CN116560227B - Robust string-stabilized vehicle fleet longitudinal control method based on generalized extended state observer - Google Patents

Abstract

The invention discloses a robust string stable vehicle fleet longitudinal control method based on a generalized expanded state observer, which includes the following steps: constructing a vehicle fleet longitudinal dynamics model based on a car-following model; designing a composite controller based on the generalized expanded state observer, combined with the above Fleet longitudinal dynamics model to obtain stable fleet input-state chords. The invention discloses a fleet longitudinal following control method based on a generalized expanded state observer and linear state feedback, which handles external interference, uncertain parameters and vehicle-to-vehicle communication faults existing in the fleet system; with the help of input-state string stability definition, It is theoretically proven that the designed control algorithm can ensure the input-state chord stability of the fleet system with non-zero initial state, parameter uncertainty and external disturbance. To improve the control effect of vehicle formation.

Description

A robust chord-stabilized platoon longitudinal control method based on generalized extended state observer

Technical Field

The invention belongs to the field of intelligent automobile fleet longitudinal following control, and in particular relates to a robust chord-stabilized fleet longitudinal control method based on a generalized extended state observer.

Background Art

In recent years, fleet system control has gradually become a hot research topic in the field of intelligent transportation. While ensuring safety, it can control vehicles in the same lane to travel in a queue with the smallest possible expected vehicle spacing, reduce the air resistance of the vehicles, reduce energy consumption, ease traffic congestion, improve the traffic capacity of the road network, and to a certain extent reduce environmental pollution and improve driving comfort.

However, existing technologies show that when there are external disturbances, uncertain parameters and vehicle-to-vehicle communication failures in the convoy system, the anti-disturbance control of the convoy system cannot effectively deal with these problems. When there is a vehicle-to-vehicle communication failure in the convoy, the acceleration of the leading vehicle cannot be obtained. At this time, the acceleration of the leading vehicle appears as mismatched interference in the state space model of the convoy system. If it is not handled properly, the performance of the system will be reduced. The existing results on the longitudinal control of the convoy cannot be directly used to solve this problem. To this end, a composite controller based on the generalized extended state observer and linear state feedback is designed. Deal with external disturbances, uncertain parameters and vehicle-to-vehicle communication failures in the convoy system. With the help of the input-state chord stability definition, it is theoretically proved that the designed control algorithm can ensure the input-state chord stability of the convoy system with non-zero initial state, parameter uncertainty and external disturbances. To improve the control effect of vehicle formation.

Summary of the invention

The purpose of the present invention is to propose a robust chord-stabilized platoon longitudinal control method based on a generalized extended state observer to improve the control effect of vehicle platooning.

To achieve the above object, the present invention provides a robust chord-stabilized convoy longitudinal control method based on a generalized extended state observer, comprising the following steps:

Construct a convoy longitudinal dynamics model based on the car-following model;

A composite controller based on the generalized extended state observer is designed and combined with the longitudinal dynamics model of the convoy to obtain a stable convoy input-state chord.

Optionally, the convoy longitudinal dynamics model includes a double-layer structure controller;

The double-layer structure controller comprises an upper layer controller and a lower layer controller;

The upper controller is used to control the following behavior of each vehicle in the convoy by adjusting the distance and speed difference between two adjacent vehicles in the convoy;

The lower-layer controller is used to adjust the actual acceleration of the vehicle to an acceleration that realizes the car-following behavior.

Optionally, the method for designing the upper controller includes: adopting a fixed time interval strategy, the expected headway distance is calculated as follows,

in, is the expected headway distance of vehicle i at time t, _vi (t) represents the speed, represents a predefined fixed time interval, l _i represents the headway distance when vehicle i is stationary;

The deviation Δs _i (t) between vehicle i and the expected headway and the speed difference Δv _i (t) between vehicle i and the preceding vehicle are calculated as follows:

_Δvi (t)＝vi _-1 (t) _-vi (t)

Where s _i (t) is the actual headway between vehicle i and the preceding vehicle.

Optionally, the method for designing the lower layer controller includes:

Where a _i (t) is the actual acceleration of vehicle i at time t, u _i (t) is the required acceleration, is the ratio of the required acceleration that vehicle i can achieve, is the lag time of the actuator to achieve the required acceleration, δ _i (t) includes parameter uncertainty and external disturbances.

Optionally, the method for constructing a state space model based on the upper-layer controller and the lower-layer controller includes:

in,

C _o = [1 0 0]

For vehicle i, define x _i (t) = [Δs _i (t), Δv _i (t), a _i (t)] ^T , are the state, measured output vector and controlled output vector, and a _i-1 (t) is the acceleration of the leading vehicle.

Optionally, the composite controller based on the generalized extended state observer includes feedforward compensation and linear state feedback regulation based on the generalized extended state observer estimate.

Optionally, the method of feedforward compensation and linear state feedback regulation based on the estimated value of the generalized extended state observer includes:

Designing a generalized extended state observer to estimate the lumped disturbance and the acceleration a _i-1 (t) of the preceding vehicle includes:

in and are the estimated values of x _i (t) and d _i (t), respectively. is the observer gain matrix to be designed;

The state estimation error and disturbance estimation error are respectively:

Where e _i (t) = [e _xi (t) ^T , e _di (t) ^T ] ^T ,

Optionally, a method for obtaining a stable fleet input-state chord includes: the dynamics of X(t) is

in,

exist Class function Ψ, Class functions Λ and σ, and positive constants c ₁ , c ₂ and c ₃ , for the initial condition x _i (0) that satisfies the following equation, the estimation error e _i (t) and the disturbance d _i (t) are expressed as:

And meet the conditions

, obtain a stable fleet input-state chord.

Technical effect of the invention: The invention discloses a robust chord-stable convoy longitudinal control method based on a generalized extended state observer, which can handle external disturbances, uncertain parameters and vehicle-to-vehicle communication failures in the convoy system; with the input-state chord-stable definition, it is theoretically proved that the designed control algorithm can ensure the input-state chord stability of the convoy system with non-zero initial state, parameter uncertainty and external disturbance, so as to improve the control effect of the vehicle formation.

BRIEF DESCRIPTION OF THE DRAWINGS

The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

Figure 1 shows a convoy system traveling on a horizontal road;

FIG2 is a block diagram of the controller of the designed generalized extended state observer;

Figure 3 is the acceleration curve of the pilot vehicle;

Figure 4 shows the estimation error (a) a _i-1 (t) estimation error (b) δ _i (t) estimation error;

Figure 5 shows the performance comparison of spacing error (a) controller of generalized extended state observer (b) linear state feedback part and communication-based feedforward compensation part (c) linear state feedback control;

Figure 6 shows the relative speed performance comparison of (a) the controller of the generalized extended state observer (b) the linear state feedback part and the communication-based feedforward compensation part (c) the linear state feedback control;

Figure 7 shows the acceleration performance comparison of (a) the controller of the generalized extended state observer (b) the linear state feedback part and the communication-based feedforward compensation part (c) the linear state feedback control;

Figure 8 shows the performance comparison of headway error RMS, relative velocity RMS, and acceleration RMS;

Figure 9 shows the estimation error of a _i (t);

Figure 10 shows the performance comparison of spacing error (a) the controller of the first generalized extended state observer (b) the controller of the second generalized extended state observer;

Figure 11 shows the relative speed performance comparison of (a) the first generalized extended state observer controller and (b) the second generalized extended state observer controller;

Figure 12 shows the acceleration performance comparison of (a) the first generalized extended state observer controller and (b) the second generalized extended state observer controller;

Figure 13 shows the performance comparison of headway error RMS, relative velocity RMS, and acceleration RMS;

FIG. 14 is a flow chart of a method for controlling longitudinal following of a vehicle fleet based on a generalized extended state observer and linear state feedback according to an embodiment of the present invention.

DETAILED DESCRIPTION

It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

As shown in FIG. 1-14 , this embodiment provides a robust chord-stabilized convoy longitudinal control method based on a generalized extended state observer, including the following steps:

In step 1, a dynamic model description of the convoy system is given based on the car-following model, specifically:

Figure 1 shows a convoy system traveling on a horizontal road, which includes a pilot vehicle and N following vehicles. In order to solve the longitudinal following control problem of the convoy under the condition of parameter uncertainty and external interference, a two-layer structure control is adopted, including an upper controller and a lower controller. The upper controller controls the following behavior of each vehicle in the convoy by adjusting the distance and speed difference between two adjacent vehicles in the convoy, while the lower controller adjusts the actual acceleration of the vehicle to the acceleration that realizes the upper-layer following behavior when there is uncertainty and external interference in the system. Next, the design of the two-layer structure controller will be introduced in detail.

Upper controller design

Since the fixed time interval strategy is more tolerant to external disturbances than the fixed headway strategy, the fixed time interval strategy is adopted here, and the expected headway can be expressed as follows:

in is the expected headway of vehicle i at time t. _vi (t) represents the speed. represents a predefined fixed time interval. _{l i} represents the headway distance when vehicle i is stationary. Therefore, for vehicle i, the deviation Δs _i (t) from the expected headway distance and the speed difference Δv _i (t) between it and the preceding vehicle can be expressed as

Δv _i (t)=v _i-1 (t)-v _i (t)#(3)

where s _i (t) is the actual headway between vehicle i and the preceding vehicle.

Lower level controller design

For the lower controller, the general vehicle longitudinal dynamics equation is used to describe the nonlinear dynamic characteristics of the vehicle. Specifically, according to the vehicle longitudinal dynamics modeling process, the vehicle longitudinal dynamics characteristics can be approximately represented by a first-order differential equation:

Where a _i (t) represents the actual acceleration of vehicle i at time t, _{and ui} (t) represents the required acceleration. is the ratio at which vehicle i can achieve the required acceleration. represents the lag time of the actuator to achieve the required acceleration. _{δ i} (t) represents the unknown but bounded uncertainty in the system, including parameter uncertainty and external disturbance. Note that here, for the convenience of composite controller design, parameter uncertainty and external disturbance are regarded as a whole as a lumped disturbance δ _i (t).

Note that lumped disturbance is a broad concept that is widely used in the field of active disturbance rejection control. It may include external disturbances, parameter uncertainties, and complex nonlinear dynamics.

State Space Model

For vehicle i, define x _i (t) = [Δs _i (t), Δv _i (t), a _i (t)] ^T , are the state, measured output vector and controlled output vector. Considering the situation where the communication fails, i.e. the acceleration a _i-1 (t) of the preceding vehicle cannot be obtained, combined with equations (2)-(4), the state space model of the entire convoy system can be summarized as

in

C _o = [1 0 0]

Step 2: The design and analysis process of the composite controller based on the generalized extended state observer is given, specifically:

The above describes a convoy system with uncertainty and external disturbances. Here, a controller is designed for the above convoy system under the condition of vehicle-to-vehicle communication failure, aiming to achieve the following two goals: 1) The output of the convoy system You can track the expected output 2) Ensure the input-state string stability of the entire fleet system. To this end, a composite controller based on generalized extended state observer and linear state feedback is designed. The composite controller includes two parts: feedforward compensation based on the estimated value of the generalized extended state observer and linear state feedback regulation.

Design and Analysis of Generalized Extended State Observer

Before designing the generalized extended state observer, the following settings are given

Assume that the unknown lumped disturbance δ _i (t) is continuously differentiable with respect to time t.

Assume that d _i (t) satisfies the condition lim _t→∞ d _i (t)＝κ ₂ , where κ ₁ and κ ₂ are positive constants.

Taking d _i (t) as a new extended state and combining (5), we can get the following extended state equation:

The variables

matrix

Depend on It is easy to know that the state of the augmented system (6) is completely observable. For the augmented system (6), the following generalized extended state observer can be designed to estimate the lumped disturbance and the acceleration a _i-1 (t) of the preceding vehicle:

in and are the estimated values of _xi (t) and _d1 (t), respectively. is the observer gain matrix to be designed.

For simplicity, the state estimation error and disturbance estimation error are defined as

Substituting (6) and (7) into (8), we get

Where e _i (t) = [e _xi (t) ^T , e _di (t) ^T ] ^T ,

Before proving that the observer estimation error is bounded, the following settings are given:

set up is Hurwitzian, then there exists a scalar Γ＞0 such that Established.

Based on the above settings and the generalized extended state observer designed above, the following conclusions can be obtained:

If the convoy system satisfies the first two settings of (6), when the observer gain vector _Li in (7) is selected so that _Aei is a Hurwitz matrix, the observer estimation error e _i (t) is bounded and can be reduced by adjusting _Li .

To obtain the above part, first, to solve the linear time-invariant differential equation (9), rewrite it as

Multiply both sides by the matrix exponent exp(-A _ei t) to get

According to the integral criterion and the properties of matrix exponential, (11) can be rewritten as

Integrating (12) over the interval 0 to t yields

Then there is

Furthermore, multiply both sides of (14) by exp(A _ei t), and according to the matrix exponential property, we have

For simplicity and without loss of generality, assume and If the observer gain _Li in (7) is selected so that _Aei is Hurwitzian, then by setting, formula (15) can be written as

The fourth inequality is given by the assumption that and (10) before setting. From (16), we can see that by selecting appropriate parameters _Li, we can get an appropriate ρ(A _ei ) to reduce the estimation error.

From (15), it can be seen that _Li can be adjusted to obtain the desired exponential convergence rate. The exponential convergence rate can ensure that the observer has good transient performance, which is of great significance in engineering implementation. In some cases, _δi (t) and _ai-1 (t) can be constant values in the steady state. In this case, the error _ei (t) converges to zero asymptotically at an exponential rate.

Design and Analysis of Composite Controller

In order to achieve the control objectives mentioned above, combined with the estimated values obtained by the generalized extended state observer, the following controller based on the generalized extended state observer is designed for system (5):

in is the feedback control gain vector, is the disturbance compensation gain vector. The principle block diagram of the controller of the generalized extended state observer designed in combination with FIG2.

To determine k _xi and k _di , substitute the control law (17) into the system (5), and we have the following closed-loop system:

Where A _fi =A _i +B _i k _xi , Obviously, A _fi can be made Hurwitzian by selecting a suitable feedback control gain _vector k _xi . The transfer function matrix is _Gyd (s)= _{Co (} sI- _Afi ) ^-1 (D+ _Bikdi ). In order to eliminate the influence of _di (t) on the output, considering lim _{t→∞d i} (t) = κ ₂ , according to the final value theorem, the condition needs to be satisfied, then k _di can be given as

Using a derivation similar to (10)-(15), we can obtain

Since e _i (t) and d _i (t) are bounded, it follows that _xi (t) is exponentially bounded.

When δ _i (t) and a _i-1 (t) are both constants in the steady state, the error e _i (t) converges to zero at an exponential rate. Therefore, x _i (t) also converges to zero at an exponential rate, which in turn means that the headway error Δs _i (t) converges to zero at an exponential rate.

Note that compared to the traditional scheme, the proposed generalized extended state observer controller method is also applicable and effective when the relevant information of a _i ( t ) is unavailable. In this case, because The control law can be designed by estimating a _i (t), where

In the traditional scheme, the state variable is selected as x _i (t) = [α _i (t), β _i (t), γ _i (t)] ^T , and the sliding variable σ _i in the equation is substituted into the equation as the control input. It is easy to see that the controller in the traditional scheme is equivalent to a composite controller composed of a linear state feedback and a feedforward compensation based on the disturbance observation value. However, the control algorithm in the traditional scheme can only solve the matching disturbance, while the control algorithm proposed here can not only solve the matching disturbance but also solve the unmatched disturbance. The control algorithm proposed here is a generalization of the control algorithm in the traditional scheme.

Compared with the existing longitudinal following control algorithm for a convoy that requires vehicle-to-vehicle communication to obtain the acceleration of the leading vehicle, the controller algorithm of the designed generalized extended state observer takes into account the working condition of communication failure in the convoy, regards the acceleration of the leading vehicle as external interference, and uniformly estimates it when estimating the lumped interference in the system. In addition, there is no requirement for vehicle-to-vehicle wireless communication, and the designed control algorithm is suitable for the scenario where some vehicles in the convoy are manually driven vehicles without broadcasting function. From this point of view, the controller method of the proposed generalized extended state observer has a wider range of application scenarios.

Analysis of Queue Chord Stability

For simplicity, remember and is the set of all following vehicles in the convoy. Then, the dynamics of X(t) can be expressed as

in

Definition if exists Class function Ψ, Class functions Λ and σ, and positive constants c ₁ , c ₂ and c ₃ , for initial conditions x _i (0) that satisfy the following equations, the estimated error e _i (t), the disturbance d _i (t)

Both

If it holds, then the convoy system is said to be input-state chord stable.

The main conclusions are given below

If the convoy system (5) satisfies the first two settings of (6), when the observer gain matrix _Li in (7) and the feedback vector _{kxi in} (17) respectively make _Aei and _Afi = _Ai + _Bikxi Hurwitz, then under the action of the designed composite control law (17), the entire convoy system is input-state chord stable.

Proof of the above part, similar to (10)-(15), we can get the solution of (20) as follows

Calculating the Euclidean norm of X(t) yields

Since A _fi is Hurwitz, the matrix is also the Hurwitz matrix. According to the previous setting of (10),

Where π＝||Π||, r＝||γ||, then (21) in the previous definition The class functions Λ and σ can be chosen as

and

at the same time The class function Ψ can be chosen as

Note that from (25), we can obtain a smaller X(t) by adjusting the parameters _kxi and _Li , thereby obtaining a smaller headway error _Δsi (t). From a practical application perspective, this can improve the traffic capacity of the road network.

Step 3: Conduct case analysis, specifically:

Here, numerical simulation is used to illustrate the effectiveness and superiority of the controller algorithm of the proposed generalized extended state observer and the correctness of the theoretical analysis. To this end, a convoy system consisting of six vehicles, including a leading vehicle and five following vehicles, is considered. In order to illustrate the superiority of the proposed control algorithm, the comparison algorithm in the simulation is a known traditional algorithm. In the following simulation, the acceleration trajectory of the leading vehicle is reconstructed using MATLAB software using the known data provided. The reconstructed acceleration trajectory is shown in Figure 3. The horizontal axis represents time and the vertical axis represents acceleration. Fixed time interval in fixed time interval strategy is set to 1s. The system parameters in the simulation are set to known system parameters, namely In the simulation, trigonometric functions are used to simulate the lumped interference δ _i (t), namely δ ₁ (t) = 0.025sint, δ ₂ (t) = 0.02sint + 0.01, δ ₃ (t) = 0.015sin(2t) + 0.03, δ ₄ (t) = 0.01sin(5t) + 0.03, δ ₅ (t) = 0.028sint. In order to ensure the stability of the entire convoy system and the stability of the queue string, the linear state feedback gain is selected as k _xi = [0.78, 0.91, -0.05]. In order to ensure that the generalized extended state observer can converge, the poles of the generalized extended state observer are set to p _geso = [-10.5, -10.4, -10.3, -10.2, -10.1] ^T. Without loss of generality, the initial value of the observer is assumed to be zero.

The known control law is u _i (t) = k _i x _i (t) + k _Fi a _i-1 (t). It includes a linear state feedback part and a communication-based feedforward compensation part. The parameters are set as

k _i =[0.78, 0.91, -0.05] and k _Fi =0.32. When a vehicle-to-vehicle communication failure occurs in the convoy system and a _i-1 (t) is unavailable, the known control method degenerates into a so-called linear state feedback control algorithm. When evaluating the algorithm, the root mean square of the headway error, relative speed and acceleration are used as evaluation indicators. The relevant simulation results are shown in Figures 4 to 8. The horizontal axis in Figures 4 to 6 and 7 represents time. The vertical axis of Figure 4(a) represents the estimated error of a _i-1 (t), while the vertical axis of Figure 4(b) represents the estimated error of δ _i (t). The vertical axis of Figure 5 represents the spacing error. The vertical axis of Figure 6 represents the relative speed. The vertical axis of Figure 7 represents acceleration.

It can be clearly observed from the simulation diagram that when there are parameter uncertainties, external disturbances, and vehicle-to-vehicle communication failures in the system, the controller algorithm of the generalized extended state observer designed here can ensure that each vehicle in the convoy follows the preceding vehicle well, as shown in Figure 5(a). In addition, its performance is comparable to the linear state feedback part and the communication-based feedforward compensation part methods. The reason behind the performance difference is that the generalized extended state observer has a very small estimation error when estimating a _i-1 (t). In some cases, a _i-1 (t) is a constant value in the steady state. In this case, the estimation error converges to zero exponentially, and at this time, the performance of the two control algorithms is basically the same. It is worth noting that when the system has a vehicle-to-vehicle communication failure, the acceleration of the preceding vehicle a _i-1 (t) appears as a mismatched disturbance in the state space model of the system. The satisfactory simulation results in the figure show that the controller control algorithm of the generalized extended state observer is insensitive to mismatched disturbances. In addition, as shown in Figure 7, under the control algorithm of the controller of the generalized extended state observer, the root mean square index of the first vehicle in the convoy system is greater than that of the subsequent vehicles, that is, the root mean square of the headway error, relative speed and acceleration decreases along the direction of the convoy, which shows that the controller control algorithm of the generalized extended state observer designed here can ensure the chord stability of the queue.

As expected, both the GESO controller and the LSFC control algorithms can reduce the spacing error caused by the acceleration of the external leader vehicle. It can be observed from Figures 3 and 7 that when the leader vehicle starts to change its acceleration, the first vehicle following it also starts to change its acceleration. Then, along the direction of the convoy, the acceleration of each vehicle in the convoy starts to change in sequence. Although both control algorithms can reduce the spacing error, it is obvious that the GESO controller algorithm proposed here can significantly reduce the spacing error and perform better. As shown in Figure 8, under the GESO controller algorithm, the RMS of the spacing error can be reduced by at least 40%. At the same time, the RMS of the relative speed is reduced by at least 12%. In addition, the RMS of the acceleration is reduced by 0.6-15%. It should be pointed out that when the parameter _kdi in the GESO controller algorithm is set to zero, the GESO controller algorithm also degenerates into a LSFC control algorithm. Therefore, the following conclusion can be drawn that the feedforward control term based on the disturbance observer can significantly improve the performance of the system.

In view of the high cost of acceleration sensors, the acceleration obtained by derivation of velocity may introduce noise into the system. In practical applications, a _i (t) may not be obtained. In this case, because in We can use the generalized extended state observer to estimate a _i (t). Then, using the estimated Design a composite controller and get Next, we will verify the effectiveness of the controller algorithm of the designed generalized extended state observer through numerical simulation when a _i (t) is not available. The selection of controller and observer parameters is the same _as that of the working condition where a _i (t) is available. The controllers are represented as the controller of the first generalized extended state observer and the controller of the second generalized extended state observer respectively. The simulation results are shown in Figures 9 to 12 and Figure 13. Figure 9 shows the estimation error of _ai (t), from which it can be seen that the estimation error of _ai (t) converges to a very small neighborhood of the origin. The vertical axis of Figure 10 represents the spacing error. The vertical axis of Figure 11 represents the relative speed. The vertical axis of Figure 12 represents the acceleration. As shown in Figures 10 to 13, the performance of the controller algorithm of the second generalized extended state observer is comparable to that of the controller algorithm of the first generalized extended state observer. This shows that the controller algorithm of the generalized extended state observer is also applicable when _ai (t) is not available.

Here, the robust chord-stable longitudinal following control problem of a convoy under the condition of vehicle-to-vehicle communication failure is studied, and a controller control algorithm of a generalized extended state observer is designed to overcome the adverse effects of parameter uncertainty, external interference and vehicle-to-vehicle communication failure on system performance. It is worth pointing out that most existing works assume that the initial working conditions of the system are zero when analyzing the chord stability of the convoy system. Different from the existing results, this patent adopts the input-state chord stability definition, fully considering the non-zero initial state, communication failure, parameter uncertainty and external disturbance in the convoy system, and theoretically proves that the controller algorithm of the designed generalized extended state observer can ensure the chord stability of the entire convoy system. Numerical simulation results show that when the convoy system encounters a vehicle-to-vehicle communication failure, the controller algorithm of the designed generalized extended state observer can not only ensure that each vehicle in the convoy follows the vehicle in front safely and smoothly, but also improve the traffic capacity of the road network; the controller algorithm of the designed generalized extended state observer performs better than the control algorithm in the traditional scheme.

The above is only a preferred specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims (2)

1. A robust chord-stabilized convoy longitudinal control method based on a generalized extended state observer, characterized in that it comprises the following steps: Construct a convoy longitudinal dynamics model based on the car-following model; Design a composite controller based on a generalized extended state observer and combine it with the longitudinal dynamics model of the convoy to obtain a stable convoy input-state chord; The longitudinal dynamics model of the convoy includes a double-layer structure controller; The double-layer structure controller comprises an upper layer controller and a lower layer controller; The upper controller is used to control the following behavior of each vehicle in the convoy by adjusting the distance and speed difference between two adjacent vehicles in the convoy; The lower controller is used to adjust the actual acceleration of the vehicle to the acceleration for achieving the car-following behavior; The method for designing the upper controller includes: adopting a fixed time interval strategy, the expected headway distance is calculated as follows: in, is the expected headway distance of vehicle i at time t, _vi (t) represents the speed, represents a predefined fixed time interval, l _i represents the headway distance when vehicle i is stationary; The deviation Δs _i (t) between vehicle i and the expected headway and the speed difference Δv _i (t) between vehicle i and the preceding vehicle are calculated as follows: _Δvi (t)＝vi _-1 (t) _-vi (t) Where s _i (t) is the actual headway between vehicle i and the preceding vehicle; The method for designing the lower layer controller includes: Where a _i (t) is the actual acceleration of vehicle i at time t, u _i (t) is the required acceleration, is the ratio of the required acceleration that vehicle i can achieve, is the lag time of the actuator to achieve the required acceleration, δ _i (t) includes parameter uncertainty and external disturbances; The composite controller based on the generalized extended state observer includes feedforward compensation and linear state feedback regulation based on the estimated value of the generalized extended state observer; The method of feedforward compensation and linear state feedback regulation based on the estimated value of the generalized extended state observer includes: Designing a generalized extended state observer to estimate the lumped disturbance and the acceleration a _i-1 (t) of the preceding vehicle includes: in and are the estimated values of x _i (t) and d _i (t), respectively. is the observer gain matrix to be designed; The state estimation error and disturbance estimation error are respectively: Where e _i (t) = [e _xi (t) ^T ,e _di (t) ^T ] ^T , The method of obtaining a stable fleet input-state string includes: the dynamics of X(t) is in, exist Class function Ψ, Class functions Λ and σ, as well as positive constants c ₁ , c ₂ and c ₃ , for the initial condition x _i (0) that satisfies the following equation, the estimation error e _i (t) and the disturbance d _i (t) are expressed as: And meet the conditions , obtain a stable fleet input-state chord. 2. The method for robust chord-stabilized convoy longitudinal control based on generalized extended state observer according to claim 1, characterized in that the method for constructing a state space model based on the upper controller and the lower controller comprises: in, C _o = [1 0 0] For vehicle i, define x _i (t) = [Δs _i (t), Δv _i (t), a _i (t)] ^T , are the state, measured output vector and controlled output vector, and a _i-1 (t) is the acceleration of the leading vehicle.