A connected vehicle platoon control method considering curved road conditions

Abstract

This invention provides a connected vehicle platoon control method considering curved road conditions, comprising the following steps: Considering a homogeneous vehicle platoon composed of multiple vehicles traveling on a curved road, the position and speed information of the preceding vehicle is acquired via wireless communication. Then, a controller is used to achieve speed tracking between following vehicles and the lead vehicle, as well as distance maintenance between adjacent vehicles, establishing a vehicle platoon tracking and control system model; setting parameter values; performing stability analysis on the vehicle platoon tracking and control system with delays and switching; solving for the control gain using matrix inequalities; if no feasible solution exists, resetting the scalar values ​​and solving the expression; calculating the average dwell time and determining whether each parameter and gain satisfy the conditions in Theorem 1; if not, resetting the parameter values ​​and repeating the process until the conditions are met. This invention addresses the problems of packet loss in vehicle communication and actuator delays under curved road conditions by establishing a vehicle platoon control system with switching and time delays.

Description

Technical Field

[0001] This invention relates to the technical field of vehicle control methods, and more particularly to a connected vehicle platoon control method that takes into account curved road conditions. Background Technology

[0002] In recent years, vehicle queue control has received widespread attention due to its great potential in alleviating traffic congestion and reducing air pollution. [1-3] The goal of vehicle platooning control is to maintain a desired distance between vehicles in the platoon and ensure they travel at the same speed. Smaller distances between vehicles help increase road capacity, alleviate traffic congestion, and effectively reduce air resistance, thereby reducing energy consumption and air pollution. Therefore, research on vehicle platooning control is of great significance. [4] .

[0003] Currently, relevant scholars have already started to study spacing strategies. [5] Workshop communication [6] Communication topology [7] and vehicle control strategies [8] Research has been conducted on vehicle platooning control in various aspects. Among these, stable and reliable inter-vehicle communication is one of the key factors in achieving vehicle platooning control objectives. Due to the nature of vehicles... High-speed movement and the limited bandwidth of communication networks can lead to the loss of transmitted data packets, thus affecting the stability of the vehicle platooning system. (Literature) [9] To address the capacity constraints and Bernoulli random packet loss problem in vehicle ad hoc networks, a platoon control algorithm is designed. This algorithm resolves network collisions and satisfies the requirements of vehicle platoon stability and zero steady-state distance error. (References)

[10] Considering the impact of network-induced delays, packet loss, and quantization errors in vehicle-to-vehicle communication on the system, a hierarchical control method was used to ensure both individual vehicle stability and platoon stability. However, the above research mainly focuses on the packet loss problem in vehicle platoon control under straight road conditions, neglecting the impact of curved road conditions on the vehicle control system.

[0004] Compared to straight road conditions, vehicle platooning control on curved roads requires consideration of factors such as vehicle heading angle, yaw angle, road gradient angle, and coordinate transformation between the vehicle coordinate system and the geodetic coordinate system. For example, the literature...

[11] This paper considers the vehicle tracking control problem on curved roads, and designs a three-step nonlinear control law to achieve speed tracking and distance maintenance between vehicles. The stability of speed and distance errors between vehicles is analyzed using Lyapunov stability theory. (References)

[12] To address the characteristics of strongly coupled, nonlinear, and overdriven connected vehicle fleets on curved roads, a cooperative adaptive fleet control strategy is proposed. The boundedness of the closed-loop control system is guaranteed by combining Lyapunov stability theory. (Reference)

[13] A looking-ahead method is proposed to avoid premature turning of following vehicles in the lateral and longitudinal coordinated control of vehicle platoons, thus achieving the goal of vehicle platoon control. It is worth noting that while the above research considers the vehicle platoon control problem under curved road conditions, it neglects the impact of unreliable inter-vehicle communication (packet loss, delay) on the control system.

[0005] Reference documents: [1]Raza H , Ioannou P .Vehicle following control design for automated highway systems[C] / / IEEE. IEEE, 1997:43-60. [2]Vahidi, A, Eskandarian. Research advances in intelligent collision avoidance and adaptive cruise control[J]. Intelligent Transportation Systems, IEEE Transactions on, 2003. [3]Loannou P. Guest editorial adaptive cruise control systems special issue. IEEE transactions on Intelligent Transportation Systems , 2003,4(3):113-114. [4] Yu Zhiying, Guo Ge. Vehicle platooning cooperative path tracking control in the context of vehicle networking[J]. Control Engineering, 2015, 22(05):804-808. Zhi-Ying YU, Guo G. Coordinated Path Following Control of VehicleFormations in Vehicular Network Environment[J]. Control Engineering of China. [5]Kato S, Tsugawa S, Tokuda K. Vehicle control algorithms forcooperative driving with automated vehicles and intervehicle communications[C] / / IEEE Intelligent Vehicles Symposium. IEEE, 2002 :155-161. [6]Yadlapalli S K, Darbha S, Rajagopal K R. Information flow and itsrelation to stability of the motion of vehicles in a rigid formation[J]. IEEETransactions on Automatic Control , 2006, 51(8) : 13 15 -1319. [7]Chehardoli H, Ghasemi A. Adaptive Centralized / DecentralizedControl and Identification of 1-D Heterogeneous Vehicular Platoons Based onConstant Time Headway Policy[J]. IEEE Transactions on IntelligentTransportation Systems, 2018:1-11. [8]Qin W B, Gomez M M, Orosz G. Stability and Frequency ResponseUnder Stochastic Communication Delays With Applications to Connected CruiseControl Design[J]. IEEE Transactions on Intelligent Transportation Systems,2016:1-16. [9]Ge G, Wen S. Communication Scheduling and Control of a Platoon ofVehicles in VANETs[J]. IEEE Transa-ctions on Intelligent TransportationSystems, 2016, 17(6):1-13.

[10] Guo G, Yue W. Hierarchical platoon control with hetero- geneousinformation feedback [J]. Control Theory Applications Iet, 2011,5(15):1766-1781

[11] Bian Y , Zhang L , Chen H. Coordinated Lateral and LongitudinalVehicle-Following Control of Connected and Automated Vehicles ConsideringNonlinear Dynamics[J]. IEEE Control Systems Letters, 2020, 4(4):1054-1059.

[12] Guo J, Wang J, Li K. Adaptive non-linear coordinated optimaldynamic platoon control of connected autonomous distributed electric vehicleson curved roads[J]. IET Intelligent Transport Systems, 2020, 14(12):1626-1637.

[13] Bayuwindra A, Ploeg J, Lefeber E, et al. Combined Longitudinaland Lateral Control of Car-Like Vehicle Platooning With Extended Look-Ahead[J]. IEEE Transactions on Control Systems Technology, 2019, PP(99):1-14.

[14] Liu

[15] Wu Ligang, Zhou Qian. Autonomous vehicle fleet control with time-varying delay and actuator saturation [J]. Control Engineering, 2018, 25(03):442-447. Li-Gang WU, Zhou Q. Autonomous Platoon Control with ActuatorSaturation and Time-varying Delay[J]. Control Engineering of China, 2018.

[16] Byrnes CI, Isidori A. Nonlinear Control Systems[J]. LectureNotes in Control&Information Sciences, 2003, 242(65):408.

[17] Li Z, Hu B, Li M, et al. String Stability Analysis for VehiclePlatooning Under Unreliable Communication Links With Event-Triggered Strategy[J]. IEEE Trans-actions on Vehicular Technology, 2019, 68(3):2152-2164.

[18] Mei J, Zheng K, Zhao L, et al. Joint Radio Resource Allocation and Control for Vehicle Platooning in LTE-V2V Network[J]. IEEE Transactionson Vehicular Technology, 2018, 67:12218-12230. Summary of the Invention In view of the technical problems mentioned in the background section, this invention provides a connected vehicle queuing control method that considers curved road conditions. The technical means employed in this invention are as follows: A method for controlling connected vehicle platooning that takes into account curved road conditions includes the following steps: Step 1: Consider driving on curved roads A homogeneous vehicle platoon, consisting of 100 vehicles, acquires the position and speed information of the leading vehicle via wireless communication. Then, a controller is used to achieve speed tracking between following and leading vehicles, as well as maintaining the distance between adjacent vehicles, thus establishing a vehicle platoon tracking and control system model; parameters are set. as well as value Step 2: Perform stability analysis on the vehicle platoon tracking control system with delay and switching; solve for the control gain using matrix inequalities. If no feasible solution exists, reset the scalar. as well as The value of the solution is obtained from equation (27); Step 3: Calculate the average length of stay And determine each parameter and gain. Check if the conditions in Theorem 1 are met; if not, reset the parameter values ​​and repeat step 2 until the conditions are met.

[0006] Compared with the prior art, the present invention has the following advantages: 1) To address the issues of packet loss in vehicle communication and actuator delay under curved road conditions, a vehicle queuing control system with switching and time delay features was established. 2) Combining switching system theory and Lyapunov stability theory, the existence conditions of the controller that can guarantee the stability of the vehicle queuing tracking control system were obtained. Finally, the effectiveness of the designed control algorithm was verified through SIMULINK simulation experiments. Attached Figure Description

[0007] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0008] Figure 1 This is a schematic diagram of a convoy model on a curved road according to the present invention.

[0009] Figure 2 This is a schematic diagram of the vehicle dynamics model of the present invention.

[0010] Figure 3 This is a schematic diagram of the shape of the curved road of the present invention.

[0011] Figure 4 For the present invention A schematic diagram showing the relationship between the infinite norm and the unit circle.

[0012] Figure 5 This is a schematic diagram of the vehicle distance error of the present invention.

[0013] Figure 6 This is a schematic diagram showing the speed of the vehicle of the present invention.

[0014] Figure 7 This is a schematic diagram of the trajectory of the vehicle of the present invention.

[0015] Figure 8 This invention is based on the application literature.

[10] The distance error of the vehicle when the controller is in the middle.

[0016] Figure 9 This invention is based on the application literature.

[10] The speed of the vehicle when the controller is activated.

[0017] Figure 10 This invention is based on the application literature.

[10] The vehicle's trajectory when the controller is in the middle. Detailed Implementation

[0018] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0019] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0020] like Figure 1 As shown, consider driving on a curved road. The vehicle convoy consists of homogeneous vehicles and employs a Predecessor-leader-following (PLF) communication topology. The lead vehicle periodically transmits its position and speed information to the following vehicles via wireless communication, while the following vehicles... The position and speed information of the vehicle in front can be obtained through wireless communication. Then, the controller can be used to achieve speed tracking between the following vehicle and the lead vehicle, as well as to maintain the distance between adjacent vehicles. In this section, the impact of communication packet loss and actuator delay on the controller is analyzed under curved road conditions, and a vehicle platoon tracking control system model is established.

[0021] like Figure 2 As shown, establish a following vehicle Vehicle dynamics model: (1) in: It's about the quality of the vehicle. The vehicle in the vehicle coordinate system longitudinal velocity; and They are vehicles The horizontal and vertical coordinates in a Cartesian coordinate system; It is the moment of inertia; It is the angular velocity of the vehicle; It is the vehicle's heading angle; It is the longitudinal force of the vehicle; It is an external torque; It is the longitudinal equivalent air drag coefficient; It is the longitudinal wind speed; It is gravitational acceleration; It is the rolling resistance coefficient of the tire; It is the road slope angle.

[0022] Since it is difficult to obtain the instantaneous airflow distribution and intensity in practice, this paper treats wind speed as an external disturbance factor. Furthermore, considering the positional error of the positioning system, it is difficult to obtain an accurate road slope angle; therefore, the road slope angle is also considered as disturbance. To facilitate the handling of disturbance quantities, it is assumed that the disturbance satisfies the condition of bounded energy, i.e. , ,in It represents the 2-norm.

[0023] To facilitate the establishment of a vehicle platooning control system, the nonlinear vehicle model (1) is linearized. Definition and These are the state matrix and input matrix of the vehicle model (1), respectively. The output matrix is ​​given. According to reference

[16] , the vehicle model (1) is linearized and decoupled into the following subsystem form. (2a) (2b) (2c) in: It is the state matrix of the matrix after linear processing; It is the input matrix of the matrix after linear processing; and It is a disturbance quantity. and They are and The coefficient matrix is ​​as follows: (3a) (3b) (3c) (3d) in: (4) (5) Assuming the curved road under study can be represented by the following... Represented by a polynomial of order, with a shape like Figure 3 As shown (6) in: , For different x-coordinates ,curve There exists a unique one. Correspondingly. is a positive integer; Indicates a constant coefficient, ( ) like Figure 1 As shown, Indicates following vehicle Along the curved road The distance traveled can be calculated using the following formula: (7) in:

[0024] set up ,Will Differentiate with respect to time and represent using the state variables defined in equation (2), following the vehicle The vehicle dynamics model under curved road conditions can be re-expressed as follows: (8) in: Indicates vehicle Speed ​​on a curved road.

[0025] Since equation (8) is nonlinear, the feedback linearization method is used.

[11] It can be expressed as shown in equation (9). (9) The coordinate transformations and inputs involved in the formula are as follows: (10) (11) here This is a new control input introduced to linearize equation (8). ; ;

[0026] As a preferred embodiment, in this document It indicates the curved distance a vehicle travels along a curved road, not the straight distance.

[0027] When a convoy travels on a curved road, an error expression is constructed using the curve distance error between vehicles to ensure the compactness of the convoy.

[0028] like Figure 1 As shown, the definition and Follow each other car The distance error and speed error between the vehicle and the vehicle in front, namely: (12) in: Indicates following vehicle The distance traveled along a curved road; Indicates following vehicle The speed. This indicates the ideal vehicle spacing.

[0029] To represent the distance and speed relationship between the lead vehicle and the following vehicles, we define... and These represent the lead vehicle and the following vehicle, respectively. The distance and speed error between them, i.e.: (13) in: Indicates the lead vehicle and the following vehicles The ideal workshop spacing. That's the speed of the lead car.

[0030] definition , Then the vehicle The state-space description can be represented as: (14) in:

[0031]

[0032] In formula (14), the following vehicle controller Specifically, it is expressed as follows: (15) in: This indicates the controller gain to be determined; The error amount, which takes into account the impact of data packet loss, is defined as follows: (16) in, Indicates following vehicle The distance information received from the vehicle ahead; Indicates following vehicle The speed information received from the vehicle ahead.

[0033] (17) in, Indicates following vehicle Information received regarding the distance traveled by the lead vehicle; Indicates following vehicle The received speed information of the lead vehicle is defined. , .

[0034] In formula (13) and The quantities corresponding to those in equation (9) represent the speeds of the lead vehicle and the following vehicle in the Cartesian coordinate system, respectively, while in equation (1) Represents the vehicle in the vehicle coordinate system The speed.

[0035] Because the vehicle platoon tracking control system uses a PLF communication topology, that is, the lead vehicle sends information to the following vehicles via wireless communication ( and ), following the car The distance traveled by the vehicle in front on a curved road can be obtained via wireless communication. and speed However, data packet loss may occur during vehicle wireless communication, thus necessitating the introduction of a handover signal. This describes whether packet loss has occurred in the system. Specifically, if the data packets are transmitted successfully, Information transmitted via wireless communication can be used by following vehicles Calculate the vehicle tracking error, and the transmission volume at this time. , , , Right now , When packet loss occurs, According to the zeroing strategy [17-18] To reset the information transmitted via wireless communication to zero, and for ease of analysis, define... Based on the above discussion, the tracking error vector can be obtained. and , and Relationship (18) in, .

[0036] Due to fuel delays and differences in information processing time among control nodes in the control system, control signal transmission is delayed, or the control signal transmitted to the actuator cannot be immediately read and applied to the controlled object, resulting in actuator delays. Define constants. Delay for actuator ( ). Assumption The actuator reads the control signal at specific times. Due to the delay, the actual control signal executed is: (19) From equations (12) and (13), the following equation transformations can be obtained: (20) Simultaneously define: (twenty one) From equations (14) and (19)-(21), we can obtain a vehicle queuing tracking control system model with switching and time delay. (twenty two) in: Represents state variables; Indicates the amount of disturbance; Indicates the system output; Indicates a switching signal; It is a coefficient matrix; and Represents the gain matrix. When The initial conditions are continuously differentiable.

[0037]

[0038]

[0039]

[0040] ; (twenty three) symbol Indicates the Kronecker product; ;express An identity matrix of order 1. .

[0041] Robust control of vehicle queuing is defined as follows: Definition 1. Under zero initial conditions If the output is below and disturbance satisfy (twenty four) The fleet system then satisfies the requirement of having a disturbance suppression degree of... ( (is a constant) Robust stability requirements.

[0043] Vehicle queuing control aims to design a controller (19) that enables vehicles to maintain the same speed and desired spacing while queuing under the influence of packet loss and delay, while satisfying the following stability indicators: 1) Queue stability: When the lead vehicle is disturbed, the tracking error of the vehicles will not be amplified and propagated along the queue, i.e., it satisfies... Queue stability requirements.

[0044] (25) 2) Robust stability: For any non-zero... and constants given under zero initial conditions Equation (24) always holds true.

[0045] To perform stability analysis on a vehicle platoon tracking control system with delays and switching, the Lyapunov function is defined as follows: (26) in , Let be a scalar. Before proceeding with the stability analysis, we first give the relevant lemmas and the definition of the mean residence time.

[0046] Definition 3. For any time interval ,make ,in: Shaking World ,but This is referred to as the average length of stay.

[0047] set up Indicates switching signal Follow the vehicle In time interval The total activation time within the specified period determines the system's packet loss rate. .

[0048] Lemma 1. Consider a vehicle platoon tracking control system (22), for a given constant time delay and scalar as well as If a positive definite matrix exists , Satisfying matrix inequalities (27) in:

[0049]

[0050] Then, following the trajectory of system (22), we can obtain (28) in:

[0051] Prove that the above holds true: Let

[0052] This is equivalent to inequality (28). Using the average dwell time and lemma 1, we can give the following conclusion.

[0053] This application sets up Theorem 1, considering a fleet tracking control system (22), given a constant time delay. and scalar and disturbance suppression degree If a positive definite matrix exists , constant At the same time, the upper limit of packet loss rate is satisfied.

[0054] This makes matrix inequalities (27) and (29) hold.

[0055] (29) The convoy tracking control system (22) satisfies the following for any dwell time. (30) The switching signal is Robust and stable. And its controller gain is:

[0056] Prove that the above holds true: Assume For switching signals exist The switching time point within the time frame, then for any Assuming

[0057] Then, from equation (28), we can obtain (31) The Lyapunov function defined by equation (26) can be obtained (32) (33) because All are solutions to matrix inequality (27), and if there exists a constant This makes equation (29) hold, and we can obtain (34) Combining equations (31) and (34), we can obtain

[0058] (35) Under zero initial conditions, we can obtain from equation (35) (36) in: And because ,therefore, (37) From equation (36), we can obtain (38) Take in the above formula arrive If equation (22) is satisfied, then the vehicle queue tracking control system (22) satisfies... Robust stability requirements.

[0059] First, the following definition is given: Definition 4. Consider the following vehicle platoon tracking control system: (39) in: express A following vehicle; Indicates a switching signal; It is a state vector; It is an external input; This is system output; yes Initial conditions that are continuously differentiable Indicates actuator delay. (Order) As in equation (39) The equilibrium solution at time. If there exists a K-type function. and So that for any initial state and any If all of the following equations hold true, then the fleet system (39) is The queue is stable.

[0060] (40) in yes norm, and if satisfy (41) At this point, system (39) is strictly The queue is stable. Based on Definition 4, Theorem 2 is given. Consider a platoon control system with switching delay (22). If matrix inequality (27) holds, then the platoon control system affected by packet loss and delay is The queue is stable, and at the same time At that time, the team was strict The queue is stable.

[0061] Proof of the above: As can be seen from the previous section, equation (38) leads to the conclusion that equation (24) holds, i.e. And it is easy to know It is an equilibrium solution of the fleet control system (20), which satisfies the condition of equation (40), so the fleet control system is queue stable.

[0062] set up For disturbance To output The transfer function matrix, for arrive The transfer function matrix. From equations (14) and (19), we can obtain... (42) in They are respectively their corresponding The Laplace transform of .

[0063] From equation (42), we can see that yes The complementary sensitivity, and due to The following relation holds true. (43) like Figure 4 As shown, due to infinite norm Equal to the distance from the origin to the point on the complex plane The distance to the farthest point on the Nyquist plot, and Located at the origin, Inside the circle with radius [blank]. Therefore, when [blank] hour, satisfy (44) Due to the output matrix in the fleet control system It is an identity matrix, so Similarly arrive The transfer function. Therefore, it can be known that... Therefore, equation (41) holds, and the vehicle control system (22) is strictly... The queue is stable.

[0064] Example 1 To verify the effectiveness of the controller, a simulation experiment was conducted on a vehicle platoon tracking control system consisting of one lead vehicle and three follower vehicles. The expression for the curved road is shown in (45). (45) in:

[0065] .

[0066] The vehicle parameters involved in the simulation experiment are shown in Table 1. Table 1 Vehicle Parameters

[0067] By solving the control algorithm, the control gain can be obtained as follows: The upper bound of the constant delay is satisfied. ,Pick The parameter values ​​involved in the algorithm are shown in Table 2: Table 2. Parameter values ​​involved in the algorithm

[0068] Simulation experiments were conducted using the controller designed in this paper, and the results are as follows: Figures 5-7 As shown.

[0069] Example 2: Next, the control algorithm proposed in this paper will be compared with that in the literature.

[10] The control algorithms in the literature are compared.

[10] The controller designed in the middle was simulated, and the results are as follows: Figure 8-10 Due to the literature

[10] The impact of packet loss in vehicle communication was not considered; it is assumed that random packet loss occurs between seconds 46 and 50. from Figures 8-10 Based on the simulation results, using the literature

[10] The designed controller cannot accurately track the speed and trajectory of the lead vehicle, and the control objective cannot be achieved.

[0070] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments. In the above embodiments of the present invention, the descriptions of each embodiment have their own emphasis; parts not described in detail in a certain embodiment can be referred to in the relevant descriptions of other embodiments. It should be understood that the disclosed technical content in the several embodiments provided in this application can be implemented in other ways.

[0071] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for controlling connected vehicle platooning considering curved road conditions, characterized in that, Includes the following steps: Step 1: Establish a vehicle dynamics model by incorporating factors related to curved roads; Step 2: Considering the data packet loss in vehicle-to-vehicle communication and the delay in vehicle actuators, establish a vehicle queue tracking control system model with switching delay. Step 3: Perform stability analysis on the vehicle queue tracking control system model with switching delay. The establishment of the vehicle platoon tracking control system model first requires the establishment of a nonlinear vehicle model, as follows: （1）； in, Indicates the mass of the vehicle. Represents the vehicle in the vehicle coordinate system longitudinal velocity; and Representing vehicles The horizontal and vertical coordinates in a Cartesian coordinate system; Indicates the moment of inertia; Indicates the angular velocity of the vehicle; Indicates the vehicle's heading angle; Indicates the longitudinal force of the vehicle; Indicates external torque; Indicates the longitudinal equivalent air drag coefficient; Indicates longitudinal wind speed; Represents gravitational acceleration; This indicates the rolling resistance coefficient of the tire; Indicates the road slope angle; Assume the disturbance satisfies the energy bounded condition, i.e. , ,in The 2-norm is used to represent the vehicle platooning control system; the nonlinear vehicle model (1) is linearized to facilitate the establishment of the vehicle platooning control system; the definition is... and Let be the state matrix and input matrix of the nonlinear vehicle model (1), respectively, where The output matrix is ​​obtained by linearizing and decoupling the nonlinear vehicle model (1) into the form of the following subsystems: （2a）； （2b）； （2c）； in, The state matrix represents the matrix after linear processing; This represents the input matrix after linear processing; and This represents the amount of disturbance. and They represent and The coefficient matrix is ​​as follows: （3a）； （3b）； （3c）； （3d）； in: (4); （5）； Use the following for curved roads Represented by a polynomial of order （6）； in, , For different x-coordinates ,curve There exists a unique one. Correspondingly; Represents positive integers; Indicates a constant coefficient. ; Indicates following vehicle Along the curved road The distance traveled along the curve, then Represented as: （7） in: ,set up ,Will Differentiate with respect to time and represent using the state variables defined in equation (2), following the vehicle The vehicle dynamics model under curved road conditions is expressed as follows: （8）； in: Indicates vehicle Speed ​​on a curved road; In the above formula Since equation (8) is nonlinear, it can be expressed as equation (9) by using feedback linearization. （9）； The coordinate transformations and inputs involved in the formula are as follows: （10）； （11） here The control input is introduced to linearize equation (8), and the following relationship exists: ； in: This represents the disturbance obtained after linearizing equation (8); and simultaneously introduces and Variables are used to characterize control inputs and The relationship between them; When a convoy travels on a curved road, to ensure the compactness of the convoy, an error expression is constructed based on the curve distance error between vehicles; [Definition] and Follow each other Then the car The distance error and speed error between the vehicle and the vehicle in front, namely: （12）； in, Indicates following vehicle The distance traveled along a curved road; Indicates following vehicle speed; This represents the ideal vehicle spacing; To represent the distance and speed relationship between the lead vehicle and the following vehicles, we define... and These represent the lead vehicle and the following vehicle, respectively. The distance and speed error between them, i.e.: （13）； in, Indicates the lead vehicle and the following vehicles The ideal workshop spacing between them; Indicates the speed of the lead vehicle; and The quantities corresponding to those in equation (9) represent the speeds of the lead vehicle and the following vehicle in the Cartesian coordinate system, respectively, while in equation (1) Represents the vehicle in the vehicle coordinate system speed; definition , Then the vehicle The state-space description can be represented as: （14）； in: ； ； In formula (14), the following vehicle controller Specifically, it is expressed as follows: （15）； in: This indicates the controller gain to be determined; The error amount that takes into account the impact of data packet loss is defined as: （16）； in, Indicates following vehicle The distance information received from the vehicle ahead; Indicates following vehicle Received speed information of the vehicle ahead; （17）； in, Indicates following vehicle Information received regarding the distance traveled by the lead vehicle; Indicates following vehicle The received speed information of the lead vehicle is defined. , .

2. The connected vehicle queuing control method considering curved road conditions according to claim 1, characterized in that, In the vehicle queue tracking control system model, a switching signal is introduced. To describe whether packet loss has occurred in the system; If the data packet transmission is successful Information transmitted via wireless communication can be used by following vehicles Calculate the vehicle tracking error, and the transmission volume at this time. , , , Right now , When packet loss occurs, According to the zeroing strategy, the information transmitted in wireless communication is zeroed out. Meanwhile, for ease of analysis, a definition is defined... Then the tracking error vector and , and The relationship between them is: （18） in, , .

3. The connected vehicle queuing control method considering curved road conditions according to claim 2, characterized in that, In the vehicle platoon tracking control system model, due to fuel delay and differences in the processing time of information at various control nodes in the control system, there is a delay in the transmission of control signals, or the control signals transmitted to the actuators cannot be immediately read and applied to the controlled object, resulting in actuator delay. A constant is defined. Delay for actuator ; Assumption The actuator reads the control signal at specific times. Due to the delay, the actual control signal executed is: （19）； From equations (12) and (13), the following equation transformations can be obtained: （20）； Simultaneously define: (twenty one) From equations (14) and (19)-(21), we obtain a vehicle queuing tracking control system model with switching and time delay characteristics: （22）； in, Represents state variables; Indicates the amount of disturbance; Indicates the system output; Indicates a switching signal; It is a coefficient matrix; and Represents the gain matrix. When Initial conditions that are continuously differentiable; ； ； ； ； （23）； symbol Indicates the Kronecker product; ,express An identity matrix of order 1. ; .

4. The connected vehicle queuing control method considering curved road conditions according to claim 3, characterized in that, Theorem 1 states: Consider a vehicle platoon tracking control system (22), for a given constant time delay and scalar and disturbance suppression degree If a positive definite matrix exists , Satisfies matrix inequalities: （27） ； in, ; ; ; Then, following the trajectory of system (22), we can obtain (28) in, .

5. A connected vehicle queuing control method considering curved road conditions according to claim 4, characterized in that, In step 3, considering the fleet tracking control system (22), a constant time delay is given. and scalar and disturbance suppression degree If a positive definite matrix exists , constant Meanwhile, the upper limit of packet loss rate is satisfied: Make matrix inequalities (27) and (29) hold. （29） The convoy tracking control system (22) satisfies the following for any dwell time. （30） The switching signal is Robust and stable; and its controller gain is: ; Consider the following vehicle platoon tracking control system: （39） in: express A following vehicle; Indicates a switching signal; It is a state vector; It is an external input; This is system output; yes Initial conditions that are continuously differentiable Indicates actuator delay; As in equation (39) Equilibrium solution at time; If K types of functions exist and Makes it possible for any initial state and any If all of the following equations hold true, then the fleet system (39) is The queue is stable; （40）。

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