Data-driven model predictive control method for connected vehicle platooning system

Abstract

The present invention discloses a data-driven model predictive control method for a connected vehicle platoon system, comprising: obtaining motion datasets of different vehicle types in the vehicle platoon system; performing data-driven modeling of the longitudinal dynamics of vehicles in the platoon using deep learning and Koopman operator theory to obtain a data-driven model; determining a communication topology and system control objectives; and designing a distributed model predictive control algorithm based on the data-driven model to implement controller design, ultimately achieving the desired stable driving of the vehicle platoon system. The present invention avoids solving non-convex optimization problems caused by nonlinear model constraints.

Description

Technical Field

[0001] The present invention relates to the technical field of connected vehicle platoon systems, and in particular to a data-driven model predictive control method for connected vehicle platoon systems. Background Art

[0002] With the rapid development of artificial intelligence and information and communications technology, the two major technologies of "intelligence" and "connectivity" are converging in the automotive field. Connected vehicle platooning is an advanced autonomous driving technology that uses vehicle networking technology to enable multiple vehicles to travel in a platoon in an efficient and safe manner. This can significantly improve traffic efficiency, enhance road safety, and reduce fuel consumption.

[0003] In recent years, research on connected vehicle platooning has yielded significant results. Given its advantages in handling multi-constrained optimization and complex systems, model predictive control (MPC) has become a mainstream technology for controlling connected vehicle platooning systems. However, most current research requires the establishment of specific vehicle models through first-principles analysis. In practice, vehicle models are complex and nonlinear, making accurate modeling difficult. Furthermore, some studies have employed linearization techniques to approximate the system model to facilitate controller design, sacrificing some nonlinear characteristics and resulting in poor control performance.

[0004] With the rapid development of artificial intelligence technology in various fields, data-driven control has gradually become a research hotspot. For controlled systems, with sufficient data support, an accurate data-driven model can be constructed through machine learning technology. For nonlinear systems, most data-driven modeling methods can obtain a highly accurate nonlinear model. However, it should be noted that for MPC algorithms, nonlinear models as model constraints also mean nonconvex optimization problems. Compared to solving convex optimization problems under linear model constraints, solving a nonconvex optimization problem requires more time with the same computing power, which reduces the real-time performance of control. Summary of the Invention

[0005] To address the problems existing in the prior art, the present invention aims to provide a data-driven model predictive control method for a connected vehicle platoon system. By combining Koopman operator theory with deep learning, the present invention reconstructs a nonlinear model into a high-dimensional linear data-driven model. A distributed MPC algorithm is then designed, targeting nonlinear controlled systems. However, when solving the MPC optimization problem, the model constraints are based on the reconstructed linear model, avoiding the non-convex optimization problem caused by the nonlinear model constraints.

[0006] To achieve the above objectives, the present invention adopts a technical solution: a data-driven model predictive control method for a connected vehicle platoon system, comprising the following steps:

[0007] Step 1: Obtain motion datasets of different vehicle types in the vehicle platoon system;

[0008] Step 2: Combine deep learning and Koopman operator theory to perform data-driven modeling on the longitudinal dynamics of vehicles in the vehicle platoon to obtain a data-driven model;

[0009] Step 3: Determine the communication topology and system control objectives;

[0010] Step 4: Based on the data-driven model, design a distributed model predictive control algorithm, implement controller design, and ultimately achieve the desired target vehicle platoon system to maintain stable driving.

[0011] As a further improvement of the present invention, the step 1 is specifically as follows:

[0012] Depending on the type of vehicle, corresponding sensors and acquisition units are deployed to collect the corresponding speed, position, acceleration and engine torque data; at the same time, data cleaning is completed, noisy data is smoothed, missing values ​​and outliers are processed to ensure data quality and consistency. Data cleaning includes deleting irrelevant data and duplicate data.

[0013] As a further improvement of the present invention, the step 2 is specifically as follows:

[0014] For a vehicle queue traveling on a straight road, there is a manned vehicle and N self-driving connected vehicles. For the connected vehicles, the state of the i-th vehicle at time k is defined as x i (k)=[p i (k),v i (k),a i (k)] T , where p, v, and a represent the position, velocity, and acceleration information of the vehicle, respectively; thus, the nonlinear longitudinal dynamic model of the vehicle is written in discrete form as shown in formula (1):

[0015] x i (k+1)=f i (x i (k),u i (k)) (1)

[0016] Where u represents the control input, which is the braking / driving torque of the vehicle; f is an unknown nonlinear function; the Koopman operator theory is used to reconstruct the nonlinear model into a linear model in a high-dimensional space, as shown in formula (2):

[0017] zi (k+1)=K i (z i (k),u i (k)) (2)

[0018] in:

[0019] z i (k) = g i (x i (k))

[0020]

[0021] Approximate the Koopman operator K by fitting a matrix through a neural network i , and at the same time seek suitable eigenfunction g and mapping transformation g by training network parameters -1 .

[0022] As a further improvement of the present invention, the neural network includes an encoding network, a prediction network, and a decoding network; wherein the encoding network upgrades the state quantity from the original space to a high-dimensional space, and its input-output relationship is shown in the following formula (3):

[0023]

[0024] The encoding network input is the original state quantity, which is output through a multi-layer fully connected network. en are the corresponding weight and bias network parameters; the final output z of the entire encoding network i (k) The original state and the multi-layer network output are concatenated into a tensor;

[0025] The prediction network is implemented in a high-dimensional space. As time evolves, the state of the reconstructed model changes. The input-output relationship of the prediction network is shown in formula (4):

[0026]

[0027] Among them F i is a finite-dimensional matrix, is an approximation of the Koopman operator, let F i =[A i ,B i ], the corresponding θ A ,θ B To predict the parameters of the network, the network weights and biases are also included;

[0028] Finally, the decoding network maps the state quantity in the high-dimensional space back to the original space, and its input-output relationship is shown in formula (5):

[0029]

[0030] where θ de To decode the parameters of the network, input the high-dimensional state z i (k), through the multi-layer fully connected network output, the original state quantity x is finally obtained i (k), define the C matrix to represent this process.

[0031] As a further improvement of the present invention, the linear model reconstructed in high-dimensional space is obtained according to the parameters of the network as shown in formula (6):

[0032]

[0033] The loss function uses a multi-step loss function. After a given data set, the output of a network with a length of m is first calculated, as shown in formula (7):

[0034]

[0035] F i m {z i (k)} represents the state information at time k+m obtained by advancing m time steps back at time k; then, the loss function shown in formula (8) is defined in the form of mean square error to describe the error of the network's prediction of future state variables:

[0036]

[0037] In order to make the network have higher precision encoding and decoding performance, the loss function shown in formula (9) is defined to describe the reconstruction error loss after encoding:

[0038]

[0039] In order to make the system have better linear evolution ability in high-dimensional linear space after reconstruction, the loss function shown in formula (10) is given:

[0040]

[0041] In order to ensure the robustness of the algorithm, the loss function shown in formula (11) is given:

[0042]

[0043] Based on the given loss function, the loss function of the entire network is shown in formula (12):

[0044]

[0045] For θ en and θ deThe penalty is to prevent overfitting, and α1 to α6 are discount factors.

[0046] As a further improvement of the present invention, in step 3, the system control goal is to hope that all vehicles in the queue maintain a desired spacing and travel at a uniform speed. The specific mathematical expression is shown in formula (13):

[0047]

[0048] where d des is the desired vehicle spacing, a constant spacing strategy is adopted, and N is the number of connected vehicles;

[0049] Based on the control objective, the communication topology is designed as a unidirectional topology in which the following vehicle only receives the status information of the preceding vehicle.

[0050] As a further improvement of the present invention, the step 4 is specifically as follows:

[0051] According to the control objective, for any vehicle in the queue, an MPC optimization problem is established based on the status information of its neighboring vehicles, and the model constraint is a data-driven model;

[0052] In each discrete cycle, the vehicle receives state information from neighboring vehicles, solves the optimization problem, and obtains the optimal control quantity sequence and the optimal state quantity sequence. At the same time, the vehicle sends the local optimal state information to neighboring vehicles.

[0053] Finally, the first one of the optimal control sequence is used as the actual control, and this cycle is repeated to eventually achieve the safe driving of the vehicle queue according to the desired goal.

[0054] As a further improvement of the present invention, according to the control target, the following distributed MPC optimization problem F is established at time t: i :

[0055]

[0056] where N p represents the prediction time domain, It represents the state quantity at time t+k predicted at time t; x ref (k|t) is the state trajectory of the manned vehicle; constraints (14a) and (14b) are the constraints of the data-driven model, and (14c), (14d) and (14e) are the constraints of the state and control variables;

[0057] Represents the hypothetical state information of the neighboring nodes that establish communication with node i, through a set Represents the set of all vehicle nodes that establish communication links with i; specifically is given by formula (15):

[0058]

[0059] Solve the optimization problem to obtain an optimal control sequence at time t The corresponding optimal state sequence is expressed as Finally, only use It is used as the actual control quantity at time t, and the rolling optimization continues at time t+1.

[0060] The beneficial effects of the present invention are:

[0061] Connected vehicle platooning is an advanced autonomous driving technology, and its main goal is to enable multiple vehicles to travel in a platoon in an efficient and safe manner, thereby improving traffic efficiency, enhancing road safety, and reducing fuel consumption. The present invention proposes a control algorithm that combines data-driven modeling with distributed MPC. First, a data-driven model of the vehicle is established using deep Koopman operator technology, and then the distributed MPC optimization problem is constructed using this model. The control input is obtained by calculation and solution, solving the problem of maintaining the desired distance and speed tracking on the straight line of the vehicle platoon. Compared with existing methods, the vehicle model is fitted by a neural network based on deep Koopman operator technology, avoiding the modeling difficulties and inaccuracies brought by first-principles modeling while realizing the reconstruction of the vehicle nonlinear model and the design of a distributed controller for the platoon system; simulation results show that the designed method can achieve the control target. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 This is a block diagram of the Koopman operator theory principle in an embodiment of the present invention;

[0063] Figure 2 This is a network structure diagram of the Koopman operator theory implemented by deep learning in an embodiment of the present invention;

[0064] Figure 3 This is a diagram showing the change process of the neural network loss function in an embodiment of the present invention;

[0065] Figure 4 A comparison diagram of the fitting effect of the vehicle data driven model position quantity and the nonlinear model in an embodiment of the present invention;

[0066] Figure 5 A comparison diagram of the fitting effect of the vehicle data driven model speed quantity and the nonlinear model in an embodiment of the present invention;

[0067] Figure 6 A comparison diagram of the fitting effect of the acceleration metric of the vehicle data-driven model and the nonlinear model in an embodiment of the present invention;

[0068] Figure 7 This is a flow chart for implementing a distributed MPC algorithm in an embodiment of the present invention;

[0069] Figure 8 This is a simulation effect diagram of distributed MPC control based on a data-driven model in an embodiment of the present invention. DETAILED DESCRIPTION

[0070] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0071] Example 1

[0072] A data-driven model predictive control method for a connected vehicle platoon system includes the following steps:

[0073] Step 1: Obtain the motion dataset of different vehicle types in the vehicle platooning system.

[0074] Step 2: Combine deep learning and Koopman operator theory to perform data-driven modeling of the longitudinal dynamics of vehicles in the vehicle platoon.

[0075] Step 3: Determine the communication topology and system control objectives.

[0076] Step 4: Based on the data-driven model, design a distributed model predictive control (DMPC) algorithm and implement the controller design to ultimately achieve the desired target stable driving of the platoon system.

[0077] In step 1, the movement data of different types of vehicles in the vehicle platoon system are obtained as follows:

[0078] Depending on the vehicle type, appropriate sensors and acquisition units are deployed to collect speed, position, acceleration, and engine torque data. Data cleaning involves removing irrelevant and duplicate data, smoothing noisy data, and processing missing and outliers to ensure data quality and consistency.

[0079] As a further improvement of the present invention, in step 2, deep learning and Koopman operator theory are combined to perform data-driven modeling of the longitudinal dynamics of vehicles in the vehicle platoon, as follows:

[0080] For a vehicle platoon traveling on a straight road, there is a manned leader vehicle (numbered 0) and N autonomous connected vehicles (numbered 1 to N). For the connected vehicles, the state of the i-th vehicle at time k is defined as x i (k)=[p i (k),v i (k),a i (k)] T, where p, v, and a represent the position, velocity, and acceleration information of the vehicle, respectively. Therefore, the nonlinear longitudinal dynamic model of the vehicle can be written into the discrete form shown in Equation (1).

[0081] x i (k+1)=f i (x i (k),u i (k)) (1)

[0082] Where u represents the control input, which is the vehicle's braking / driving torque. f is an unknown nonlinear function. Using the Koopman operator theory, the above nonlinear model is reconstructed into a linear model in a high-dimensional space, as shown in Equation (2).

[0083] z i (k+1)=K i (z i (k),u i (k)) (2)

[0084] in

[0085] z i (k) = g i (x i (k))

[0086]

[0087] Koopman operator theory implementation framework is as follows Figure 1 As shown, z in high-dimensional space i The state quantity x in the original space i Through mapping changes, in Koopman operator theory, this transformation is achieved through the eigenfunctions g, which is a linear combination of the characteristic functions of the Koopman operator. At the same time, in order to obtain the state quantity x(t) of the original space, it is only necessary to use the mapping transformation g -1 , this mapping transformation is called Koopman modes. i is the Koopman operator, specifically K i is a nonlinear function f i In the corresponding representation in high-dimensional space, the dimension of the Koopman operator is often very large or even infinite in dimension. In this case, a finite-dimensional matrix is ​​needed to approximate it. In particular, after the model is reconstructed, for the control input u i The key to the Koopman operator theory is to find a suitable eigenfunction g and then solve the approximation of the Koopman operator based on empirical data.

[0088] For controlled systems, the traditional approach is to use the Extended Mode Decomposition (EDMD) method to solve the least squares solution based on empirical data to approximate the Koopman operator. This embodiment combines deep learning and EDMD methods to construct a nonlinear model of vehicle longitudinal motion. Specifically, a matrix is ​​fitted through a neural network to approximate the Koopman operator, and the appropriate eigenfunction g and Koopmanmodesg are found by training the network parameters. -1 , the network structure is as follows Figure 2 As shown in Figure 2, the entire network consists of three parts: the encoder network (Encoder), the prediction network (Predict), and the decoder network (Decoder). The encoder network upgrades and reconstructs the state quantity from the original space to a high-dimensional space. Its input-output relationship is shown in the following formula (3).

[0089]

[0090] The encoding network input is the original state quantity, which is output through a multi-layer fully connected network, θ en are the corresponding weight and bias network parameters. Finally, the output z of the entire encoding network is i (k) The original state and the multi-layer network output are concatenated into a tensor.

[0091] The prediction network is implemented in high-dimensional space. As time evolves, the state transformation process of the reconstructed model is carried out. The input-output relationship of the prediction network is shown in formula (4).

[0092]

[0093] Among them F i is a finite-dimensional matrix, which is an approximation of the Koopman operator. In order to facilitate the design of the controller, let F i =[A i ,B i ], so the corresponding one is θ A ,θ B To predict the parameters of the network, the network weights and biases are also included.

[0094] Finally, the decoding network maps the state quantity in the high-dimensional space back to the original space, and its input-output relationship is shown in formula (5).

[0095]

[0096] where θ de To decode the parameters of the network, input the high-dimensional state z i (k), through the multi-layer fully connected network output, the original state quantity x can be finally obtainedi (k), define the C matrix to represent this process.

[0097] At this point, based on the parameters of the above network, the linear model reconstructed in high-dimensional space can be obtained as shown in formula (6).

[0098]

[0099] In order to achieve higher fitting accuracy of the network, the loss function uses the multi-step loss function (MSE). After a given data set, we first need to calculate the output of a network with a length of m, as shown in formula (7).

[0100]

[0101] F i m {z i (k)} represents the state information at time k + m obtained by moving m time steps forward at time k. Then, the loss function shown in Equation (8) is defined in the form of mean square error to describe the error of the network's prediction of future state variables.

[0102]

[0103] In particular, in order to make the network have higher precision encoding and decoding performance, the loss function shown in formula (9) is defined to describe the reconstruction error loss after encoding.

[0104]

[0105] In order to make the system have better linear evolution ability in high-dimensional linear space after reconstruction, the loss function shown in formula (10) is given.

[0106]

[0107] In order to ensure the robustness of the algorithm, the loss function shown in formula (11) is given.

[0108]

[0109] Based on the loss function given above, the loss function of the entire network is shown in formula (12).

[0110]

[0111] For θ en and θ de The penalty is to prevent overfitting, and α1 to α6 are discount factors.

[0112] In step 3, the communication topology and system control objectives are determined as follows:

[0113] The control objective is to hope that all vehicles in the queue maintain the desired spacing and travel at a constant speed. The specific mathematical expression is shown in formula (13).

[0114]

[0115] where d des To achieve the desired vehicle spacing, a constant spacing strategy is adopted.

[0116] Therefore, based on this control goal, the communication topology is designed as a PF topology. As one of the most basic topologies of the connected vehicle platoon system, the PF topology is a unidirectional topology, where the rear vehicle only receives status information from the front vehicle.

[0117] In step 4, based on the data-driven model, a distributed model predictive control (DMPC) control algorithm is designed to implement the controller design, ultimately achieving the desired target stable driving of the platoon system, as follows:

[0118] According to the control objective (13), the following distributed MPC optimization problem F can be established at time t: i

[0119]

[0120] where N p represents the prediction time domain, It represents the state quantity at time t+k predicted at time t. ref (k|t) is the leader vehicle's state trajectory. Constraints (14a) and (14b) are model constraints, which are the data-driven model trained in step 2. (14c), (14d), and (14e) are constraints on the state and control variables.

[0121] Represents the hypothetical state information of the neighboring nodes that establish communication with node i, through a set Represents the set of all vehicle nodes that establish communication links with i; specifically is given by formula (15):

[0122]

[0123] Solving the above optimization problem can obtain an optimal control sequence at time t The corresponding optimal state sequence can be expressed as Finally, only use Used as the actual control quantity at time t, and at time t+1, rolling optimization continues. The distributed MPC algorithm implementation process is as follows Figure 7 shown.

[0124] This embodiment first combines deep learning and Koopman operator technology to reconstruct the nonlinear vehicle model into a linear model in a high-dimensional space by training network parameters, and at the same time realizes data-driven modeling of this linear model, and then constructs a distributed MPC optimization problem based on the model. In each control cycle, the local node only needs to collect the state information of the neighboring nodes with which it communicates to solve its own optimization problem, thereby ultimately achieving the control target of the connected vehicle fleet. Compared with existing methods, the model used realizes end-to-end modeling based on a large amount of data, avoiding the modeling difficulties and inaccuracies brought about by first-principles modeling, and avoiding the solution of non-convex optimization problems brought about by nonlinear model constraints. Simulation results show that the designed method can achieve the control target.

[0125] Example 2

[0126] A data-driven model predictive control method for a connected vehicle platoon system, comprising:

[0127] A. Obtain vehicle motion dataset:

[0128] Given a vehicle platoon, consisting of a manned leader vehicle numbered 0, and five unmanned connected vehicles, numbered 1 to 5 from right to left, all vehicles are assumed to be isomorphic.

[0129] First, a single vehicle of the same model in the platoon system is simulated to drive irregularly on a 100-m straight lane according to the nonlinear model shown in Equation (16), thereby generating 10,000 sets of random position, velocity, acceleration, and starting or braking torque data sets.

[0130]

[0131] Where p(t), v(t), and a(t) represent the position, velocity, and acceleration of the vehicle, respectively. c(t) is the starting or braking torque and is also the control input. τ is the engine inertia delay. Q is the air density. M, A, and C are the vehicle's starting or braking torques and are also the control inputs. d and d m denote the mass, cross-sectional area, damping coefficient and mechanical resistance of the vehicle respectively, Indicates air resistance. Specific parameter values ​​are shown in Table 1 below.

[0132] Table 1. Vehicle parameters

[0133]

[0134] B. Network construction and training:

[0135] The simulation is implemented based on Python and Pytorch deep learning framework Figure 2 The network structure is shown in Table 2.

[0136] Table 2. Network parameters

[0137]

[0138] For neural network training, the Adam optimizer is used instead of the traditional gradient descent algorithm and NVIDIA's CUDA platform to iteratively train the network. For the data in step A, 60% of the data in the dataset is selected as the training set, 20% of the data is used as the validation set, and 20% of the data is used as the test set. The final network training loss and validation loss change process is as follows Figure 3 As shown in the figure, the final loss function approaches 0 infinitely and there is no overfitting. Finally, the trained model is saved locally.

[0139] C. Model Validation

[0140] In order to verify the degree of fit between the trained model and the original nonlinear model, a set of data is randomly extracted from the test set as the input of the training model and the input of the original nonlinear model respectively. The comparison effect of the position is as follows: Figure 4 As shown, the speed comparison effect is as follows Figure 5 As shown, the same acceleration comparison effect is as follows Figure 6 As shown in the figure, the trained model can achieve a relatively accurate fit for the nonlinearities of position, velocity, and acceleration. Theoretically, achieving a more accurate fit requires more data, and the data must be free of noise.

[0141] D. Distributed MPC algorithm simulation implementation:

[0142] Based on the distributed optimization problem shown in formula (14), the distributed MPC algorithm implementation flow chart is as follows: Figure 7 As shown. The discrete period is 0.1s, and the prediction time domain length N in the algorithm p =20, using the constant spacing strategy, the expected vehicle spacing d des =5m, where the leader vehicle maintains a constant speed at an initial speed of 10m / s. max =-u min =6. Finally, as the optimization progresses, the specific algorithm implementation process is as follows Figure 7 As shown, the CVXPY solver is used to solve the MPC optimization problem, and the final simulation diagram is as follows Figure 8As shown in the figure, the position and speed change curves, position error and speed error change curves of the five vehicles are simulated respectively. Finally, the five vehicles follow the leader vehicle with a distance of 5m and a uniform speed of 10m / s.

[0143] The above-described embodiments merely represent specific implementations of the present invention. While the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, and all such variations and improvements fall within the scope of protection of the present invention.

Claims

1. A data-driven model predictive control method for a connected vehicle platoon system, characterized in that: The following steps are involved: Step 1: Obtain motion datasets of different vehicle types in the vehicle platoon system; Step 2: Combine deep learning and Koopman operator theory to perform data-driven modeling on the longitudinal dynamics of vehicles in the vehicle platoon to obtain a data-driven model; The step 2 is specifically as follows: For a vehicle queue traveling on a straight road, there is a manned vehicle and N self-driving connected vehicles. For the connected vehicles, the state of the i-th vehicle at time k is defined as x i (k)=[p i (k),v i (k),a i (k)] T , where p, v, and a represent the position, velocity, and acceleration information of the vehicle, respectively; thus, the nonlinear longitudinal dynamic model of the vehicle is written in discrete form as shown in formula (1): x i (k+1)=f i (x i (k),u i (k)) (1) Where u represents the control input, which is the braking / driving torque of the vehicle; f is an unknown nonlinear function; the Koopman operator theory is used to reconstruct the nonlinear model into a linear model in a high-dimensional space, as shown in formula (2): z i (k+1)=K i (z i (k),u i (k)) (2) in: z i (k)=g i (x i (k)) Approximate the Koopman operator K by fitting a matrix through a neural network i , and at the same time seek suitable eigenfunction g and mapping transformation g by training network parameters -1 ; Step 3: Determine the communication topology and system control objectives; Step 4: Based on the data-driven model, design a distributed model predictive control algorithm, implement controller design, and ultimately achieve the desired target vehicle platoon system to maintain stable driving.

2. The data-driven model predictive control method for a connected vehicle platoon system according to claim 1, characterized in that: The step 1 is specifically as follows: Depending on the type of vehicle, corresponding sensors and acquisition units are deployed to collect the corresponding speed, position, acceleration and engine torque data; at the same time, data cleaning is completed, noisy data is smoothed, missing values ​​and outliers are processed to ensure data quality and consistency. Data cleaning includes deleting irrelevant data and duplicate data.

3. The data-driven model predictive control method for a connected vehicle platoon system according to claim 1, characterized in that: The neural network includes an encoding network, a prediction network, and a decoding network; wherein the encoding network upgrades the state quantity from the original space to a high-dimensional space, and its input-output relationship is shown in the following formula (3): The encoding network input is the original state quantity, which is output through a multi-layer fully connected network, θ en are the corresponding weight and bias network parameters; the final output z of the entire encoding network i (k) The original state and the multi-layer network output are concatenated into a tensor; The prediction network is implemented in a high-dimensional space. As time evolves, the state of the reconstructed model changes. The input-output relationship of the prediction network is shown in formula (4): Among them F i is a finite-dimensional matrix, is an approximation of the Koopman operator, let F i =[A i ,B i ], the corresponding θ A ,θ B To predict the parameters of the network, the network weights and biases are also included; Finally, the decoding network maps the state quantity in the high-dimensional space back to the original space, and its input-output relationship is shown in formula (5): where θ de To decode the parameters of the network, input the high-dimensional state z i (k), through the multi-layer fully connected network output, the original state quantity x is finally obtained i (k), define the C matrix to represent this process.

4. The data-driven model predictive control method for a connected vehicle platoon system according to claim 3, characterized in that: According to the parameters of the network, the linear model reconstructed in high-dimensional space is shown in formula (6): The loss function uses a multi-step loss function. After a given data set, the output of a network with a length of m is first calculated, as shown in formula (7): F i m {z i (k)} represents the state information at time k+m obtained by advancing m time steps back at time k; then, the loss function shown in formula (8) is defined in the form of mean square error to describe the error of the network's prediction of future state variables: In order to make the network have higher precision encoding and decoding performance, the loss function shown in formula (9) is defined to describe the reconstruction error loss after encoding: In order to make the system have better linear evolution ability in high-dimensional linear space after reconstruction, the loss function shown in formula (10) is given: In order to ensure the robustness of the algorithm, the loss function shown in formula (11) is given: Based on the given loss function, the loss function of the entire network is shown in formula (12): For θ en and θ de The penalty is to prevent overfitting, and α1 to α6 are discount factors.

5. The data-driven model predictive control method for a connected vehicle platoon system according to claim 4, characterized in that: In step 3, the system control goal is to ensure that all vehicles in the queue maintain a desired spacing and travel at a constant speed. The specific mathematical expression is shown in formula (13): where d des is the desired vehicle spacing, a constant spacing strategy is adopted, and N is the number of connected vehicles; Based on the control objective, the communication topology is designed as a unidirectional topology in which the following vehicle only receives the status information of the preceding vehicle.

6. The data-driven model predictive control method for a connected vehicle platoon system according to claim 5, characterized in that: The step 4 is specifically as follows: According to the control objective, for any vehicle in the queue, an MPC optimization problem is established based on the status information of its neighboring vehicles, and the model constraint is a data-driven model; In each discrete cycle, the vehicle receives state information from neighboring vehicles, solves the optimization problem, and obtains the optimal control quantity sequence and the optimal state quantity sequence. At the same time, the vehicle sends the local optimal state information to neighboring vehicles. Finally, the first one of the optimal control sequence is used as the actual control, and this cycle is repeated to eventually achieve the safe driving of the vehicle queue according to the desired goal.

7. The data-driven model predictive control method for a connected vehicle platoon system according to claim 6, characterized in that: According to the control objective, the following distributed MPC optimization problem F is established at time t: i : where N p represents the prediction time domain, It represents the state quantity at time t+k predicted at time t; x ref (k|t) is the state trajectory of the manned vehicle; constraints (14a) and (14b) are the constraints of the data-driven model, and (14c), (14d) and (14e) are the constraints of the state and control variables; Represents the hypothetical state information of the neighboring nodes that establish communication with node i, through a set Represents the set of all vehicle nodes that establish communication links with i; specifically is given by formula (15): Solve the optimization problem to obtain an optimal control sequence at time t The corresponding optimal state sequence is expressed as Finally, only use It is used as the actual control quantity at time t, and the rolling optimization continues at time t+1.

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