereby improving the system performance.

[0017] Furthermore, the state-space expression in the vehicle dynamics model of this invention is as follows:

[0018]

[0019] Where t represents time, x i,p ,x i,v ,x i,a This represents the measurable system state, specifically the position, velocity, and acceleration of the i-th vehicle. They are x i,p ,x i,v ,x i,a The derivative of w i U represents the time-varying input disturbance of the i-th vehicle. i (t) is the control input for the i-th vehicle. τ i >0 indicates the engine time constant of the i-th vehicle.

[0020] Furthermore, the specific method for compensating for external disturbances and unknown nonlinear terms in the time-varying gain extended state observer of the present invention is as follows:

[0021]

[0022] Among them, e i,r For observer error, To extend the state of the state observer, and They represent The derivative of τ, where p is the scaling gain, and τ is the derivative of τ. i Let u represent the engine time constant of the i-th vehicle. i λ1 and λ2 are the control inputs for the i-th vehicle, and λ1 and λ2 are positive constants. It is a continuous function, defined as follows:

[0023]

[0024] in,

[0025] Furthermore, the present invention utilizes a tracking differentiator to estimate the derivative of the virtual controller.

[0026] A second aspect of the present invention provides a vehicle queuing control system with a time-varying gain extended state observer, comprising:

[0027] The model building module is configured to: build a vehicle dynamics model;

[0028] The signal compensation module is configured as follows: a time-varying gain extended state observer designed to compensate for external interference and unknown nonlinear terms, and combined with the tracking differentiator output signal, a virtual controller and an actual controller are constructed using the backstepping method.

[0029] The control module is configured to use a piecewise function form for the time-varying gain of the extended state observer, which can precisely control the gain to adapt to different conditions, thereby improving the accuracy and flexibility of the observer and realizing distributed, fast, fixed-time anti-interference queue tracking control.

[0030] A third aspect of the present invention provides a medium having a program stored thereon, characterized in that, when the program is executed by a processor, it implements the steps in the vehicle queue control method with a time-varying gain extended state observer described above.

[0031] A fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that the processor executes the program to implement the steps in the vehicle queue control method with a time-varying gain extended state observer described above.

[0032] This invention addresses uncertain vehicle platooning systems with disturbances. Based on a time-varying gain extended state observer and fixed-time stability theory, a distributed, fast, fixed-time disturbance-resistant platooning tracking control strategy is designed. First, a time-varying gain extended state observer is designed to estimate external disturbances. This method not only has a rigorous observation error convergence stability analysis process but also mitigates the "initial differential peak" phenomenon in traditional linear extended state observation methods. Second, a fast fixed-time backstepping controller with superior performance compared to fixed-time control strategies is constructed, achieving rapid convergence within a fixed time. Finally, utilizing time-varying gain extended state observer estimation and fixed-time stability theory, a fast fixed-time control method is derived within the backstepping framework.

[0033] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0034] (1) In order to achieve vehicle system stability within a fixed time, this invention constructs a fast fixed-time backstepping controller, which outperforms the fixed-time control strategy. When the system state approaches the equilibrium point, this invention replaces the nonlinear term with a linear term to obtain a faster convergence speed.

[0035] (2) This invention proposes a time-varying gain extended state observer to improve observation accuracy and system robustness. Compared with the traditional linear extended state observer, the proposed time-varying gain extended state observer can suppress the initial peak phenomenon, thereby improving the transient performance of the system.

[0036] (3) The time-varying gain proposed in this invention adopts a piecewise function form, which can precisely control the gain to adapt to different conditions, thereby improving the accuracy and flexibility of the observer. In addition, compared with the nonlinear extended state observer, the proof process of the observer system is simpler and more rigorous.

[0037] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0038] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0039] Figure 1 This is a structural framework diagram of the vehicle queuing system of the present invention;

[0040] Figure 2 This is a flowchart illustrating the tracking control method for the first follower vehicle based on a constant spacing strategy according to the present invention.

[0041] Figure 3 This is a schematic diagram of an actual vehicle queue provided in Embodiment 1 of the present invention;

[0042] Figure 4 This is a schematic diagram of the time-varying gain variation curve of the present invention;

[0043] Figure 5 This is a schematic diagram of the distributed queue control technology for the first follower based on a fast fixed-time control strategy, as described in this invention.

[0044] Figure 6 This is a reference speed curve diagram of the vehicle leading the invention;

[0045] Figure 7 This invention provides a real-time position curve of a vehicle queue comprising one leader and three followers.

[0046] Figure 8 This invention provides a real-time speed curve of a vehicle convoy comprising one leader and three followers.

[0047] Figure 9 This invention presents a real-time spacing tracking error and speed error curve for a vehicle convoy comprising one leader and three followers.

[0048] Figure 10 This is a comparison chart of the errors between the time-varying gain extended state observer designed in this invention and the traditional linear extended state observer. Detailed Implementation

[0049] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0050] It should be noted that the following detailed description is illustrative and intended to provide further explanation of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. Without conflict, embodiments and features thereof in the invention can be combined with each other.

[0051] Example 1

[0052] like Figure 2 As shown, Embodiment 1 of the present invention provides a vehicle queue control method with a time-varying gain extended state observer, comprising the following steps:

[0053] (1) Establish a vehicle dynamics model under external disturbances and unknown nonlinear terms;

[0054] (2) Design a time-varying gain extended state observer to compensate for external disturbances and unknown nonlinear terms, and combine it with the output signal of the tracking differentiator to construct a virtual controller and an actual controller using the backstepping method.

[0055] (3) Distributed fast fixed-time anti-interference queue tracking control is realized in the backstepping method by using a time-varying gain extended state observer and Lyapunov stability analysis.

[0056] Before establishing a vehicle dynamics model, it is necessary to acquire the state and parameter information of each vehicle. Through information transmission between the leader vehicle and multiple follower vehicles, each follower vehicle can obtain the state and parameter information of other vehicles in real time. The state information includes the vehicle's position, velocity, and acceleration information.

[0057] Based on the state and parameter information of each vehicle, and considering external disturbances and unknown nonlinear terms, a vehicle dynamics model based on Newton's second law is established.

[0058] The vehicle queuing system addressed in this embodiment consists of the following components: Figure 1 As shown, the dynamic model of the i-th vehicle is transformed into a state-space expression as follows:

[0059]

[0060] Where t represents time, x i,p ,x i,v ,x i,a This represents the measurable system state, specifically the position, velocity, and acceleration of the i-th vehicle. They are x i,p ,x i,v ,x i,a The derivative of w i U represents the time-varying input disturbance of the i-th vehicle.i (t) is the control input for the i-th vehicle. τ i >0 indicates the engine time constant of the i-th vehicle.

[0061] Secondly, a simplified linearized leader system model was designed:

[0062]

[0063] Where, x 0,p ,x 0,v This represents the measurable system state, namely the leader's position and velocity. They are x 0,p ,x 0,v The derivative of .

[0064] In vehicle platoon control, system disturbances are typically caused by unknown factors such as turbulence, wind, drag, and internal influences. To achieve stable and continuous tracking control, a time-varying gain extended state observer is used to handle external disturbances, as follows:

[0065]

[0066] Among them, e i,r For observer error, To extend the state of the state observer, Hehe They represent The derivative of τ, where p is the scaling gain, and τ is the derivative of τ. i Let u represent the engine time constant of the i-th vehicle. i λ1 and λ2 are the control inputs for the i-th vehicle, and λ1 and λ2 are positive constants. It is a continuous function, and η(t) is a time-varying gain, defined as follows:

[0067]

[0068] in, It is a constant that satisfies η0 is a constant, and ρ is a constant that controls the growth rate of η(t).

[0069] For a vehicle queuing control system, the spacing error based on a constant spacing strategy can be denoted as:

[0070] e i,p (t)=x i-1,p (t)-x i,p (t)-l i-1 (t)-d i (t)

[0071] Among them, z i,pThe tracking error for the i-th vehicle after transformation is used to construct a new error transformation:

[0072] z i,p =e i,p

[0073] z i,v =x i,v -α i,p

[0074] z i,a =x i,a -α i,v

[0075] To estimate the virtual controller α i,p ,α i,v Given the derivative of , design the following tracking differentiator:

[0076] Since sigmoid functions are monotonic, bounded, and symmetric, they are suitable as tracking functions for tracking differentiators. While maintaining the symmetric property, an improved sigmoid function is designed using amplitude and exponential factors, as follows:

[0077] Sig(∈;d,f,g)=sign(∈)·∣d[(1+e -f ) -1 -0.5]∣ g

[0078] Where d is an amplitude factor that adjusts the output amplitude, f and g are exponential factors satisfying g = h / k, where h and k are positive odd numbers. |·| ensures that Sig(∈) is meaningful in the real number domain, and the sign(∈) is a sign function, ensuring that Sig(∈) is an odd function relative to the equilibrium point. Based on the improvement of the sigma function, a tracking differentiator is designed:

[0079]

[0080] Where, φ i,p,1 ,φ i,p,2 It tracks the state of the differentiator. They are φ i,p,1 ,φ i,p,2 The derivative, It is a design constant, ε i (t) is the input of the tracking differentiator technique. As the parameter g increases, the concavity / convexity of the Sig function near the equilibrium point is effectively altered, gradually transitioning from a convex to a concave function and approaching 0. + This means that equations based on the tracking differentiator have both high-speed tracking capability and high convergence stability.

[0081] Further consider the error signal of the tracking differentiator:

[0082]

[0083] in, Error signal The upper or lower bound of φ. i,p,1 ,φ i,p,2 It tracks the state of the differentiator. They are φ i,p,1 ,φ i,p,2 The derivative, They are α i,p ,α i,v The derivative of . Furthermore, by scaling the inequality, we obtain:

[0084]

[0085] Where ξ i,p ,ξ i,v is the inequality scaling factor.

[0086] Design a virtual controller α within the inverse stepping framework. i,p ,α i,v as follows:

[0087]

[0088] Where γ1>0, β1>0, γ2>0, β2>0 are suitable design parameters, and a, b, r, s are positive odd numbers satisfying a>b and r <s,

[0089] Based on the system state-space equations, the virtual controller, and the tracking error signal, the tracking error signal z... i,p ,z i,v ,z i,a Differentiation yields:

[0090]

[0091] To analyze whether the designed virtual and actual controllers can achieve internal and chain stability for the entire vehicle queue, we select the following Lyapunov candidate function V:

[0092]

[0093] Subsequently, the actual controller u i =u i (t) can be obtained:

[0094]

[0095] in, γ3>0 and β3>0 are the design parameters.

[0096] Differentiate the selected Lyapunov function V and combine it with the derivative of the tracking error. Calculation yields:

[0097]

[0098] From this, we can calculate:

[0099]

[0100] Substituting further into the formula, we get:

[0101]

[0102] To ensure the generality of the proof, we define γ1=γ2=γ3=γ and β1=β2=β3=β.

[0103] This invention guarantees the fixed-time stability of observer estimation error and tracking error, which are zero for any t ≥ T0. Eight different cases are analyzed to demonstrate the stability of fast fixed-time estimation:

[0104] (1) When |z i,p |≥1, |z i,v |≥1, |z i,a When |≥1, we have

[0105]

[0106] (2) When |z i,p |<1,|z i,v |<1,|z i,a |<1, there is

[0107]

[0108] (3) When |z i,p |≥1, |z i,v |≥1, |z i,a |<1, there is

[0109]

[0110] (4) When |z i,p |≥1, |z i,v |<1,|z i,a |<1, there is

[0111]

[0112] (5) When |z i,p |<1,|z i,v|≥1, |z i,a |≥1, there is

[0113]

[0114] (6) When |z i,p |<1,|z i,v |<1,|z i,a |≥1, there is

[0115]

[0116] (7) When |z i,p |<1,|z i,v |≥1, |z i,a |<1, there is

[0117]

[0118] (8) When |z i,p |≥1, |z i,v |<1,|z i,a |≥1, there is

[0119]

[0120] For the entire vehicle queue, the derivative of V can be further written as:

[0121]

[0122] in,

[0123] Therefore, it can be concluded that all signals in the vehicle queuing system are stable at a fixed time. i,p ,z i,v ,z i,a The system converges to the origin within a fixed time interval, independent of initial conditions. It achieves internal stability within a fixed time interval. Based on the stability analysis above, the stability of the string has been proven. Therefore, the stability of the system has been proven.

[0124] To demonstrate the feasibility, effectiveness, and correctness of this example, the present invention provides the following simulation examples:

[0125] In this simulation experiment, a practical controller based on a fixed-time strategy was designed for a vehicle platoon system with external disturbances. This controller aims to maintain the position of followers in the platoon synchronized with the time-varying position of the leader under external disturbances and unknown nonlinear terms. Furthermore, in addition to achieving synchronization, the system's tracking accuracy and transient performance were improved. The leader's time-varying reference speed was used for driving under approximate highway conditions.

[0126] First, the system model parameters are given: vehicle mass m1 = 1000 kg, m2 = 1600 kg; engine time constant τ1 = τ2 = τ3 = 0.5 s; vehicle length l0 = 2 m, l1 = 2.5 m, l2 = 4 m; and the desired safety clearance d between vehicles. i =8m. Secondly, the leader's time-varying reference velocity:

[0127]

[0128] The external disturbance term is: w i = 2sin(0.2πt); The initial value of the system state is: x 0,p =32.5,x 1,p (0) = 22.5, x 2,p (0)=12,x 3,p (0)=0,x 0,v (0)=x 1,v (0)=x 2,v (0)=x 3,v (0) = 15, x 0,a (0)=x 1,a (0)=x 2,a (0)=x 3,a (0) = 0; The relevant parameters of the virtual controller and the actual controller are: a = 25, b = 18, r = 18, s = 25, γ1 = 55, γ2 = 20, γ3 = 120, β1 = 260, β2 = 280, β3 = 550; The relevant parameters of the sigmoid function are: d = 5, f = 5, h = 5, k = 3; The relevant parameters of the tracking differentiator are: The correlation coefficients of the extended state observer are: ρ = 7, η0 = 20, p = 1. The inequality scaling constant is: ξ 1,p =ξ 2,p =ξ 3,p =ξ 1,v =ξ 2,v =ξ 3,v =0.05.

[0129] The effectiveness of this simulation is further illustrated by referring to the accompanying diagram:

[0130] Simulation results are as follows Figures 5-8 The simulation results are shown in the figure. Figure 5 It depicts the positional changes of the vehicle platoon, regardless of whether the leader is accelerating, decelerating, or being disturbed, with no overlapping or collisions between vehicle positions, and the vehicles remain stable in the desired positions. Figure 6 This demonstrates that vehicles 1-3 effectively tracked the leader's vehicle. Figure 7It was demonstrated that the spacing error of the vehicle platoon meets the string stability requirements in vehicle platoon tracking control and is controlled within a bounded region within a fixed time. Figure 7 The figure below shows that the relative speed is actually stable over a fixed period of time, indicating that the speeds of driven vehicles 1-3 can track the speed of the lead vehicle. Figure 8 The error comparison chart of the time-varying gain extended state observer and the traditional linear extended state observer is presented. It can be seen that after the system starts running, the time-varying gain extended state observer experiences a significant error in a short period of time. Then, the time-varying gain extended state observer's estimate of the disturbance gradually approaches the actual disturbance. Therefore, the time-varying gain extended state observer can enable the system to have good transient performance. Thus, the simulation proves the effectiveness of the proposed control scheme.

[0131] This paper proposes a distributed, fast, fixed-time queue tracking control method based on a time-varying gain extended state observer and a tracking differentiator for a vehicle queuing system with time-varying unknown external disturbances. A fast fixed-time controller is designed to improve convergence accuracy and speed. The time-varying gain extended state observer estimates the external disturbances in real time, effectively suppressing the phenomenon of "initial differential peaks." The stability analysis of the observer system is discussed in different cases, and the time-varying gain extended state observer has a more rigorous and simple stability proof process. By designing a fast fixed-time backstepping control method, the system state converges to the desired signal within a fixed time. Then, the stability analysis is systematically proved using Lyapunov's stability theorem. Finally, simulation examples verify the feasibility of the proposed vehicle queuing control method.

[0132] Example 2

[0133] Embodiment 2 of the present invention provides a vehicle queuing control system with an extended state observer, comprising:

[0134] The model building module is configured to: build a vehicle dynamics model;

[0135] The signal compensation module is configured as follows: a time-varying gain extended state observer is designed to compensate for external disturbances and unknown nonlinear terms of the model. Based on the time-varying gain extended state observer and fixed-time stability theory, a virtual controller and an actual controller are constructed using the backstepping method.

[0136] The control module is configured to design a time-varying gain based on an extended state observer, which implements the steps in the vehicle queue control method with a time-varying gain extended state observer as described in the first aspect of the present invention.

[0137] The more detailed steps are the same as in Example 1, and will not be repeated here.

[0138] Example 3

[0139] Embodiment 3 of the present invention provides a medium on which a program is stored. When the program is executed by a processor, it implements the steps in the vehicle queue control method with a time-varying gain extended state observer as described in Embodiment 1 of the present invention.

[0140] The more detailed steps are the same as in Example 1, and will not be repeated here.

[0141] Example 4

[0142] Embodiment 4 of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the vehicle queue control method with a time-varying gain extended state observer as described in Embodiment 1 of the present invention.

[0143] The more detailed steps are the same as in Example 1, and will not be repeated here.

[0144] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A vehicle queuing control method with a time-varying gain extended state observer, characterized in that, Includes the following steps: (1) Under the conditions of external disturbance and unknown nonlinear terms, a vehicle dynamics model is established; before establishing the vehicle dynamics model, the state information and parameter information of each vehicle are also obtained. Through the information transmission between the leader vehicle and multiple follower vehicles, each follower vehicle can obtain the state information and parameter information of other vehicles in real time; the state information includes the vehicle's position information, speed information and acceleration information. The state-space expression in the vehicle dynamics model is: ； in, Indicates time, Represents the measurable system state, i.e., the first... The vehicle's position, speed, and acceleration They are The derivative, Indicates the first Time-varying input disturbance of the vehicle It is the first Vehicle control inputs; Indicates the first The engine time constant of a vehicle; (2) Design a time-varying gain extended state observer to compensate for external disturbances and unknown nonlinear terms, and combine it with the output signal of the tracking differentiator to construct a virtual controller and an actual controller using the backstepping method; use the tracking differentiator to estimate the derivative of the virtual controller; The time-varying gain in the extended state observer is as follows: ； in, It is a constant. It is a time-varying gain. It is a constant control The growth rate; The specific method for compensating for external disturbances and unknown nonlinear terms using a time-varying gain extended state observer is as follows: ； in, For observer error, To extend the state of the state observer, and They represent The derivative, It is the scaling gain. Let represent the engine time constant of the i-th vehicle. It is the control input for the vehicle. It is a positive number. It is a continuous function, defined as follows: ； in, ; (3) Distributed fast fixed-time anti-interference queue tracking control is realized in the backstepping method by using a time-varying gain extended state observer and Lyapunov stability analysis.

2. A medium having a program stored thereon, characterized in that, When the program is executed by the processor, it implements the steps in the vehicle queue control method with a time-varying gain extended state observer as described in claim 1.

3. An electronic device, comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the vehicle queue control method with a time-varying gain extended state observer as described in claim 1.

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