Lane keeping predictive control method for asymptotically stable tracking

Abstract

The invention belongs to the technical field of lane keeping assistance, and discloses an asymptotically stable tracking lane keeping prediction control method, which comprises the following steps: S1, fitting based on a Koopman theory and a DMD algorithm to obtain a vehicle linearization model, and constructing a linear parameter variation prediction model in combination with the vehicle linearization model and a lane keeping model; s2, two expected state planning modes are designed, the first mode is to calculate an expected state based on a vehicle-road coordinate conversion formula, and the second mode is to calculate the expected state by means of a linear parametric prediction model and a road curvature-yaw velocity conversion formula; s3, designing a prediction controller based on the linear parametric prediction model and the maximum robust positive invariant set theory, wherein the input of the prediction controller is a vehicle feedback state and one of the expected states; the output of the predictive controller is the control quantity acting on the vehicle. In conclusion, according to the method, the calculation speed is increased while the nonlinear characteristic of the vehicle is reserved, and asymptotically stable tracking can be effectively achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of lane keeping assist, and in particular relates to a lane keeping prediction control method for asymptotically stable tracking. Background Art

[0002] Lane keeping assist (LKA) technology is one of the core functions of advanced driver assistance systems (ADAS), which aims to help drivers reduce traffic accidents caused by lane deviation by actively intervening in vehicle steering or issuing warnings. After more than ten years of development, through the complementarity of cameras, millimeter-wave radars and high-precision maps, LKA technology has long been upgraded from "deviation correction" to "full-speed lane centering (LCC)", and combined with adaptive cruise control (ACC), it can achieve L2 autonomous driving.

[0003] At present, in the field of LKA controller design, vehicle dynamics modeling includes two types of linear and nonlinear models. In most working conditions, two-degree-of-freedom, three-degree-of-freedom, and five-degree-of-freedom linear or nonlinear models are used to design controllers. Among them, linear models are generally suitable for small curvature turning conditions, and cannot fully reflect the nonlinear characteristics of the vehicle in the face of high-speed and large curvature conditions; however, the nonlinear model has a heavy computational burden and it is difficult to meet the real-time requirements of the controller. For the emerging data-driven modeling method, it has the disadvantages of data dependence, interpretability and safety risks, and poor scene migration. Secondly, how to ensure the asymptotic stability of the system is also a difficult problem faced by LKA technology. Although the linear quadratic regulator (LQR) can guarantee the essential asymptotic stability, it is only applicable to unconstrained linear models. Model predictive control (MPC) can explicitly handle constraints and is applicable to both linear and nonlinear models, but most MPC controllers do not theoretically guarantee the asymptotic stability of the LKA system.

[0004] In summary, linear models are difficult to reflect the nonlinear characteristics of vehicles under extreme conditions, and the use of nonlinear models to design controllers requires solving non-convex optimization problems. This contradiction puts higher demands on vehicle modeling: it is necessary to improve the accuracy of modeling while taking into account the real-time performance of the controller. In addition, designing a predictive controller that can theoretically guarantee the asymptotic stability of the LKA system is also a difficult problem that needs to be solved in the field of LKA technology. Summary of the invention

[0005] In view of this, in order to solve the problems raised in the above background technology, the purpose of the present invention is to provide a lane keeping prediction control method with asymptotically stable tracking.

[0006] To achieve the above object, the present invention provides the following technical solutions:

[0007] A lane keeping prediction control method with asymptotically stable tracking, comprising:

[0008] S1. Fit a linearized vehicle model based on Koopman theory and DMD algorithm, and construct a linear parameter-varying prediction model by combining the linearized vehicle model with a lane-keeping model;

[0009] S2. Design two expected state planning modes. Mode 1 calculates the expected state based on the vehicle-road coordinate transformation formula, and Mode 2 calculates the expected state by means of the linear parameter-varying prediction model and the road curvature-yaw rate transformation formula;

[0010] S3. Design a predictive controller based on the linear parameter-varying prediction model and the maximum robust positive invariant set theory, and

[0011] the input of the predictive controller is the vehicle feedback state and one of the expected states;

[0012] the output of the predictive controller is the control quantity acting on the vehicle.

[0013] Preferably, in step S1, the steps of fitting a linearized vehicle model based on Koopman theory and DMD algorithm include:

[0014] With the sampling time collect the input and output data of a three-degree-of-freedom nonlinear vehicle dynamics model, and construct a data matrix;

[0015] Fit a linearized vehicle model based on Koopman theory, DMD algorithm and the data matrix, and the linearized vehicle model is the Koopman linearized model of the three-degree-of-freedom nonlinear vehicle dynamics model:

[0016] ;

[0017] wherein, is the state quantity of the model at time , , are the longitudinal speed, lateral speed, and yaw rate of the vehicle respectively; is the control quantity of the model at time , are the front wheel steering angle and the rear wheel longitudinal force of the vehicle respectively; the matrix is the optimal linear fitting operator.

[0018] Preferably, in step S1, the lane-keeping model is expressed as:

[0019] ;

[0020] wherein, is the preview distance, and The lateral error and yaw angle error between the current position of the vehicle and the center position of the lane ahead and, the desired yaw rate when the vehicle travels to the center position of the lane ahead .

[0021] Preferably, in the step S1, the linear parameter-varying prediction model is expressed as:

[0022] ;

[0023] wherein, , , , the state variable is consistent with the Koopman linearization model, that is , represents the bounded modeling error between the linear parameter-varying prediction model and the actual system.

[0024] Preferably, in the step S2, the vehicle-road coordinate transformation formula is expressed as:

[0025] ;

[0026] wherein, , , are the position and yaw angle of the vehicle's center of mass in the road coordinate system, is the desired longitudinal vehicle speed.

[0027] Preferably, in the step S2, the road curvature-yaw rate transformation formula is expressed as:

[0028] ; wherein, is the lane center curvature, is the desired longitudinal vehicle speed

[0029] Preferably, any of the desired states includes a desired lateral velocity sequence, a desired yaw rate sequence, and a desired longitudinal velocity.

[0030] Preferably, in the step S3, designing a predictive controller based on the linear parameter-varying prediction model and the maximum robust positive invariant set theory includes:

[0031] Designing a predictive controller framework based on the linear parameter-varying prediction model;

[0032] Using the maximum robust positive invariant set theory to design the terminal elements acting on the predictive controller framework, and the terminal elements include a terminal control gain and a terminal penalty matrix .

[0033] Preferably, in the step S3, the vehicle feedback state includes the lane center trajectory point coordinate sequence, the heading angle sequence, and the curvature sequence detected by the sensor.

[0034] Preferably, in the step S3:

[0035] At each sampling moment , input the current vehicle feedback state and the current desired state ;

[0036] Adopt the maximum robust positive invariant set as the terminal invariant set of the predictive controller, solve the control sequence of the predictive controller, and use the first element of the control sequence as the control variable;

[0037] The control sequence is expressed as: ; where is the prediction horizon;

[0038] The control variables include the front wheel steering angle and the rear wheel longitudinal force.

[0039] In summary, before the vehicle starts, arbitrarily select one of the two desired state planning modes of Mode 1 and Mode 2, and the vehicle travels at the desired longitudinal speed; at each sampling moment, accept the lane center trajectory point coordinate sequence, the heading angle sequence, and the curvature sequence detected by the sensor as the current vehicle state; then input these data into the desired state planning layer, and plan the desired lateral speed sequence and yaw rate sequence within the prediction horizon according to the pre-selected mode; then input the planned desired state sequence and the vehicle state into the predictive controller together, and the output control variables are the front wheel steering angle and the rear wheel longitudinal force, which act on the vehicle system to control the vehicle to travel stably in the lane center.

[0040] Compared with the prior art, the present invention has the following beneficial effects:

[0041] (1) Fast data-driven modeling based on mathematical models and Koopman theory: The present invention directly collects the input and output data of the three-degree-of-freedom nonlinear vehicle dynamics model, and uses Koopman theory to fit and obtain a globally linearized model. This method does not require time-consuming and laborious collection of a large amount of real vehicle data, and only needs to change the vehicle model parameters to obtain the Koopman linearized models of different vehicles.

[0042] (2) Balancing modeling accuracy and controller real-time performance: The Koopman linearized model adopted when designing the predictive controller in the present invention evolves the nonlinear system in a linear manner in the state space, which not only ensures the prediction accuracy of the model, but also greatly reduces the computational burden.

[0043] (3) Predictive control scheme for guaranteed asymptotically stable tracking: The present invention uses the theory of the maximum robust positive invariant set to design the terminal elements of the predictive controller, so as to theoretically guarantee the asymptotically stable tracking of the lane-keeping closed-loop control system for the desired lane center trajectory. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 is the principle block diagram of the lane-keeping predictive control method with asymptotically stable tracking of the present invention;

[0045] Figure 2 is the geometric schematic diagram of the lane-keeping model;

[0046] Figure 3 is the comparison result diagram of the state variable dynamic responses of the Koopman linearized model, the three-degree-of-freedom vehicle model and the Carsim vehicle model;

[0047] Figure 4 is the verification diagram of the accuracy of the desired state planning in Mode 1 and Mode 2;

[0048] Figures 5 - 10 is the comparison diagram of the simulation results of simulating the extreme driving conditions. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0049] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0050] Embodiment 1

[0051] Referring to Figure 1 the schematic diagram shown, a lane-keeping predictive control method with asymptotically stable tracking provided by the present invention specifically includes:

[0052] S1. Based on the Koopman theory and the DMD algorithm, a vehicle linearized model is fitted, and a linear parameter-varying predictive model is constructed by combining the vehicle linearized model and the lane-keeping model.

[0053] Specifically:

[0054] S11. Establish a three-degree-of-freedom non-linear vehicle dynamics model:

[0055] ;

[0056] Wherein, , , They are the longitudinal vehicle speed, lateral vehicle speed, and yaw rate respectively. , They are the front wheel steering angle and the longitudinal force of the rear wheel respectively. Since rear-wheel drive is considered, the longitudinal force of the front wheel is zero. is the unsprung mass of the vehicle. is the moment of inertia of the vehicle. , They are the distances from the center of mass to the front and rear axles respectively. , They are the lateral and longitudinal aerodynamic drag coefficients respectively. , They are the lateral and longitudinal frontal areas respectively. is the air density. , They are the lateral forces of the front and rear wheels respectively.

[0057] , They are expressed by the magic tire formula respectively as:

[0058] ;

[0059] Among them, , , , are the front wheel parameters. , , , are the rear wheel parameters. , They are the sideslip angles of the front and rear wheels respectively.

[0060] , The calculation formulas are respectively:

[0061] ;

[0062] ;

[0063] In summary, in the three-degree-of-freedom nonlinear vehicle dynamics model, the model state variables and the model control variables are defined.

[0064] S12. Collect the input and output data of the three-degree-of-freedom nonlinear vehicle dynamics model at the sampling time to construct a data matrix:

[0065] ;

[0066] Among them , are respectively the sampling times The state variables and control variables are and predicted.

[0067] S13. Based on the Koopman theory, the DMD algorithm, and the data matrix, a vehicle linearization model is fitted, and the vehicle linearization model is the Koopman linearization model of the three-degree-of-freedom nonlinear vehicle dynamics model;

[0068] Based on the DMD algorithm, the following linear relationship exists in the data matrix:

[0069] ;

[0070] where , , the optimal linear fitting operator is obtained by solving the least squares problem where is the Frobenius norm;

[0071] Finally, the Koopman linearization model is obtained:

[0072] ;

[0073] where is the state variable of the model at time is the control variable of the model at time

[0074] S14. According to the Figure 2 geometric relationship, a lane keeping model is constructed:

[0075] ;

[0076] where is the preview distance, and are the lateral error and the heading angle error between the current position of the vehicle and the lane center position ahead at , is the desired yaw rate of the vehicle when it travels to the lane center position ahead at .

[0077] S15. Combine the vehicle linearization model and the lane keeping model to construct a linear parameter-varying prediction model:

[0078] ;

[0079] where , , , the state variable , the control variable is consistent with the Koopman linearization model, that is , represents the bounded modeling error between the linear parametric prediction model and the actual system.

[0080] S2. Design two expected state planning modes:

[0081] (1) Mode 1 is to calculate the expected state based on the vehicle-road coordinate transformation formula;

[0082] At the known expected longitudinal vehicle speed , the vehicle-road coordinate transformation formula is expressed as:

[0083] ;

[0084] Among them, , , are the position and heading angle of the vehicle's center of mass in the road coordinate system;

[0085] Define the model state variable , the control variable , after linearization, discretize with the sampling time to obtain the linear time-varying discrete model , where:

[0086] ;

[0087] Adopt the MPC method to solve the following quadratic programming problem at each sampling time :

[0088]

[0089] Among them, is the prediction horizon, , are positive definite weight matrices, is the vehicle pose state at the sampling time , is based on predicted moment state, is the corresponding expected state, is the control variable to be solved within the prediction horizon, , are the lower and upper limits of the control variable.

[0090] From the above, form the control sequence ,

[0091] Specifically, the obtained control sequence That is, the desired lateral velocity of the vehicle within the prediction horizon sequence, desired yaw rate sequence (the desired longitudinal velocity, lane center trajectory point coordinates, heading angle sequence, and vehicle state within the input prediction horizon).

[0092] (2) Mode 2 is to calculate the desired state by means of a linear parameter-varying prediction model and a road curvature-yaw rate conversion formula;

[0093] At the sampling moment , based on the current vehicle state and the linear parameter-varying prediction model, the lateral velocity sequence can be predicted and used as the desired lateral velocity sequence at the sampling moment ;

[0094] The desired longitudinal velocity is known, and the desired lane center curvature sequence is input. Through the road curvature-yaw rate conversion formula the desired yaw rate sequence can be obtained, where is the lane center curvature;

[0095] Thus, the desired lateral velocity sequence and desired yaw rate sequence (the desired longitudinal velocity, lane center curvature sequence within the input prediction horizon, and the control sequence solved by the predictive controller) can be solved.

[0096] S3. Design a predictive controller based on the linear parameter-varying prediction model and the maximum robust positive invariant set theory, and

[0097] the input of the predictive controller is the vehicle feedback state and one of the desired states;

[0098] the output of the predictive controller is the control quantity acting on the vehicle.

[0099] Specifically, the vehicle feedback state includes the lane center trajectory point coordinate sequence, heading angle sequence, and curvature sequence detected by sensors;

[0100] Specifically, for the two planning modes provided in step S2, the desired lateral velocity sequence and desired yaw rate sequence can both be calculated. By combining the desired longitudinal velocity, the desired state can be formed (that is, both modes realize the conversion of lane information into the vehicle desired state). In practical applications, one of the planning modes is selected in a pre-set manner (before the vehicle starts), and thus the corresponding desired state is solved based on this planning mode.

[0101] S31. Design a predictive controller framework based on the linear parameter-varying prediction model;

[0102] At each sampling instant , the input vehicle state and the desired state are used to solve the following convex optimization problem based on MPC, and the first element of the obtained control sequence is used as the control input for the vehicle:

[0103]

[0104] where is the state predicted at the -th sampling instant;

[0105] Define as the corresponding desired state:

[0106] ;

[0107] are the control inputs to be solved within the prediction horizon and form the control sequence:

[0108]

[0109] In summary is a positive definite state error weight matrix, is a positive definite control input weight matrix, is the terminal penalty matrix, , are the lower and upper bounds of the state variables, , are the lower and upper bounds of the control inputs, and are the coefficient matrices of the terminal invariant set obtained by the maximum robust positive invariant set theory; and are respectively called the terminal penalty and the terminal inequality constraint, which together form the terminal elements to ensure asymptotically stable tracking of the desired state.

[0110] S32. Design the terminal elements acting on the prediction controller framework using the maximum robust positive invariant set theory;

[0111] Define , , , , the terminal control gain and the terminal penalty matrix are obtained by solving the discrete algebraic Riccati inequality:

[0112]

[0113] Assume the modeling error , the error system , the state quantity error constraint set in the form of a polyhedron , the control quantity constraint set and the error constraint set :

[0114]

[0115] Adopt the maximum robust positive invariant set in the form of a polyhedron as the terminal invariant set, and its mathematical description is , and the solution process includes:

[0116] step1: Initialization: , ;

[0117] step2: Obtain the robust one-step backward reachable set of each vertex of the polytope system:

[0118]

[0119] step3: Iteration: ;

[0120] step4: Termination condition: If , then ; Otherwise, let , and return to step2.

[0121] In summary, before the vehicle starts, any one of the two desired state planning modes of Mode 1 and Mode 2 is selected, and the vehicle travels at the desired longitudinal speed; at each sampling moment, the vehicle accepts the lane center trajectory point coordinate sequence, heading angle sequence, and curvature sequence detected by the sensor as the current vehicle state; then these data are input into the desired state planning layer, and the desired lateral speed sequence and yaw rate sequence within the prediction time domain are planned according to the pre-selected mode; after that, the planned desired state sequence and the vehicle state are jointly input into the prediction controller, and the output control quantities are the front wheel steering angle and the rear wheel longitudinal force, which act on the vehicle system to control the vehicle to stably travel in the lane center.

[0122] Please refer to Figures 3 - 10 , the present invention provides a specific embodiment to verify the prediction accuracy of the Koopman linearization model and the effectiveness of the two desired state planning modes, and verifies the effect of the lane keeping prediction control method on the Carsim-Simulink co-simulation platform.

[0123] The Carsim vehicle selects the E-class Sedan, which is set to front-wheel steering and rear-wheel drive. The tires are 225 / 60R18, and the parameter settings of the three-degree-of-freedom nonlinear vehicle dynamics model are the same as those of the Carsim vehicle.

[0124] 1. Koopman linearization model verification:

[0125] Sampling time , control variable 、 The sampling ranges of 、 are 、 、 respectively, and the sampling ranges of state variables 、 、 are

[0126] The initial values of state variables are selected as , and the control variable is selected as , , Figure 3 shows the evolution of state variables of the Koopman linearization model, the three-degree-of-freedom vehicle model, and the Carsim vehicle model under the action of this control variable; it can be seen from Figure 3 that the Koopman linearization model and the three-degree-of-freedom vehicle model have high fitting accuracy and can fully evolve the nonlinear characteristics of real vehicles

[0127] 2. Verification of two expected state planning modes:

[0128] Make the Carsim vehicle drive along the road with a longitudinal speed of 25 m / s and a curvature change as shown in Figure 4 , and collect the vehicle state variables as the real expected state. Then obtain the planned expected states under Mode 1 and Mode 2 respectively; it can be seen from Figure 4 that the expected states planned by Mode 1 and Mode 2 fit well with the real values, which verifies the availability of the two expected state planning modes.

[0129] 3. Verification of lane keeping effect:

[0130] The lane width of the Chinese standard highway is 3.75 m, the road surface adhesion coefficient is , and the maximum road curvature is . In order to verify the superiority of the present invention under extreme working conditions, set the expected longitudinal speed of the vehicle , drive on the lane with a curvature change as shown in Figure 5 , and the maximum curvature , the expected state planning mode selects mode 1, and the predictive controller is solved using the "quadprog" solver on Matlab. The simulation results are as Figures 6 - 10 .

[0131] Figure 6 The curve graph of the expected state planned by the longitudinal speed, lateral speed, and yaw rate tracking mode 1 of the vehicle. It can be seen that the predictive controller designed by the present invention can stably track the expected state.

[0132] Figure 7 The curve graph of the lateral error and heading deviation between the vehicle and the center line of the lane. The maximum lateral error is only 0.065m, and the maximum heading error is only 1.61deg, and the final errors can all converge to zero.

[0133] Figure 8 The curve graph of the front wheel steering angle and the rear wheel longitudinal force during the tracking process. It can be seen that the changes of these two control variables are relatively gentle and smooth, and do not exceed the preset constraints.

[0134] Figure 9 The comparison graph of the actual driving trajectory and the reference trajectory of the Carsim vehicle. The two trajectories are very close, and the error is consistent with Figure 8 described.

[0135] Figure 10 The statistical graph of the solution time of the predictive controller during the simulation process. The maximum solution time is only 0.0017s, which is much less than the sampling time of 0.01s.

[0136] The above results show that: the Koopman linear model described in the present invention effectively guarantees the real-time performance of the predictive controller while fully retaining the nonlinear characteristics of the vehicle; the two expected state planning modes described in the present invention can both ensure the accuracy of the planning, and the predictive control method described in the present invention can achieve asymptotic stable tracking of the expected lane center trajectory.

[0137] Embodiment 2

[0138] Based on the above Embodiment 1, this embodiment builds a lane keeping predictive control system, including:

[0139] A linear parameter-varying predictive model; the linear parameter-varying predictive model is constructed based on the vehicle linearization model and the lane keeping model, and the vehicle linearization model is obtained by fitting based on the Koopman theory and the DMD algorithm;

[0140] An expected state planner; having two alternative expected state planning modes. Mode 1 is to calculate the expected state based on the vehicle-road coordinate transformation formula, and mode 2 is to calculate the expected state by means of the linear parameter-varying predictive model and the road curvature-yaw rate transformation formula;

[0141] Predictive controller; the predictive controller is designed based on the combination of a linear parameter-varying prediction model and the theory of the maximum robust positive invariant set, and the predictive controller takes the vehicle feedback state and one of the desired states as inputs and the control quantity acting on the vehicle as the output.

[0142] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A lane keeping predictive control method for asymptotic stable tracking, characterized in that, Including: S1. Fit a vehicle linearized model based on the Koopman theory and the DMD algorithm, and construct a linear parameter-varying prediction model by combining the vehicle linearized model with the lane-keeping model; S2. Design two expected state planning modes. Mode 1 calculates the expected state based on the vehicle-road coordinate transformation formula, and Mode 2 calculates the expected state by means of the linear parameter-varying prediction model and the road curvature-yaw rate transformation formula; S3. Design a predictive controller based on the linear parameter-varying prediction model and the maximum robust positive invariant set theory, and the input of the predictive controller is the vehicle feedback state and one of the expected states; the output of the predictive controller is the control quantity acting on the vehicle.

2. The lane keeping predictive control method for asymptotic stable tracking according to claim 1, wherein In the step S1, the steps of fitting a vehicle linearized model based on the Koopman theory and the DMD algorithm include: With the sampling time Collect the input and output data of the three-degree-of-freedom nonlinear vehicle dynamics model to construct a data matrix; Fit a vehicle linearized model based on the Koopman theory, the DMD algorithm and the data matrix, and the vehicle linearized model is the Koopman linearized model of the three-degree-of-freedom nonlinear vehicle dynamics model: ； Among them, is the state quantity of the time model, , , are the longitudinal speed, lateral speed, and yaw rate of the vehicle respectively; is the control quantity of the time model, , are the front wheel angle and rear wheel longitudinal force of the vehicle respectively; the matrix is the optimal linear fitting operator.

3. The lane keeping predictive control method for asymptotic stable tracking according to claim 2, characterized in that: In the step S1, the lane-keeping model is expressed as: ； Among them, is the preview distance, and are the lateral error and yaw angle error between the current position of the vehicle and the center position of the lane ahead at . is the desired yaw rate when the vehicle travels to the center position of the lane ahead at .

4. A lane keeping predictive control method for asymptotic stable tracking according to claim 3, characterized in that: In the step S1, the linear parameter-varying prediction model is expressed as: ； Among them, , , , the state variable , the control variable is consistent with the Koopman linearization model, that is , represents the bounded modeling error between the linear parametric prediction model and the actual system.

5. A lane keeping predictive control method for asymptotic stable tracking according to claim 1, characterized in that: In the step S2, the vehicle-road coordinate transformation formula is expressed as: ； Among them, , , are the position and heading angle of the vehicle's center of mass in the road coordinate system, is the desired longitudinal vehicle speed.

6. The lane keeping predictive control method for asymptotic stable tracking according to claim 1, characterized in that: In the step S2, the road curvature-yaw rate transformation formula is expressed as: ; wherein, is the lane center curvature, is the desired longitudinal vehicle speed.

7. A lane keeping predictive control method for asymptotic stable tracking according to claim 5 or 6, characterized in that: Any one of the expected states includes an expected lateral velocity sequence, an expected yaw rate sequence and an expected longitudinal velocity.

8. A lane keeping predictive control method for asymptotic stable tracking according to claim 1, characterized in that In the step S3, designing a predictive controller based on the linear parameter-varying prediction model and the maximum robust positive invariant set theory includes: Design a predictive controller framework based on the linear parameter-varying prediction model; The terminal element acting on the predictive controller framework is designed by using the maximum robust positive invariant set theory, and the terminal element includes a terminal control gain and a terminal penalty matrix .

9. A lane keeping predictive control method for asymptotic stable tracking according to claim 1 or 8, characterized in that: In the step S3, the vehicle feedback state includes the lane center trajectory point coordinate sequence, the heading angle sequence and the curvature sequence detected by the sensor.

10. A lane keeping predictive control method for asymptotic stable tracking according to claim 9, characterized in that, In the step S3: At each sampling moment , the current vehicle feedback state and the current desired state are input to the predictive controller; Use the maximum robust positive invariant set as the terminal invariant set of the predictive controller, solve the control sequence of the predictive controller, and use the first element of the control sequence as the control quantity; The control sequence is expressed as: ; where is the prediction time domain; The control quantity includes the front wheel steering angle and the rear wheel longitudinal force.

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