A Vehicle Longitudinal Model Predictive Control Method Combining Long Short-Term Memory Network and Kalman Filter

Abstract

The present invention discloses a longitudinal model predictive control method for vehicles integrating long short-term memory network and Kalman filter. The steps include: establishing a vehicle longitudinal dynamics model considering the speed change of the leading vehicle as the prediction model of the MPC control framework; using the LTSM model to predict the acceleration value of the leading vehicle at each moment according to the historical acceleration of the leading vehicle and substituting it into the MPC control framework to calculate the corresponding control quantity; if the leading vehicle is an HDV, calculating the vehicle state estimation value at each moment, performing Kalman filter processing, and then substituting it into the MPC control framework; if the leading vehicle is a CAV, obtaining the actual value of the vehicle state in real time and substituting it into the MPC control framework; performing longitudinal control on the vehicle according to the control quantity of each control cycle. The present invention solves the problems of decreased control performance and poor stability of intelligent connected vehicles in the case of uncertainties in the environment and model parameters, and improves the vehicle operation efficiency while ensuring safety and comfort.

Description

Technical Field

[0001] The present invention relates to the fields of connected autonomous vehicles and traffic control, and particularly to a vehicle longitudinal model predictive control method integrating long short-term memory network and Kalman filter. Background Art

[0002] As one of the important technologies for autonomous vehicle control, vehicle platoon control inevitably has a large number of mismatches between the real object and the model due to external (environmental) disturbances, parameter variations, and neglected dynamic factors, which often has a great impact on the performance of the control system. How to ensure that all vehicles in the platoon move at a consistent speed while maintaining an ideal inter-vehicle distance under the conditions of considering factors such as measurement noise and model uncertainty in the real driving environment has always been the research focus of autonomous driving technology.

[0003] The rapid development of connected and autonomous vehicles (CAVs) has attracted wide attention. As an important part of future transportation, CAVs can monitor the surrounding environment in real time through advanced sensors, radars, cameras and other devices, quickly identify potential dangers, and take corresponding measures to avoid accidents. And CAVs can communicate with traffic infrastructure and other vehicles in real time to optimize the driving route and reduce traffic congestion, which has obvious advantages over traditional vehicles in improving driving safety and efficiency.

[0004] However, for the vehicle platoon following problem, if the leading vehicle followed by the CAV is also a CAV, the status information can be accurately obtained through vehicle-to-vehicle (V2V) communication between vehicles, and the error can be ignored; if the leading vehicle followed by the CAV is a human-driven vehicle (HDV), the state estimation of the leading HDV by the CAV only relies on sensor measurement, which will cause certain deviation in the control process. Therefore, it is necessary to estimate the vehicle state of the CAV at the next moment considering this deviation. Although the current technology takes into account the process noise and measurement noise existing in the vehicle state update process and uses Kalman filter for fusion to reduce the uncertainty of state estimation, it does not consider that the acceleration of the leading vehicle is unmeasurable at the state update moment when the leading vehicle is an HDV; at the same time, most of the current research regards the acceleration of the leading vehicle as a fixed value in the MPC prediction framework, which will also cause a certain degree of decline in control accuracy to some extent. Summary of the Invention

[0005] The technical problem to be solved by the present invention: Aiming at the above problems of the prior art, a vehicle longitudinal model predictive control method integrating long short-term memory network and Kalman filter is provided. The long short-term memory network is used to predict the acceleration of the leading vehicle, and the predicted acceleration of the leading vehicle is used to calculate the optimal control input and state update of the model. At the same time, the Kalman filter is used to reduce the uncertainty and measurement noise brought by the prediction, so as to realize the accurate estimation of the state.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0007] A vehicle longitudinal model predictive control algorithm integrating long short-term memory network and Kalman filter, comprising the following steps:

[0008] Establish a vehicle longitudinal dynamics model considering the speed change of the vehicle in front and use it as the prediction model of the MPC control framework;

[0009] Use the long short-term memory network model to predict the acceleration value of the vehicle in front at each moment according to the historical acceleration information of the vehicle in front;

[0010] Substitute the predicted acceleration value of the vehicle in front at each moment into the prediction model of the MPC control framework to calculate the control quantity at the corresponding moment and add it to the control sequence;

[0011] If the vehicle in front is a human-driven vehicle HDV, calculate the vehicle state estimation value at each moment, then perform Kalman filtering on the vehicle state estimation value at each moment to obtain the optimal vehicle state estimation value at each moment, and finally substitute the optimal vehicle state estimation value at each moment into the prediction model of the MPC control framework;

[0012] If the vehicle in front is a connected and autonomous vehicle CAV, obtain the actual vehicle state value at each moment in real time, and then substitute the actual vehicle state value at each moment into the prediction model of the MPC control framework;

[0013] Perform longitudinal control on the vehicle according to the specified control quantity in the control sequence of each control cycle.

[0014] Furthermore, when establishing the vehicle longitudinal dynamics model considering the speed change of the vehicle in front, it includes:

[0015] For each vehicle in the connected and autonomous vehicle fleet, respectively consider the speed change of the vehicle in front of each vehicle to establish a corresponding single-vehicle longitudinal dynamic model, and then integrate the single-vehicle longitudinal dynamic models of each vehicle to obtain the dynamic model of the connected and autonomous vehicle fleet, and use it as the vehicle longitudinal dynamics model considering the speed change of the vehicle in front;

[0016] Discretize the single-vehicle longitudinal dynamic models of each vehicle respectively, set the prediction time domain of the model to be equal to the control time domain and consider the acceleration change of the vehicle in front to obtain the corresponding state prediction equation;

[0017] Simultaneously use comfort, efficiency, and control input as the optimal control objectives to construct the objective function and constraint conditions of the vehicle longitudinal dynamics model considering the speed change of the vehicle in front

[0018] Furthermore, the expression of the single-vehicle longitudinal dynamic model is as follows:

[0019]

[0020] where X is the system state variable, U is the system control input, d is the system disturbance, and u n is the system input, and A, B1, and B2 are all coefficient matrices of the state-space equation, and a n-1 is the acceleration of the vehicle in front of the vehicle, a n , v n are respectively the difference between the actual distance and the desired distance between the vehicle and the vehicle in front, the relative speed with the vehicle in front, the acceleration of the vehicle itself, the speed, n is the serial number of the vehicle in the fleet of connected autonomous vehicles, and τ n is the engine time constant of the vehicle, and t d is the desired time interval.

[0021] Furthermore, the expression of the dynamic model of the fleet of connected autonomous vehicles is as follows:

[0022]

[0023] where X P =(Δe1 s , Δe1 v , a1, v1, Δe2 s , Δe2 v , a2, v2, …, Δe N s , Δe N v , a N , v N ), is the system state variable of each vehicle in the fleet of connected autonomous vehicles, where Δe N s , Δe N v , a N , v N are respectively the difference between the actual distance and the desired distance between the Nth vehicle in the fleet of connected autonomous vehicles and the vehicle in front, the relative speed with the vehicle in front, the acceleration of the vehicle itself, and the speed; A P , B1 P , B2 P are all augmented coefficient matrices of the state-space equation, U P =(u1, u2, …, u N ), is the system control input of each vehicle in the fleet of connected autonomous vehicles, where u N is the system input of the Nth vehicle in the fleet of connected autonomous vehicles, and d p =(a0, a1, …, a N-1), is the system perturbation of each vehicle in the connected and autonomous vehicle fleet, where a N-1 is the acceleration of the vehicle in front of the Nth vehicle in the connected and autonomous vehicle fleet.

[0024] Furthermore, the state prediction equation is expressed as follows:

[0025]

[0026] where are all coefficient matrices of the discretized state space equation, represents to the power of j, A j-1 represents to the power of j - 1, I is a 4×4 identity matrix, t s is the sampling time of the system, u(k|k) represents the predicted state input at time k, u(k + j - 1|k) represents the predicted control input at time k for time k + j - 1, x(k + j|k) represents the state prediction of the system at time k for time k + j, w(j) is the disturbance input; w(k + j - 1|k) represents the acceleration of the vehicle in front at the j - 1th future time point, j = 1, 2…, N.

[0027] Furthermore, after obtaining the corresponding state prediction equation, it also includes: changing the state prediction equation to relax the assumption that the acceleration of the vehicle in front remains unchanged within the prediction time domain. The expression of the changed state prediction equation is as follows:

[0028]

[0029] y(k + j|k) = Cx(k + j|k)

[0030] where u(k - 1) is the optimal control quantity at time k - 1, Δu(k|k) represents the state input increment at time k, Δu(k + j - 1|k) represents the predicted control input increment at time k for time k + j - 1, y(k + j|k) represents the measurable output of the system, and C is the identity matrix.

[0031] Furthermore, the expression of the objective function is as follows:

[0032]

[0033] The constraint condition expression is as follows:

[0034]

[0035] where y ref (k + N|k) is the reference trajectory, Represents a quadratic function, where Q and R are the error and input weighting matrices respectively, ε is the slack variable, p is the weight of the slack variable, and Δu(k + j|k) represents the predicted control input increment from time k to time k + j. Are respectively the lower and upper limit values of the artificially set parameters corresponding to the measurable output of the system, y min 、y max Are respectively the minimum and maximum values corresponding to the measurable output of the system. Are respectively the lower and upper limit values of the artificially set parameters corresponding to the predicted control input, u min 、u max Are respectively the minimum and maximum values corresponding to the predicted control input. Are respectively the lower and upper limit values of the artificially set parameters corresponding to the predicted control input increment, Δu min 、Δu max Are respectively the minimum and maximum values corresponding to the predicted control input increment.

[0036] Furthermore, the expression of the vehicle state estimation value at each moment is as follows:

[0037]

[0038] Where Is the estimated value of the state variable at time k, u(k - 1) is the optimal control quantity at time k - 1, ω(k - 1) is the acceleration of the vehicle in front at time k - 1, and x kal (k - 1) is the optimal estimated value of the state variable at time k - 1 after Kalman filtering.

[0039] Furthermore, when performing Kalman filtering on the vehicle state estimation value at each moment, the following steps are included:

[0040] Calculate the covariance of the optimal estimated value of the state variable at the previous moment, and calculate the Kalman gain at the current moment. The expressions are as follows:

[0041]

[0042] Where K K Is the Kalman gain at time k, Is the sum of the covariance P(k - 1) of the optimal estimated value of the state variable at time k - 1 and the Gaussian noise covariance Q θ , R ξ Is the measurement value covariance, C is the proportionality coefficient of the state variable, Is the state update matrix;

[0043] Obtain the measured value of the vehicle state at the current moment, correct the estimated value of the vehicle state at the current moment according to the measured value of the vehicle state at the current moment and the Kalman gain, and obtain the optimal estimated value of the vehicle state at the current moment. The expression is as follows:

[0044]

[0045] Among them, x kal (k) is the optimal estimated value of the state variable at time k, is the estimated value of the state variable at time k, is the measured value of the state variable at time k.

[0046] Furthermore, the specified control quantity in the control sequence of each control cycle specifically refers to the first control quantity in the control sequence.

[0047] Compared with the prior art, the advantages of the present invention are as follows:

[0048] (1) Compared with the traditional longitudinal control method for vehicle platoons, the present invention uses the LSTM method for acceleration prediction, and updates the control quantity with the predicted acceleration during the MPC calculation process, improving the control accuracy.

[0049] (2) Compared with the traditional longitudinal control method for vehicle platoons, the model of the present invention is established in the scenario where CAV platoons follow HDVs, and it is assumed that CAV vehicles can obtain the acceleration information of the preceding vehicle in real time through V2V communication, while CAVs and HDVs cannot obtain the acceleration information of the preceding vehicle in real time, further conforming to the actual situation.

[0050] (3) Compared with the traditional longitudinal control method for vehicle platoons, the present invention uses the Kalman filtering algorithm to filter the calculation errors caused by measurement noise and uncertain parameters of the preceding vehicle, reducing the uncertainty of the model.

[0051] (4) Compared with the traditional longitudinal control method for vehicle platoons, the present invention significantly improves the operation efficiency of the platoon on the premise of considering driving safety, comfort and energy consumption. Description of the Drawings

[0052] Figure 1 is the flowchart of the embodiment of the present invention.

[0053] Figure 2 is the control structure diagram of the present invention.

[0054] Figure 3 is the schematic diagram of the example scenario of the present invention.

[0055] Figure 4 is the acceleration curve of the leading vehicle during the simulation time period of the present invention.

[0056] Figure 5 Acceleration curve of four following vehicles using the K-MPC method of the present invention.

[0057] Figure 6 Acceleration curve of four following vehicles using the L-MPC method of the present invention.

[0058] Figure 7 Acceleration curve of four following vehicles using the K-L-MPC method of the present invention.

[0059] Figure 8 Gap error curve of four following vehicles using the K-MPC method of the present invention.

[0060] Figure 9 Gap error curve of four following vehicles using the L-MPC method of the present invention.

[0061] Figure 10 Gap error curve of four following vehicles using the K-L-MPC method of the present invention. Detailed implementation manners

[0062] The present invention will be further described below in conjunction with the accompanying drawings of the specification and specific preferred embodiments, but the protection scope of the present invention is not limited thereby.

[0063] This embodiment proposes a vehicle longitudinal model predictive control method (K-L-MPC) that combines a long short-term memory network (LSTM) and a Kalman filter. This method solves the problems of degraded control performance and poor stability of intelligent connected vehicles in the presence of uncertainties in the environment and model parameters. By rewriting the vehicle longitudinal dynamics equation and relaxing the assumption that the acceleration of the leading vehicle remains constant within the prediction horizon, an LSTM model is used to predict the acceleration value of the leading vehicle within the future time window and substitute it into the MPC framework to obtain the optimal control quantity. During the state update process, a Kalman filter is designed to estimate the state variables, eliminating the interference of measurement noise and uncertain model parameters, thereby improving the control accuracy of the model. The method flow of this embodiment is as Figure 1 shown, and specifically includes the following steps:

[0064] S1) Establish a vehicle longitudinal dynamics model considering the speed change of the leading vehicle and use it as the prediction model of the MPC control framework;

[0065] S2) Use the LSTM model to predict the acceleration value of the leading vehicle at each future moment based on the historical acceleration information of the leading vehicle;

[0066] S3) Substitute the predicted acceleration value of the leading vehicle at each moment into the prediction model of the MPC control framework, calculate the optimal control quantity corresponding to the moment, and add it to the control sequence;

[0067] S4) If the leading vehicle is a human-driven vehicle HDV, calculate the estimated vehicle state at each moment, then perform Kalman filtering on the estimated vehicle state at each moment to obtain the optimal estimated vehicle state at each moment, and finally substitute the optimal estimated vehicle state at each moment into the prediction model of the MPC control framework;

[0068] If the leading vehicle is a connected and autonomous vehicle CAV, obtain the actual vehicle state at each moment in real time, and then substitute the actual vehicle state at each moment into the prediction model of the MPC control framework;

[0069] S5) Rolling horizon optimization, perform longitudinal control on the vehicle according to the specified control quantity in the control sequence of each control period, so as to achieve vehicle longitudinal control.

[0070] The following is a specific description of each step.

[0071] In step S1 of this embodiment, when establishing a vehicle longitudinal dynamics model considering the speed change of the leading vehicle, the following steps are included:

[0072] S1.1) For each vehicle in the connected and autonomous vehicle fleet, establish a corresponding single-vehicle longitudinal dynamic model considering the speed change of the leading vehicle of each vehicle. The expression of the single-vehicle longitudinal dynamic model is as follows:

[0073]

[0074] Among them, X is the system state variable, U is the system control input, d is the system disturbance, u n is the system input, A, B1, and B2 are all coefficient matrices of the state space equation, a n-1 is the acceleration of the leading vehicle of the vehicle, a n , v n are respectively the difference between the actual distance and the desired distance between the vehicle and the leading vehicle, the relative speed with the leading vehicle, the acceleration of the vehicle itself, the speed, n is the serial number of the vehicle in the connected and autonomous vehicle fleet, τ n is the engine time constant of the vehicle, t d is the desired time interval

[0075] S1.2) Integrate the single-vehicle longitudinal dynamic model of each vehicle to obtain the dynamic model of the connected and autonomous vehicle fleet, and use it as the vehicle longitudinal dynamic model considering the speed change of the leading vehicle;

[0076] Considering the vehicle longitudinal following scenario as Figure 2 shown, for a CAV fleet composed of N vehicles, the state variable of this system can be defined as X P =(Δe1 s ,Δe1v , a1, v1, Δe2 s , Δe2 v , a2, v2, …, Δe N s , Δe N v , a N , v N ), where Δe N s , Δe N v , a N , v N are respectively the difference between the actual distance and the desired distance of the Nth vehicle in the connected and autonomous vehicle fleet from the vehicle in front, the relative speed to the vehicle in front, the acceleration of the vehicle itself, and the speed; the control input is defined as U P =(u1, u2, …, u N ), where u N is the system input of the Nth vehicle in the connected and autonomous vehicle fleet, and the disturbance of the system is d p =(a0, a1, …, a N-1 ), a0 represents the acceleration of the leading vehicle followed by the fleet, and a N-1 is the acceleration of the vehicle in front of the Nth vehicle in the connected and autonomous vehicle fleet. Therefore, the matrix form of the dynamic model of the CAV fleet with N vehicles can be expressed as:

[0077]

[0078]

[0079] where, A P , B1 P , B2 P are all coefficient matrices of the augmented state space equation

[0080] S1.3) Based on the longitudinal dynamics model of a single vehicle, use the forward Euler method to discretize the longitudinal dynamic model of each vehicle respectively, set the prediction horizon of the model equal to the control horizon and consider the change in the acceleration of the vehicle in front, and obtain the corresponding state prediction equation, the expression is as follows:

[0081]

[0082] where, are all coefficient matrices of the discretized state space equation, represents to the power of j, A j-1 represents to the power of j - 1, I is a 4×4 identity matrix, t s$T_s$ is the sampling time of the system, $u(k|k)$ represents the predicted state input at time $k$, $u(k + j - 1|k)$ represents the predicted control input at time $k$ for time $k + j - 1$, $x(k + j|k)$ represents the state prediction of the system at time $k$ for time $k + j$, $w(j)$ is the disturbance input; $w(k + j - 1|k)$ represents the acceleration of the leading vehicle at the $(j - 1)$-th future time point, $j = 1, 2, \cdots, N$;

[0083] After establishing the vehicle longitudinal dynamics model considering the speed change of the leading vehicle in this embodiment, the assumption that the acceleration of the leading vehicle remains unchanged within the prediction horizon is relaxed. Assuming that the control process is achieved through incremental control $\Delta u$, then the predicted control input at time $k$ for time $k + j$ is the sum of the predicted control input at time $k$ for time $k + j - 1$ and the incremental predicted control input at time $k$ for time $k + j$. The expression is as follows:

[0084] $u(k|k)=\Delta u(k|k)+u(k - 1)$

[0085] $u(k + j|k)=u(k + j - 1|k)+\Delta u(k + j|k)$

[0086] Among them, $u(k|k)$ represents the predicted state input at time $k$, $\Delta u(k|k)$ represents the incremental state input at time $k$, and $u(k - 1)$ is a known quantity at time $k$, and so on.

[0087] Thus, the vehicle prediction equation is rewritten in the following form:

[0088]

[0089] $Dw(j), j = 1, 2, \cdots, N$

[0090] Among them, $u(k - 1)$ is the optimal control quantity at time $k - 1$, $\Delta u(k|k)$ represents the incremental state input at time $k$, $\Delta u(k + j - 1|k)$ represents the incremental predicted control input at time $k$ for time $k + j - 1$, $y(k + j|k)$ represents the measurable output of the system, and $C$ is the identity matrix;

[0091] S1.4) Simultaneously take comfort, efficiency, and control input as the optimal control objectives, and construct the objective function and constraint conditions of the vehicle longitudinal dynamics model considering the speed change of the leading vehicle.

[0092] Specifically, while considering improving the comfort of the vehicle in this embodiment, the loss of vehicle efficiency is minimized as much as possible. Taking comfort, efficiency, and control input as the optimal control objectives simultaneously, the expression of the objective function of the model is as follows:

[0093]

[0094] To ensure the safe driving of vehicles, the headway between adjacent vehicles must meet the minimum safety distance; to ensure the operation efficiency of vehicles, the relative speed between vehicles must also be controlled within a certain range; due to the constraints of the controller performance, the change in the control quantity of each vehicle must also be less than a certain value; of course, boundary constraints also need to be imposed on the running speed and acceleration. Finally, to prevent the situation where no feasible solution can be obtained due to overly strict constraints, a relaxation vector is introduced to soften the original strict constraints. The constraint expression of the model is as follows:

[0095]

[0096] Among them, y ref (k + N|k) is the reference trajectory, represents a quadratic function, Q and R are the error and input weighting matrices respectively, ε is the relaxation variable, p is the weight of the relaxation variable, Δu(k + j|k) represents the predicted control input increment from time k to time k + j, are the lower and upper limit values of the artificially set parameters corresponding to the measurable output of the system respectively, y min and y max are the minimum and maximum values of the measurable output of the system respectively, are the lower and upper limit values of the artificially set parameters corresponding to the predicted control input respectively, u min and u max are the minimum and maximum values of the predicted control input respectively, are the lower and upper limit values of the artificially set parameters corresponding to the predicted control input increment respectively, Δu min and Δu max are the minimum and maximum values of the predicted control input increment respectively.

[0097] In step S2 of this embodiment, the LSTM model is used to predict the acceleration value of the leading vehicle within the future time window according to the historical acceleration information of the leading vehicle. Specifically, it includes:

[0098] First, an LSTM model is established. The LSTM can learn the information and internal data characteristics hidden in the long-term historical acceleration, realize the accurate prediction of the disturbance quantity, and reduce the MPC control error.

[0099] Then, the LSTM model is trained using the acceleration time series of the leading vehicle during following driving. Specifically, a training data set is generated from the historical acceleration data, and the training set and the test set are divided. The acceleration characteristics are learned through the training set data, and the prediction effect is tested on the test set. The prediction length of the LSTM prediction model is the same as the prediction domain length in the MPC.

[0100] Finally, within each control time period, the historical acceleration data of the leading vehicle within a fixed time window is input into the trained LSTM model to predict the acceleration value of the leading vehicle at each moment within the future prediction time domain.

[0101] In step S3 of this embodiment, the acceleration of the leading vehicle predicted at each moment is substituted into the MPC control framework to obtain the optimal control quantity at this moment. Specifically, the obtained acceleration prediction value is used as the perturbation term d in the formula described above. p =(a0, a1, …, a N-1 ), on the premise of satisfying the constraint conditions and minimizing the objective function, the objective function is a convex function, the constraint conditions are linear, this problem can be regarded as a quadratic programming convex optimization problem, this problem is solvable and there is an optimal solution. Finally, by solving this quadratic programming convex optimization problem, the optimal control input at this moment can be obtained as the optimal control quantity.

[0102] In step S4 of this embodiment, considering the case where the leading vehicle is an HDV vehicle, the acceleration a of the leading vehicle n-1 cannot be measured at time k - 1 and can only be estimated. Therefore, there will inevitably be a calculation error between the estimated state calculated during the state update process and the true state x(k). Let the error In addition, due to the inability to communicate with each other, there will also be a measurement noise during the measurement of the vehicle state. Assume the measurement noise Therefore, the Kalman filter algorithm is used to correct this part of the error and reduce the interference caused by them. The relevant calculation and derivation process is as follows:

[0103] In this embodiment, the expression of the vehicle state estimation value at each moment is as follows:

[0104]

[0105] Among them is the estimated value of the state variable at time k, u(k - 1) is the optimal control quantity at time k - 1, ω(k - 1) is the acceleration of the leading vehicle at time k - 1, and x kal (k - 1) is the optimal estimated value of the state variable at time k - 1 after Kalman filter processing.

[0106] When performing Kalman filter processing on the vehicle state estimation value at each moment, the following steps are included:

[0107] Calculate the covariance of the optimal estimated value of the state variable at the previous moment, and calculate the Kalman gain at the current moment. The expressions are as follows:

[0108]

[0109] Among them, KK is the Kalman gain at time k, represents the covariance of the predicted value, specifically the covariance P(k - 1) of the optimal estimated value of the state variable at time k - 1 and the Gaussian noise covariance Q θ The sum of R ξ is the measurement covariance, C is the proportionality coefficient of the state variable, is the state update matrix;

[0110] Obtain the measurement value of the vehicle state at the current moment, and correct the estimated value of the vehicle state at the current moment according to the measurement value of the vehicle state at the current moment and the Kalman gain to obtain the optimal estimated value of the vehicle state at the current moment. The expression is as follows:

[0111]

[0112] where x kal (k) is the optimal estimated value of the state variable at time k, is the estimated value of the state variable at time k, is the measurement value of the state variable at time k.

[0113] As Figure 3 shown, first obtain the optimal control input u(k - 1) at time k - 1 through the MPC controller. There is an inaccurate state calculation amount and an inaccurate state observation amount Then use the Kalman filter to filter the state variable with noise, use the state variable obtained after Kalman filtering as the parameter to update the Kalman filter, and finally use the state variable x kal (k) obtained after Kalman filtering is substituted into the prediction model of the MPC control framework to enter a new round of rolling optimization to obtain the best system input at the next moment.

[0114] In step S5 of this embodiment, since MPC solves an optimization problem in each control cycle and obtains a control sequence, only the first control quantity of this sequence is executed, and then this process is repeated in the next cycle. Through the rolling optimization method, MPC can adaptively respond to the changes of the system, thereby realizing the precise control of the vehicle queue.

[0115] Next, specific experiments are used to verify the effect of the method of this embodiment.

[0116] Set the engine time constant of the vehicle to t = 0.4s, the vehicle body length to l = 3m, and the sampling time of the system to t s = 0.1s. Specificize the constraint conditions of the system according to actual requirements as follows:

[0117] Table 1. Constraint Parameter Settings

[0118]

[0119] Set the weight of the slack variable to p = 3, and set the output and input slack variable coefficients according to Table 3-2.

[0120] Table 2. Slack Variable Coefficient Settings

[0121]

[0122] Consider the calculation error and measurement error during vehicle driving, and assume that they both follow a normal distribution. The specific parameter settings of each error term are as follows.

[0123] Table 3. Error Variable Settings

[0124]

[0125] In addition, set the system output matrix C = diag(1, 1, 1, 1), that is, directly output the state of the system. Adopt the safety distance algorithm with a fixed time interval, set the minimum safety distance d0 = 5m, and then the controller optimization parameter settings of the model are as follows.

[0126] Table 4. Control Parameter Settings

[0127]

[0128] In this embodiment, several indicators are selected to evaluate the performance of the CAV queue under different control strategies:

[0129] (1) The maximum value of the square of the relative speed of the follower vehicle (e v ) 2 max and the maximum value of the square of the gap error (e s ) 2 max , and its calculation formula is:

[0130]

[0131] In the formula, T is the total simulation duration, and here it is taken as 150s.

[0132] (2) The sum of the squares of the relative speeds of the follower vehicle is sum(e v ) 2 and the sum of the squares of the gap errors is sum(e s ) 2 , and its calculation formula is:

[0133]

[0134] To demonstrate the significance of the K-L-MPC method, a vehicle queue consisting of five vehicles including the leading vehicle was simulated using Python. The leading vehicle used the LSTM test set data in the above-mentioned dataset as its acceleration value, and the initial states of all vehicles were set to zero. The simulation time was 150 seconds. Figure 4 It is the acceleration curve of the leading vehicle during the simulation period.

[0135] The acceleration curves of the four following vehicles are shown in the figure, where Figure 5 is the acceleration curve of the K-MPC method, Figure 6 is the acceleration curve of the L-MPC method, Figure 7 is the acceleration curve of the K-L-MPC method.

[0136] As can be seen from the figure, the acceleration of the following vehicles using the K-MPC method fluctuates slightly and frequently. The reason is that the four following vehicles cannot obtain the acceleration information of their preceding vehicles in advance, and use the acceleration of the preceding vehicle at the previous moment to replace the acceleration in the future prediction horizon, resulting in large fluctuations in the calculated control quantity each time, and thus causing acceleration oscillation. Using the L-MPC method, the first vehicle among the following vehicles cannot accurately obtain the information of the leading vehicle, resulting in an increase in model uncertainty during the control process, thereby causing violent oscillation of the system control quantity and increasing the amplitude of the acceleration fluctuation up and down. For the K-L-MPC method, the acceleration change amplitude of all vehicles is the smallest and the acceleration value is maintained in a relatively low range, and the acceleration fluctuation amplitude of the four vehicles decreases with the upstream direction of the queue. From the results in the figure, the string stability of this method can be basically obtained, that is, the acceleration change of the leading vehicle will not be amplified with the upstream direction of the queue. Therefore, compared with the K-MPC method and the L-MPC method, the K-L-MPC method can effectively reduce the fluctuation of the actual acceleration of the vehicle itself, indicating that the Kalman filter combined with the LSTM prediction model can well filter out the external interference signals, which can not only improve the anti-interference ability of the control system, but also improve the ride comfort performance.

[0137] The following vehicle gap error values of the four following vehicles during the simulation period are shown in the figure, where Figure 8 is the gap error curve of the K-MPC method, Figure 9 is the gap error curve of the L-MPC method, Figure 10 is the gap error curve of the K-L-MPC method.

[0138] It can be seen from the figure that the inter-vehicle gap error curve of the K-MPC method is similar to its acceleration curve, with small fluctuation amplitude and relatively frequent fluctuations. The error curve of the first following vehicle of the L-MPC method is relatively disordered, while the inter-vehicle gap error curve of the K-L-MPC method combines the advantages of the two methods, with small fluctuation amplitude and regular shape. Further, the sum(e s ) 2 of the first following vehicle of K-MPC is 49.92, and (e s ) 2 max is 0.30. The sum(e s ) 2 of the first following vehicle of L-MPC is 55.89, and (e s ) 2 max is 0.32. The sum(e s ) 2 of the first following vehicle of K-L-MPC is 48.06, and (e s ) 2 max is 0.24. This result shows that introducing LSTM to predict the acceleration of the leading vehicle is more in line with the actual situation than assuming that the speed of the leading vehicle remains unchanged within the prediction time domain. On this basis, adding a Kalman filter to filter the calculation error and measurement error, the system can obtain a more reasonable control quantity, so as to reduce the relative inter-vehicle distance error.

[0139] The above is only the preferred implementation mode of the present invention. The protection scope of the present invention is not limited to the above embodiments. All technical solutions within the idea of the present invention belong to the protection scope of the present invention. It should be pointed out that for those of ordinary skill in the art of this technology, several improvements and refinements made without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims

1. A vehicle longitudinal model predictive control method integrating long short-term memory network and Kalman filter, characterized in that, Including the following steps: Establish a vehicle longitudinal dynamics model considering the speed change of the leading vehicle and use it as the prediction model of the MPC control framework; Use a long short-term memory network model to predict the acceleration value of the leading vehicle at each moment based on the historical acceleration information of the leading vehicle; Substitute the predicted acceleration value of the leading vehicle at each moment into the prediction model of the MPC control framework to calculate the control quantity at the corresponding moment and add it to the control sequence; If the leading vehicle is a human-driven vehicle HDV, calculate the vehicle state estimation value at each moment, then perform Kalman filtering on the vehicle state estimation value at each moment to obtain the optimal vehicle state estimation value at each moment, and finally substitute the optimal vehicle state estimation value at each moment into the prediction model of the MPC control framework; If the leading vehicle is a connected and autonomous vehicle CAV, obtain the actual vehicle state value at each moment in real time, and then substitute the actual vehicle state value at each moment into the prediction model of the MPC control framework; Perform longitudinal control on the vehicle according to the specified control quantity in the control sequence of each control cycle.

2. The vehicle longitudinal model predictive control method integrating long short-term memory network and Kalman filter according to claim 1, characterized in that When establishing a vehicle longitudinal dynamics model considering the speed change of the leading vehicle, it includes: For each vehicle in the connected and autonomous vehicle fleet, respectively consider the speed change of the leading vehicle of each vehicle to establish a corresponding single-vehicle longitudinal dynamic model, and then integrate the single-vehicle longitudinal dynamic models of each vehicle to obtain the dynamic model of the connected and autonomous vehicle fleet, and use it as the vehicle longitudinal dynamics model considering the speed change of the leading vehicle; Discretize the single-vehicle longitudinal dynamic models of each vehicle respectively, set the prediction horizon of the model to be equal to the control horizon and consider the acceleration change of the leading vehicle to obtain the corresponding state prediction equation; Simultaneously take comfort, efficiency, and control input as the optimal control objectives, and construct the objective function and constraint conditions of the vehicle longitudinal dynamics model considering the speed change of the leading vehicle.

3. The vehicle longitudinal model predictive control method integrating long short-term memory network and Kalman filter according to claim 2, characterized in that, The expression of the single-vehicle longitudinal dynamic model is as follows: where X is the system state variable, U is the system control input, d is the system disturbance, and u n is the system input, and A, B1, and B2 are all coefficient matrices of the state - space equation. a n-1 is the acceleration of the vehicle in front, a n , v n are respectively the difference between the actual distance and the desired distance between the vehicle and the vehicle in front, the relative speed with the vehicle in front, the acceleration of the vehicle itself, and the speed. n is the serial number of the vehicle in the connected autonomous vehicle fleet, and τ n is the engine time constant of the vehicle, and t d is the desired time interval.

4. The vehicle longitudinal model predictive control method integrating a long short-term memory network and a Kalman filter according to claim 3, characterized in that, The expression of the dynamic model of the connected and autonomous vehicle fleet is as follows: A i 4×4 = A; i = 1, 2, …, N where, X P =(Δe1 s , Δe1 v , a1, v1, Δe2 s , Δe2 v , a2, v2, …, Δe N s , Δe N v , a N , v N ), is the system state variable of each vehicle in the connected and autonomous vehicle fleet, where Δe N s , Δe N v , a N , v N are respectively the difference between the actual distance and the desired distance between the Nth vehicle in the connected and autonomous vehicle fleet and the preceding vehicle, the relative speed with the preceding vehicle, the acceleration of the vehicle itself, and the speed; A P , B1 P , B2 P are all coefficient matrices of the augmented state space equation, U P =(u1, u2, …, u N ) is the system control input of each vehicle in the connected and autonomous vehicle fleet, where u N is the system input of the Nth vehicle in the connected and autonomous vehicle fleet, d p =(a0, a1, …, a N-1 ), is the system disturbance of each vehicle in the connected and autonomous vehicle fleet, where a N-1 is the acceleration of the preceding vehicle of the Nth vehicle in the connected and autonomous vehicle fleet.

5. The vehicle longitudinal model predictive control method integrating long short-term memory network and Kalman filter according to claim 4, characterized in that The expression of the state prediction equation is as follows: D = [A j-1 B2 A j-2 B2…B2]; Among them, are all coefficient matrices of the state-space equation after discretizing continuous time, represents to the power of j, A j-1 represents to the power of j - 1, I is a 4×4 identity matrix, t s is the sampling time of the system, u(k|k) represents the predicted state input at time k, u(k + j - 1|k) represents the predicted control input at time k for time k + j - 1, x(k + j|k) represents the state prediction of the system at time k for time k + j, w(j) is the disturbance input; w(k + j - 1|k) represents the acceleration of the leading vehicle at the j - 1th future time point, j = 1, 2…, N.

6. The vehicle longitudinal model predictive control method integrating long short-term memory network and Kalman filter according to claim 5, characterized in that, After obtaining the corresponding state prediction equation, it further includes: changing the state prediction equation to relax the assumption that the acceleration of the leading vehicle remains unchanged within the prediction horizon, and the expression of the changed state prediction equation is as follows: Where, u(k - 1) is the optimal control quantity at the (k - 1)th moment, Δu(k|k) represents the state input increment at the kth moment, Δu(k + j - 1|k) represents the predicted control input increment at the kth moment for the (k + j - 1)th moment, y(k + j|k) represents the measurable output of the system, and C is the identity matrix.

7. The vehicle longitudinal model predictive control method integrating long short-term memory network and Kalman filter according to claim 6, characterized in that, The expression of the objective function is as follows: The expression of the constraint condition is as follows: where y ref (k + N|k) is the reference trajectory, representing a quadratic function, Q and R are the error and input weighting matrices respectively, ε is the slack variable, p is the weight of the slack variable, and Δu(k + j|k) represents the predicted control input increment from time k to time k + j, are the lower and upper limit values of the artificially set parameters corresponding to the measurable output of the system, y min and y max are the minimum and maximum values corresponding to the measurable output of the system respectively, are the lower and upper limit values of the artificially set parameters corresponding to the predicted control input, u min and u max are the minimum and maximum values corresponding to the predicted control input respectively, are the lower and upper limit values of the artificially set parameters corresponding to the predicted control input increment, Δu min and Δu max are the minimum and maximum values corresponding to the predicted control input increment respectively.

8. The vehicle longitudinal model predictive control method integrating long short-term memory network and Kalman filter according to claim 7, characterized in that The expression of the vehicle state estimation value at each moment is as follows: Among them is the estimated value of the state variable at time k, u(k - 1) is the optimal control quantity at time k - 1, ω(k - 1) is the acceleration of the vehicle in front at time k - 1, and x kal (k - 1) is the optimal estimated value of the state variable at time k - 1 after Kalman filtering processing.

9. The vehicle longitudinal model predictive control method integrating long short-term memory network and Kalman filter according to claim 1, characterized in that When performing Kalman filtering on the vehicle state estimation value at each moment, it includes the following steps: Calculate the covariance of the optimal estimation value of the state variable at the previous moment, and calculate the Kalman gain at the current moment, and the expressions are as follows: Among them, K K is the Kalman gain at time k, is the covariance P(k - 1) of the optimal estimate of the state variable at time k - 1 and the Gaussian noise covariance Q θ sum, R ξ is the measurement covariance, C is the proportionality coefficient of the state variable, is the state update matrix; Obtain the measured value of the vehicle state at the current moment, and correct the estimated value of the vehicle state at the current moment according to the measured value of the vehicle state at the current moment and the Kalman gain to obtain the optimal estimated value of the vehicle state at the current moment, and the expression is as follows: where x kal (k) is the optimal estimated value of the state variable at time k, is the estimated value of the state variable at time k, is the measured value of the state variable at time k.

10. The vehicle longitudinal model predictive control method integrating long short-term memory network and Kalman filter according to claim 1, characterized in that The specified control quantity in the control sequence of each control period specifically refers to the first control quantity in the control sequence.

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