A Distributed Model Predictive Control Method for Mixed Vehicle Platoon

Abstract

The present invention discloses a distributed model predictive control method for a mixed vehicle queue. First, the mixed vehicle queue is divided into a plurality of interrelated local mixed vehicle queues; then, based on the following model of the networked autonomous driving vehicle and the human-driven vehicle, the model of each local mixed queue is established; secondly, based on the local mixed queue model, according to the model predictive control algorithm, the overall control problem of the mixed vehicle queue is established; finally, in combination with the alternating direction multiplier method, a distributed model predictive controller is constructed for each local mixed queue to realize the formation control of the mixed vehicle queue as a whole. The effectiveness of the proposed method is verified by conducting experiments on the MATLAB simulation platform. The experimental results show that the present invention can ensure that the networked autonomous driving vehicles and human-driven vehicles in the mixed vehicle queue achieve a good formation effect, and the networked autonomous driving vehicles can travel in formation with a smaller vehicle-to-vehicle distance, which effectively improves the traffic capacity.

Description

Technical Field

[0001] The present invention relates to the fields of autonomous driving, hybrid vehicle platooning, and vehicle networking, and more particularly to a hybrid vehicle platoon distributed model predictive control method based on an alternating direction multiplier method, which is used to implement platoon control of a hybrid vehicle platoon that includes human-driven vehicles and networked autonomous driving vehicles, thereby increasing traffic capacity and reducing resource consumption. Background Art

[0002] With the development of autonomous driving technology, the platooning of connected autonomous vehicles on highways has attracted widespread attention from researchers. Multi-vehicle cooperative platooning control provides a new solution and approach to ensure travel safety, improve traffic capacity and reduce fuel consumption. Vehicle platooning aims to ensure that all vehicles in the same group travel at a common speed while ensuring that the desired inter-vehicle distance between adjacent vehicles is maintained. However, in real traffic environments, it is unrealistic to completely use connected autonomous vehicles for platoon control, because the number of traditional cars controlled by human drivers in the world today is still rising. In the long term, there will be a mixed vehicle platoon system where human-driven vehicles and connected autonomous vehicles coexist. Although with the development of vehicle networking technology, human-driven vehicles in the future mixed vehicle platoon can use wireless communication technologies such as vehicle-to-vehicle (V2V) to share their own status information with the connected autonomous vehicles in the platoon, and the connected autonomous vehicles in the mixed vehicle platoon are both information receivers and can send information to other connected autonomous vehicles. However, this traffic environment with random mixing of human-driven vehicles and connected autonomous vehicles still poses great challenges to the modeling and control of vehicle platoons.

[0003] In response to the above problems, domestic and foreign scholars have conducted a lot of research. Ge et al. analyzed the following behaviors of human-driven vehicles and connected autonomous vehicles in a mixed vehicle queue under non-emergency conditions, and modeled a mixed vehicle queue with only one connected autonomous vehicle following at the end of the queue. Huang et al. considered the situation where there are multiple connected autonomous vehicles in the mixed vehicle queue, and considered the dynamic differences of following between human-driven vehicles and connected autonomous vehicles. They used the optimal speed model and the simplified kinematic model to describe the behaviors of human-driven vehicles and connected autonomous vehicles, respectively, and established a mixed vehicle queue model suitable for a fixed number of vehicles and vehicle order. In the above study, different following models were used for human-driven vehicles and connected autonomous vehicles in the mixed vehicle queue, which can well reflect the dynamics of different vehicles in the mixed vehicle queue. However, the above model is only applicable to mixed vehicle queues with fixed vehicle order or fixed number of vehicles and vehicle order, rather than vehicle queues with random mixture of human-driven vehicles and connected autonomous vehicles.

[0004] The purpose of hybrid vehicle platoon control is to design a vehicle platoon longitudinal motion control system so that the vehicles in the platoon can travel at a common speed while maintaining the set inter-vehicle distance. Common control methods include PID control, sliding mode control, fuzzy control, and intelligent control methods that combine reinforcement learning, artificial neural networks, and other methods. Based on the state of connected autonomous vehicles traveling in a platoon, Chirs et al. designed a nonlinear PID controller for throttle and brake to control vehicle acceleration and braking. However, the selection of PID parameters in the control process is highly dependent on the existing following data. Gao et al. proposed a data-based adaptive dynamic programming optimal control algorithm for the platoon control problem of connected autonomous vehicles. Although the algorithm does not depend on the specific vehicle dynamics model, it also requires a large amount of vehicle motion data. More importantly, the control methods mentioned above cannot handle the control quantity constraints and state quantity constraints during vehicle motion. To this end, some scholars apply model predictive control to the cruise control of connected autonomous vehicles.

[0005] Model predictive control achieves effective control of connected autonomous vehicles by predicting system dynamics, optimizing given objectives, and handling actuators, state constraints, and disturbances. Wu et al. designed a model predictive controller with braking and acceleration delays to ensure that autonomous vehicles can achieve good platooning even with limited sensor range. Maxim et al. used a distributed model predictive control algorithm to ensure that each vehicle in the platoon can follow the preset position trajectory when there is no delay between vehicles. They compared the control effects of controllers that solve unconstrained optimization problems and those that solve optimization problems with added control variable increment constraints. The results showed that the latter has significant performance improvements. Lan et al. proposed a distributed minimum-maximum model predictive control algorithm in the presence of inter-vehicle communication delays and realistic constraints to ensure leader-follower string stability. The proposed control algorithm also reduces the communication burden because each vehicle in the platoon only needs to transmit its current acceleration to the adjacent following vehicle. Although the above-mentioned distributed model predictive controllers have achieved certain results in improving traffic flow platoon control effects and improving road safety, they are all designed based on partial vehicle information in the vehicle platoon, rather than based on the overall control objectives of the vehicle platoon. A mixed vehicle platoon is a complex system with close interactions between vehicles, so it is necessary to develop a distributed model predictive controller that takes into account the overall control indicators of the mixed vehicle platoon.

[0006] Taking the above factors into consideration, the present invention makes the following improvements: First, a new type of mixed vehicle queue model is proposed. Different from the models proposed by Ge et al. and Huang et al., this new type of mixed vehicle queue model can be used to describe the situation of random mixing of networked autonomous driving vehicles and human-driven vehicles, without pre-defining the number of vehicles or vehicle sorting in the mixed vehicle queue; secondly, by introducing the alternating direction multiplier method, the design of the distributed model predictive controller of each local mixed queue is completed under the control target of the overall mixed vehicle queue rather than the control target of each local mixed queue, thereby realizing the overall formation control of the mixed vehicle queue. Summary of the invention

[0007] The present invention proposes a distributed model predictive control method for a mixed vehicle queue. The method is based on the alternating direction multiplier method and the model predictive control algorithm. By designing a distributed model predictive controller for the networked autonomous driving vehicles in the mixed vehicle queue, the distributed formation control of the mixed vehicle queue is effectively realized under the overall control target of the mixed vehicle queue, thereby improving the traffic capacity. The specific implementation steps are as follows:

[0008] Step 1: Divide the mixed vehicle queue into multiple interrelated local mixed vehicle queues

[0009] In real traffic conditions, connected autonomous vehicles and human-driven vehicles are randomly mixed in a mixed vehicle queue. According to the position of the connected autonomous vehicles in the mixed vehicle queue, the mixed vehicle queue can be divided into multiple interconnected local mixed vehicle queues. Each local mixed vehicle queue contains at most two connected autonomous vehicles, which are the head and tail vehicles of the local mixed queue. However, if the head and tail vehicles of the mixed vehicle queue are human-driven vehicles, then the local mixed queues at the head and tail of the mixed vehicle queue will only contain one connected autonomous vehicle. The interconnectedness of the local mixed queues is reflected in the fact that two adjacent local mixed queues will cover the same connected autonomous vehicle.

[0010] Step 2: Establish a local mixed queue model

[0011] In a mixed vehicle platoon, the human-driven vehicle is controlled by the driver based on driving experience, while the networked autonomous driving vehicle is controlled by the distributed model predictive controller designed by the present invention. Therefore, before establishing a local mixed platoon model, it is necessary to first establish a dynamic model of the networked autonomous driving vehicle and the human-driven vehicle in non-emergency situations.

[0012] (1) Establishing a dynamic model of human-driven vehicle following

[0013] In the present invention, the dynamic behavior of human driving a vehicle following can be described by an intelligent driver model, and the model expression is:

[0014]

[0015] Among them, v j Indicates the current speed of vehicle #j; h j represents the current following distance of vehicle #j; a represents the maximum acceleration of the vehicle, b represents the comfortable deceleration of the vehicle; v0 represents the free flow speed; s0 represents the minimum following distance; T j represents the minimum following distance of vehicle #j; l represents the length of vehicle #(j-1). By adjusting the above parameters, the differences in the following dynamics of different human-driven vehicles can be expressed.

[0016] When the mixed vehicle queue reaches equilibrium, the speeds of all vehicles should approach the desired speed v * , combined with formula (1), we can get the equilibrium following distance of human-driven vehicles: The The expression is:

[0017]

[0018] At the system equilibrium point Nearby, define the small error Δh about the following distance and following speed j and Δv j , where Δv j =v j -v * , Further, in By performing Taylor expansion on equation (1) and ignoring high-order terms, we can obtain the linear car-following dynamic model of human-driven vehicles with respect to errors, which is expressed as follows:

[0019]

[0020] in,

[0021]

[0022] (2) Establishing a dynamic model for connected autonomous driving vehicles

[0023] In the present invention, the following dynamic model expression of the networked autonomous driving vehicle is:

[0024]

[0025] Among them, u j Represents the control input of the connected autonomous driving vehicle #j.

[0026] In order to improve the safety of the connected autonomous driving vehicle when driving at different speeds, the connected autonomous driving vehicle in the present invention adopts a spacing policy of constant headway, so the expected following distance of the connected autonomous driving vehicle is The expression is:

[0027]

[0028] Among them, τ j represents the fixed headway of the connected autonomous driving vehicle #j; Indicates the minimum following distance. The model parameters of different connected autonomous driving vehicles can also be different, so that the setting is more in line with the random mixing of vehicles in the actual mixed vehicle queue.

[0029] Referring to the linearization process of the car-following dynamic model of human-driven vehicles, the linear car-following dynamic model of the connected autonomous driving vehicle with respect to error can be obtained, and its expression is shown in the following formula:

[0030]

[0031] (3) Establishing a local mixed queue model

[0032] Assume that the coverage of the i-th local mixed queue in the mixed vehicle queue is from vehicle #(j+1) to #(j+n), let x j =[Δh j Δv j ] T Based on formulas (3) and (6), the local mixed queue model can be established, and its expression is as follows:

[0033] Y i =C c X i (8)

[0034] Here j∈HDV means vehicle #j is a human-driven vehicle, and j∈CAV means vehicle #j is a connected autonomous vehicle.

[0035]

[0036] In summary, the specific expression of formula (7) is related to the specific number of vehicles in the local mixed queue, the vehicle order and the vehicle model parameters, so formulas (7) and (8) can be used to describe the dynamics of any local mixed queue in the mixed vehicle queue.

[0037] Step 3: Establish the mixed vehicle platoon control problem

[0038] In the present invention, we hope to achieve the overall formation control of the mixed vehicle queue by regulating the driving behavior of the networked autonomous driving vehicles. Therefore, the vehicles in the mixed vehicle queue should at least consider the following performance indicators:

[0039] ① The speed of each vehicle in the mixed vehicle queue and the expected speed v * The error between them should be as small as possible;

[0040] ② The following distance and expected following distance of each vehicle in a mixed vehicle queue The error between them should be as small as possible;

[0041] ③ The fuel consumption of connected autonomous vehicles in mixed vehicle platoons is as low as possible during driving;

[0042] At the same time, the following constraints also need to be considered: the safety of connected autonomous vehicles in mixed vehicle queues must be ensured at all times during driving.

[0043] Under the above performance indicators and constraints, the local mixed queue model described in step 2 will be used to establish the overall optimization problem of the mixed vehicle queue.

[0044] By discretizing formulas (7) and (8), we can obtain the prediction model expression of the local mixed queue #i:

[0045]

[0046] Where A = TA c +I;B u =TB cu ; B d =TB cd ; Here T represents the sampling interval; I represents the identity matrix with dimension 2n.

[0047] According to the model predictive control principle, the prediction time domain is set to p, the control time domain is set to m, and m = p. Set the current time to k, and take the k time as the prediction point to establish the prediction output equation of the local mixed queue #i in the p time domain based on the prediction model (9), and its expression is shown as follows:

[0048]

[0049] in,

[0050]

[0051] Assume that there are q connected autonomous vehicles in the local mixed queue #i, and each connected autonomous vehicle should satisfy the control constraint u min ≤u j (k+β|k)≤u max,β=0,…,m-1 and state constraint y min ≤y j (k+α|k)≤y max ,α=1,…,p, then The following relationship should be satisfied:

[0052]

[0053] in, represents the Kronecker product. If A is an a×b matrix and B is a c×d matrix, is an ac×bd matrix; ones(qm,1) is a qm×1 matrix of all ones.

[0054] In order to convert the state quantity constraint into a processable form, the human-driven vehicles in the local mixed queue #i can be made to satisfy the state quantity constraint -inf≤y j (k+α|k)≤inf,α=1,…,p, where -inf and inf represent negative infinity and positive infinity respectively. This is because the human driving behavior is simulated by the intelligent driver model, and the intelligent driver model itself has ensured the vehicle's own following safety. Based on the predicted output equation (10) of the local mixed queue #i in the p time domain, the state quantity of the local mixed queue #i is The following relationship should be satisfied:

[0055]

[0056] in,

[0057]

[0058] Combining formula (10) with further derivation, formula (12) can be written as the following inequality:

[0059]

[0060] In summary, if Ω i is the constraint matrix that the local mixed queue #i should satisfy during the control process, then Ω i It is the intersection of the control quantity constraint (11) and the state quantity constraint (13).

[0061] Based on the prediction output equation (10) of the above local mixed queue #i and the constraint set Ω i , assuming that there are N local mixed queues in the mixed vehicle queue, the cost function of the mixed vehicle queue at time k in the prediction time domain can be obtained, and its expression is:

[0062]

[0063] Among them, Γ y and Γ u are the weight matrices of the state quantity output and control quantity input of the local hybrid queue #i; R i is the reference output matrix.

[0064] Step 4: Construct a distributed model predictive controller based on the alternating direction multiplier method

[0065] Under the algorithm framework of the alternating direction multiplier method, the control problem (14) of the mixed vehicle queue at time k can be solved in parallel by each local mixed queue controller. The specific implementation process is as follows.

[0066] (1) Introducing auxiliary variables And set

[0067] (2) Introducing the dual variable λ i , construct the augmented Lagrangian function, whose function expression is shown as follows:

[0068]

[0069] (3) Alternately optimize variables on the controller of local hybrid queue #i and λ i .

[0070] a. Random initialization and λ i ,get and

[0071] b. Update pass and Calculate new The update rule is as follows:

[0072]

[0073] c. Update The relevant information obtained by updating Calculate the new value of

[0074] Indicates that under the global objective of mixed vehicle platoon control In order to express more intuitively Update rule, assuming p = 1. The two components of are the control inputs of the head and tail vehicles of the local mixed queue #i at time k. According to the way of dividing the mixed vehicle queue into local mixed queues in step 1, it can be seen that the tail vehicle of the local mixed queue #i and the head vehicle of the local mixed queue #(i+1) are the same networked autonomous driving vehicle. Similarly, the tail vehicle of the local mixed queue #(i-1) and the head vehicle of the local mixed queue #i are the same networked autonomous driving vehicle. Therefore, when p = 1, The update rule is as follows. This update rule still applies when P takes any value.

[0075]

[0076] in, express The first component of express The second component of .

[0077] d. Update λ i , the relevant and The new λ is calculated from the value of i ,λ i The update rule is as follows:

[0078]

[0079] e. Determine whether the preset maximum number of iterative calculations has been reached. If so, stop the iteration, and each local mixed queue distributed controller outputs the corresponding control quantity component at time k to act on the connected autonomous driving vehicle at the rear; otherwise, return to step b and continue iterating. BRIEF DESCRIPTION OF THE DRAWINGS

[0080] Figure 1 The speed trajectory of the head vehicle of the mixed vehicle queue provided by the example of the present invention

[0081] Figure 2 Distributed control structure of mixed vehicle platoon provided by the present invention

[0082] Figure 3 The following speed changes of some vehicles in the mixed vehicle queue during the simulation period provided by the example of the present invention

[0083] Figure 4 The following distance changes of some vehicles in the mixed vehicle queue during the simulation period provided by the example of the present invention

[0084] Figure 5 The following acceleration changes of some vehicles in the mixed vehicle queue during the simulation period provided by the example of the present invention

[0085] Figure 6 The change of the cost function value J of the mixed vehicle platoon control provided by the example of the present invention DETAILED DESCRIPTION

[0086] The following will describe the examples of the present invention in detail with reference to the accompanying drawings so that those skilled in the art can better understand the present invention. The examples described below are some examples of the present invention, not all examples. Based on the examples in the invention, all other embodiments obtained by ordinary technicians in the field without creative work should be within the scope of protection of the present invention.

[0087] The example of the present invention simulates the mixed traffic scene and the following behavior of human-driven vehicles therein through the MATLAB simulation platform, and uses MATLAB related functions and statements to build a distributed model predictive controller for controlling networked autonomous driving vehicles. Finally, the data of the mixed vehicle queue obtained by simulation is processed and analyzed to obtain experimental results. The specific implementation steps are described in detail below.

[0088] Step 1: Experimental scenario design

[0089] In this example, a mixed vehicle platoon with a leading vehicle on a single lane is considered, which contains a total of 20 vehicles. The trajectory of the leading vehicle is as follows: Figure 1 In addition, #5, #8, #11, #14, #17, and #20 in the mixed vehicle queue are connected autonomous vehicles, and the rest are human-driven vehicles. In order to better meet the actual traffic conditions, the model parameters of the connected autonomous vehicles and human-driven vehicles in the example are not exactly the same.

[0090] Step 2: Simulation parameter configuration

[0091] First, in the simulation environment, the speed of each vehicle is 0m / s and the distance between vehicles is 6m in the initial state.

[0092] Secondly, the vehicle parameters of the connected autonomous vehicles in the mixed vehicle queue are shown in Table 1, the common parameters of human-driven vehicles are shown in Table 2, and the other different vehicle parameters are shown in Table 3. In addition, during the driving process, the control volume of the 6 connected autonomous vehicles should be within [-5m / s 2 ,1m / s 2 ], the following speed cannot be less than 0m / s, and the following distance cannot be less than 2m.

[0093] Finally, in the distributed model predictive control algorithm, the sampling period T is set to 0.1s; the prediction time domain p is set to 30, and the control time domain m is set to 30; due to the different orders of magnitude of the state quantity and the control quantity, let Γ y :Γ u =1:28.

[0094] Table 1 Parameters of connected autonomous driving vehicles

[0095]

[0096] Table 2 Common parameters of human-driven vehicles

[0097]

[0098] Table 3 Other parameters of human-driven vehicles

[0099]

[0100] Step 3: Construction and solution of distributed model predictive controller

[0101] In this example, according to the positions of the six connected autonomous vehicles, the mixed vehicle queue of 20 vehicles can be divided into six local mixed vehicle queues, that is, six distributed model predictive controllers need to be built for the six connected autonomous vehicles. The schematic diagram is shown in the figure. Figure 2 As shown in Figure 2, since the construction process of the six distributed model predictive controllers is consistent at each discrete control step, only how to construct the distributed model predictive controller C2 at the initial time t = 0s is described in detail here.

[0102] (1) Establish a model of local mixed queue #2.

[0103] like Figure 2 As shown, the local mixed queue #2 includes cars #5, #6, #7, and #8, and its head car is car #4. The model expression of the local mixed queue #2 is as follows:

[0104]

[0105] For a mixed vehicle platoon with a leading vehicle, its expected speed v * is equal to the real-time speed v1 of the leading vehicle. * =v1=0m / s, combined with the vehicle parameters of #6 and #7 set in step 2, we can get k 1,6 =k 1,7 =1; k 2,6 =k 2,7 =0; k 3,6 =k 3,7 =-1.6. Combining the vehicle parameters of #5 and #8, we can get τ5 = 1s; τ8 = 1.2s. In summary, the correlation matrix expression in the above model expression can be obtained as:

[0106]

[0107] b5=[-1 1] T ,b8=[-1.2 1] T ,b6=b7=[0 0] T ,u5=u5,u8=u8,u6=u7=0

[0108] (2) Establishing the mixed vehicle platoon optimization problem

[0109] By discretizing the model of the local mixed queue #2 obtained above, its prediction model expression can be obtained:

[0110]

[0111] in,

[0112] A=TA c +I,B u =TB cu ,B d =TB cd ,C c =I 8×8

[0113] Furthermore, when m=p=30, the prediction output equation of the local mixed queue #2 in the p time domain at the initial moment can be obtained, and its expression is shown in the following equation:

[0114]

[0115] in,

[0116]

[0117] Similarly, after obtaining the prediction output equations of all other local mixed queues, the cost function of the mixed vehicle queue at the initial moment in the prediction time domain can be written, and its expression is shown in the following formula:

[0118]

[0119] (3) Determine the constraint matrix Ω2 that the local mixed queue #2 should satisfy during the control process

[0120] First, by Figure 2 It can be seen that there are two connected autonomous vehicles in the local mixed queue #2. Combined with the relevant experimental parameters set in step 2, we can get The following relationship should be satisfied:

[0121]

[0122] Similarly, the state of local mixed queue #2 The following relationship should be satisfied:

[0123]

[0124] Substituting the relevant experimental parameters set in step 2 into formula (12), we can obtain:

[0125]

[0126] Combining equation (21) with further derivation, equation (24) can be written as the following inequality:

[0127]

[0128] In summary, the intersection of equation (23) and equation (25) is the constraint matrix Ω2 that the local hybrid queue #2 should satisfy during the control process.

[0129] (4) Based on the alternating direction multiplier method, minimize the overall control cost of the mixed vehicle platoon

[0130] 4.1 Introducing auxiliary variables And set

[0131] 4.2 Introducing the dual variable λ i , construct the augmented Lagrangian function, whose function expression is shown as follows:

[0132]

[0133] 4.3 Alternating optimization variables on the controller of local hybrid queue #i and λ i The specific process is now described by still taking the local mixed queue #2 as an example.

[0134] a. Random initialization and λ2:

[0135] b. Update according to formula (16)

[0136]

[0137] Here, let ρ2 = 1; Solving equation (27) yields The specific value of .

[0138] c. Update according to formula (17)

[0139] Similarly, we can calculate The value of Some of the values ​​are shown below.

[0140]

[0141] according to The value of The update rule (17) can be used to To update, The update is as follows:

[0142]

[0143] d. Update λ2 according to formula (18):

[0144]

[0145] The above steps are a complete iterative solution process of the distributed model predictive controller C2 of the local hybrid queue #2. Repeat the above iterative solution process until the maximum number of iterative solutions N is reached. max =3, controller C2 output The second component u8(k) acts on car #8. At the same time, the distributed model predictive controller C of other local mixed queues i ,i=1,…,6 also outputs the corresponding control amount component to act on the connected autonomous driving vehicle at the tail of the local mixed queue. At the next control moment, repeat the above steps until the simulation ends.

[0146] Step 4: Experimental results

[0147] Figure 3-5 The platooning effect of some vehicles in the mixed vehicle queue in this example under the action of the distributed model predictive controller is shown. Figure 3 , Figure 4 and Figure 5 The following speed change diagram, following distance change diagram and following acceleration change diagram of vehicles #1, #4, #5, #19 and #20 during the formation process are shown respectively. The dotted line in the figure depicts the behavior trajectory of the connected autonomous driving vehicle, and the solid line depicts the behavior trajectory of the human-driven vehicle. Figure 3 It shows that when the speed of vehicle #1 reaches stability, the connected autonomous vehicles in the mixed vehicle platoon can also reach the same equilibrium speed; Figure 4 It shows that during the following process, the connected autonomous driving vehicle always maintains an appropriate following distance with the vehicle in front, and its following distance and following distance overshoot are much smaller than those of human-driven vehicles, which is conducive to improving traffic capacity; moreover, Figure 3-5 This shows that the connected autonomous driving vehicle did not violate the pre-set control quantity constraints and safety constraints on following speed and following distance during the following process. Figure 6 It represents the change of the control cost function value of the mixed vehicle platoon as a whole during the simulation. Figure 6It shows that when the speed of vehicle #1 gradually stabilizes, the J value will gradually decrease to 0, which means that the overall control target of the mixed vehicle queue in this example is achieved. In summary, the distributed model predictive control method proposed in the present invention realizes the formation control of the mixed vehicle queue and improves the road traffic capacity.

Claims

1. A distributed model predictive control method for mixed vehicle platoons, Features: The method consists of four parts: first, according to the position of the networked autonomous driving vehicles in the mixed vehicle queue, the mixed vehicle queue is divided into multiple interrelated local mixed vehicle queues; second, based on the kinematic model of the intelligent networked vehicle and the human-driven vehicle, each local mixed queue model is established, and the model is expressed in a unified form; third, based on multiple local mixed queue models, according to the model predictive control algorithm, the overall control problem of the mixed vehicle queue is established; fourth, based on the alternating direction multiplier method, a distributed model predictive controller is constructed for each local mixed queue in the mixed vehicle queue to realize the overall formation control of the mixed vehicle queue; In the mixed vehicle queue, connected autonomous vehicles and human-driven vehicles are randomly mixed, and human-driven vehicles can also share their movement information with connected autonomous vehicles through their own wireless vehicle-connected devices; each local mixed vehicle queue divided according to the spatial positions of connected autonomous vehicles contains at most two connected autonomous vehicles, namely the head vehicle and the tail vehicle of the local mixed vehicle queue; if the head vehicle and the tail vehicle of the mixed vehicle queue are human-driven vehicles, then the local mixed queues at the head and tail of the mixed vehicle queue only contain one connected autonomous vehicle; the mutual correlation of local mixed queues in the mixed vehicle queue is reflected in that two adjacent local mixed queues will cover the same connected autonomous vehicle; The local mixed platoon model is designed as follows: First, the following behavior of human-driven vehicles in the mixed vehicle platoon can be described by an intelligent driver model, and the model expression is: Among them, v j Indicates the current speed of vehicle #j; h j represents the current following distance of vehicle #j; a represents the maximum acceleration of the vehicle, b represents the comfortable deceleration of the vehicle; v 0 represents the free flow speed; s 0 Indicates the minimum following distance; T j represents the minimum following distance of vehicle #j; l represents the length of vehicle #(j-1); by adjusting the above parameters, the differences in the following dynamics of different human-driven vehicles can be reflected; At the system equilibrium point Nearby, define Δv j =v j -v * , And by linearizing equation (1), we get the linear car-following dynamic model of human driving vehicle with respect to error, which is expressed as follows: in, Secondly, the following dynamic model expression of the connected autonomous driving vehicle in the mixed vehicle platoon is designed as follows: Among them, u j represents the control input of the connected autonomous driving vehicle #j; since the connected autonomous driving vehicle adopts a spacing policy of constant headway, its expected following distance is The expression is: Among them, τ j represents the fixed headway of the connected autonomous driving vehicle #j; Indicates the minimum following distance; the model parameters of different connected autonomous driving vehicles are different; Referring to the linearization process of the car-following dynamic model of human-driven vehicles, the linear car-following dynamic model of the connected autonomous driving vehicle with respect to error can be obtained, and its expression is shown in the following formula: Finally, assuming that the local mixed queue #i covers vehicles #(j+1) to #(j+n) in the mixed vehicle queue, let x j =[Δh j Δv j ] T Based on formulas (2) and (5), the model expression of the local mixed queue #i can be designed as: Y i =C c X i (7) Where j∈HDV means that vehicle #j is a human-driven vehicle, j∈CAV means that vehicle #j is a connected autonomous vehicle, and The establishment of the local mixed queue #i model is based on the linear following dynamic model of the connected autonomous vehicles and human-driven vehicles in the local mixed queue #i. That is to say, the specific expression of the local mixed queue #i model needs to be determined according to the specific number of vehicles in the local mixed queue #i, the vehicle order and the relevant vehicle model parameters; Assuming that there are N local mixed queues in the mixed vehicle queue, the control problem of the mixed vehicle queue at time k is designed as follows: First, discretize formulas (6) and (7) to obtain the prediction model expression of the local mixed queue #i: Where A = TA c +I;B u =TB cu ; B d =TB cd ; Here T represents the sampling interval; I represents the identity matrix with dimension 2n; Secondly, let the prediction time domain p be equal to the control time domain m. According to the model predictive control algorithm, take time k as the prediction point and establish the prediction output equation of the local mixed queue #i in the p time domain based on the prediction model (8). Its expression is shown in the following formula: in, Finally, based on the prediction output equation (9) of the local mixed platoon #i, the control problem of the mixed vehicle platoon at time k can be written as follows: Among them, Γ y and Γ u are the weight matrices of the state quantity output and control quantity input of the local hybrid queue #i; R i is the reference output matrix; Ω i is the constraint matrix that the local hybrid queue #i should satisfy during the control process; Assume that there are q connected autonomous vehicles in the local mixed queue #i, and the constraint matrix Ω i The design is as follows: First, the control quantity constraint of the local mixed queue #i is designed as shown in the following formula: in, represents the Kronecker product. If A is an a×b matrix and B is a c×d matrix, is an ac×bd matrix; ones(qm,1) is a qm×1 matrix of all 1s; u min and u max They are the upper and lower bounds of the control quantity constraint range of the connected autonomous driving vehicle at each control step; Secondly, the state constraint of the local mixed queue #i is designed as follows: Among them, y min and max are the upper and lower bounds of the state quantity constraints of the connected autonomous driving vehicle and the human-driven vehicle on the following vehicle speed error and following vehicle spacing error at each control step, and: Combining formula (9) with further derivation, formula (12) can be written as the following inequality: Finally, taking the intersection of the control quantity constraint (11) and the state quantity constraint (13), we can obtain the constraint matrix Ω that the local mixed queue #i should satisfy during the control process: i ; The process of constructing a distributed model predictive controller for a local mixed queue based on the alternating direction multiplier method is as follows: a. Introducing auxiliary variables And set b. Introducing the dual variable λ i , construct the augmented Lagrangian function, whose function expression is shown as follows: c. Alternately optimize variables on the distributed model predictive controller of each local hybrid queue and λ i , until the preset maximum number of iterative calculations is reached, each local hybrid queue distributed controller outputs the corresponding control quantity component at time k to act on the connected autonomous driving vehicle at the rear; Simultaneously and alternately optimizing variables on a distributed model predictive controller for each local hybrid queue and λ i , alternately optimize the variables on the controller of the local hybrid queue #i and λ i The process is as follows: a. Random initialization and λ i ,get and b. Update pass and Calculate new The update rule is as follows: c. Update Updated related Calculate the new value of According to the way that mixed vehicle queues are divided into local mixed queues, the head vehicle and the tail vehicle of local mixed queue #i are also the tail vehicle of local mixed queue #(i-1) and the head vehicle of local mixed queue #(i+1) respectively; in order to express it more intuitively Update rule, assuming that the prediction time domain p = 1, then The two components of are the control inputs of the head and tail vehicles of the local mixed queue #i at time k; therefore, when p = 1, The update rule is as follows; this update rule still applies when P takes any value; in, express The first component of express The second component of d. Update λ i , the relevant and The new λ is calculated from the value of i ,λ i The update rule is as follows: e. Determine whether the preset maximum number of iterative calculations has been reached. If so, stop the iteration, and each local mixed queue distributed controller outputs the corresponding control quantity component at time k to act on the connected autonomous driving vehicle at the rear; otherwise, return to step b and continue iterating.

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