An adaptive dynamic evolving direct data-driven vehicle trajectory tracking control method

Abstract

The application provides a kind of direct data driven vehicle trajectory tracking control method of adaptive dynamic evolution, comprising: in each control cycle of vehicle control system, according to the real-time collected vehicle input and output data sequence, the linear independence index of data in current buffer is calculated, and the buffer data is dynamically updated according to the calculation result, to obtain buffer historical data;Buffer historical data is mapped to the local ego coordinate system with the vehicle mass center at the current time as the origin and the vehicle head direction as the X axis;Based on the local ego coordinate system, a predictive control optimization model containing a virtual set point and double regularization is constructed, which is converted into a quadratic programming problem by algebraic reconstruction;Solve the quadratic programming problem online to obtain the optimal control sequence in the local ego coordinate system, and extract the first control quantity of the optimal control sequence as the control command to act on the steering and power actuators of the vehicle control system.The application improves the driving safety of the vehicle.

Description

Technical Field

[0001] This invention relates to the field of autonomous driving control technology, and in particular to an adaptive, dynamically evolving direct data-driven vehicle trajectory tracking control method. Background Technology

[0002] As the automotive industry shifts towards electrification, intelligence, connectivity, and sharing, autonomous driving technology has become a hot research area in the contemporary automotive industry. In the autonomous driving control system, the control module, as the key to enabling autonomous vehicle driving, directly determines the safety and stability of driving.

[0003] While traditional modular control schemes can handle simple driving tasks, their drawbacks, such as error amplification and parameter complexity, are becoming increasingly apparent. Model predictive control (MPC), due to its excellent constraint handling capabilities and look-ahead optimization characteristics, has been widely used in trajectory tracking. However, traditional MPC relies heavily on accurate vehicle dynamics models, resulting in high modeling costs and significant performance degradation under conditions of difficult parameter calibration, nonlinear coupling, and road disturbances.

[0004] In recent years, "data-driven predictive control (DPC)," which allows for prediction directly from data without explicit modeling, has become a research hotspot. Direct data-driven control, in particular, avoids explicit system identification and directly uses input-output data for prediction. Based on Willems' fundamental lemma, DPC extracts system features directly from input-output data by constructing a Hankel matrix, thus circumventing the complex modeling process. However, applying DPC to real-world vehicle trajectory tracking still faces three major technical challenges: (1) Nonlinear geometric distortion problem: When the vehicle moves over a wide range, the state data in the global coordinate system exhibits strong nonlinear characteristics. Since traditional DPC constructs the Hankel matrix based on linear assumptions, this geometric distortion will cause prediction failure and make it difficult to guarantee tracking accuracy under complex working conditions.

[0005] (2) Problem of failure of continuous excitation condition: When the vehicle is running in a straight line or under steady-state conditions, the linear correlation between the collected data is extremely high, which leads to the rank deficiency phenomenon of the Hankel matrix. This makes it impossible for the system to meet the "continuous excitation" condition, which in turn causes the controller to be unable to solve or the results to diverge.

[0006] (3) Conflict between strong noise and hard constraints: Vehicle sensors generally have large noise, while vehicle physical actuators have strict hard constraints. Directly fitting the data can easily lead to severe fluctuations in the control quantity, or even exceed the vehicle's physical limits, seriously affecting driving comfort and safety.

[0007] Most existing DPC methods address only one aspect of the aforementioned problems in isolation, lacking a systematic approach that integrates spatiotemporal geometric correction, proactive data quality management, and robust constraint solving. Therefore, researching a data-driven control algorithm capable of handling strong nonlinearity, high noise, and closed-loop stability is of significant theoretical and practical value for promoting the practical application of autonomous driving technology. Summary of the Invention

[0008] In view of this, the present invention provides an adaptive dynamic evolution direct data-driven vehicle trajectory tracking control method, which solves the nonlinear problem by local coordinate reconstruction in space, solves the data degradation problem by adaptive dynamic evolution mechanism of historical data in time, and solves the robustness problem by virtual setpoint and dual regularization at the optimization level.

[0009] One aspect of the present invention provides an adaptive dynamic evolution direct data-driven vehicle trajectory tracking control method, comprising: within each control cycle of the vehicle control system, calculating the linear independence index of data in the current buffer based on real-time acquired vehicle input / output data sequences, and dynamically updating the buffer data according to the calculation results to obtain historical buffer data; mapping the historical buffer data to a local vehicle coordinate system with the vehicle's centroid at the current moment as the origin and the vehicle's heading direction as the X-axis; constructing a predictive control optimization model including a virtual setpoint and double regularization based on the local vehicle coordinate system, and transforming it into a quadratic programming problem through algebraic reconstruction; solving the quadratic programming problem online within each control cycle of the vehicle control system to obtain the optimal control sequence in the local vehicle coordinate system, and extracting the first control quantity of the optimal control sequence as a control command to act on the steering and power actuators of the vehicle control system.

[0010] Optionally, the method further includes: collecting the latest status response data of the vehicle after executing the control command; using the latest status response data as a new vehicle input / output data sequence to update the historical data in the buffer for calculation of the next control cycle.

[0011] Optionally, the step of calculating the linear independence index of the data in the current buffer and dynamically updating the buffer data according to the calculation result includes: calculating the minimum singular value of the Hankel matrix composed of the data in the current buffer as the linear independence index; comparing the minimum singular value with a preset threshold, and determining whether the data in the current buffer meets the continuous stimulus condition according to the comparison result; if the continuous stimulus condition is met, then the first update strategy is executed; if the continuous stimulus condition is not met, then the second update strategy is executed.

[0012] Optionally, the first update strategy is to update the buffer using a first-in-first-out strategy; the second update strategy is to activate an information compensation mechanism; wherein the information compensation mechanism is to refuse to remove historical data frames with high excitation characteristics in the buffer and only replace the data frames that contribute the least to the data richness; or to superimpose a jitter excitation signal that meets the amplitude limit on the current control output.

[0013] Optionally, determining whether the data in the current buffer meets the continuous excitation condition based on the comparison result specifically includes: before updating the data in each control cycle, assuming that the buffer is updated using a first-in-first-out strategy, pre-calculating the minimum singular value of the updated Hankel matrix; if the pre-calculated minimum singular value is greater than a preset threshold, it is determined that the continuous excitation condition is met; if the pre-calculated minimum singular value is not greater than the preset threshold, it is determined that the continuous excitation condition is not met.

[0014] Optionally, the preset threshold is calibrated through offline simulation, specifically including: obtaining the distribution range of singular values ​​of historical data of the vehicle under straight-line and steering conditions; combining the distribution range of singular values ​​of historical data and the covariance intensity estimation of sensor measurement noise, setting a minimum boundary value that allows the Hankel matrix to maintain linear independence after noise interference is removed as the preset threshold.

[0015] Optionally, the objective function of the predictive control optimization model It adopts a quadratic form structure, consisting of a trajectory tracking error term, a control input term, and a double regularization term:

[0016] in, For the current time step, To predict the number of steps, To predict the length of the time domain; and In time Predicted future The input and output trajectories of the step; and These are the online optimized virtual input setpoints and virtual output setpoints, respectively. Set a point for the global objective; The weight vector when constructing a predictive control optimization model based on data; Relaxation variables introduced to handle data noise and local linearization errors; This is the weight matrix for the control quantity cost term, corresponding to the penalty for the predicted control quantity deviating from the virtual input setpoint; This is the weight matrix for the output cost term, corresponding to the penalty for the predicted output deviating from the virtual output setpoint; This is the weight matrix for the virtual setpoint penalty term, corresponding to the penalty for the virtual output setpoint deviating from the global target setpoint; and These are regularization parameters, used to apply to the weight vector. and slack variables The norm is used for regularization constraints to reduce the impact of noise and prevent slack variables from becoming too large.

[0017] Optionally, the dual regularization term includes: a first regularization term, which suppresses multiplication noise in historical data in the buffer and prevents overfitting by penalizing the L2 norm of the data combination weight vector; and a second regularization term, which compensates for sensor additive noise and local modeling errors by introducing an initial state relaxation variable.

[0018] In another aspect, the present invention provides an electronic device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of an adaptive dynamic evolution direct data driven vehicle trajectory tracking control method as described in any of the preceding claims.

[0019] In another aspect, the present invention provides a computer storage medium storing a computer program that, when executed by a processor, implements the steps of an adaptive dynamic evolution direct data-driven vehicle trajectory tracking control method as described in any of the preceding claims.

[0020] Compared with the prior art, the present invention has the following beneficial effects: (1) This invention effectively solves the problem of geometric distortion in extreme conditions such as sharp turns and U-turns for autonomous vehicles, significantly improving driving safety. This invention maps the strongly nonlinear trajectory in the global coordinate system to the local vehicle coordinate system by performing local spatiotemporal coordinate reconstruction based on the current pose. This spatial dimension geometric alignment technology ensures that the data-driven model always unfolds near the origin of the state space, thereby greatly improving the prediction accuracy and path compliance of the vehicle in complex scenarios such as curves and U-turns at intersections, and effectively avoiding the risk of the vehicle running off the path due to model linear distortion.

[0021] (2) This invention overcomes the potential data degradation problem in steady-state cruise conditions of autonomous driving by adaptively and dynamically evolving historical data. This invention abandons the rigid data update mode in traditional data-driven methods and establishes a dynamic evolution mechanism that can perceive data incentive characteristics in real time. In "low-incentive" scenarios such as long-distance straight-line driving, this mechanism can spontaneously lock "high-value" historical data with rich dynamic characteristics, ensuring that the Hankel matrix always meets the continuous incentive conditions, greatly improving the reliability of the system under all operating conditions.

[0022] (3) This invention balances robustness in high-noise environments with ride comfort, achieving "human-like" smooth trajectory tracking. This invention constructs an optimization model that includes a virtual setpoint and dual regularization. The dual-layer buffer mechanism prevents the vehicle from rigidly correcting itself when faced with sensor disturbances or unreachable target paths, instead finding the optimal balance point within the range of physical feasibility, effectively eliminating actuator jitter. Combined with dual regularization terms targeting multiplicative and additive noise, this solution not only protects the hardware lifespan of the vehicle's steering and powertrain systems but also significantly reduces passenger motion sickness, providing a smoother driving experience closer to human driving habits.

[0023] (4) This invention improves real-time computational efficiency in high-speed autonomous driving scenarios and enhances the system's emergency response capability. Although this invention deals with a complex nonlinear tracking problem, it reduces the original problem to a standard convex quadratic programming (QP) problem with extremely high computational efficiency through local spatiotemporal reconstruction. This enables the algorithm to achieve millisecond-level rolling time-domain solutions on a vehicle-mounted platform with limited computing power, ensuring that the vehicle can make optimal control decisions as soon as it encounters sudden obstacles or drastic changes in road conditions, thus guaranteeing the determinism of real-time closed-loop control. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. By reading the detailed description of the embodiments below, the advantages and benefits of the solutions will become clear to those skilled in the art. The accompanying drawings are only for illustrating preferred embodiments and are not intended to limit the present invention. In the accompanying drawings: Figure 1 This is a flowchart of the steps of the method of the present invention.

[0025] Figure 2 This is a schematic diagram of a monorail bicycle model.

[0026] Figure 3 This is a schematic diagram illustrating the principle of the pure tracking method for vehicle lateral control.

[0027] Figure 4 A schematic diagram of system input and output data to meet continuous excitation requirements.

[0028] Figure 5 This diagram illustrates the comparison of the final trajectory tracking performance using historical data of varying richness.

[0029] Figure 6 Flowchart of the information gatekeeper mechanism.

[0030] Figure 7 This is a schematic diagram of spatiotemporal coordinate reconstruction.

[0031] Figure 8 This is a pseudocode diagram of a nonlinear data-driven predictive control algorithm.

[0032] Figure 9 This diagram illustrates the comparison of trajectory tracking performance between traditional MPC and the Nonlinear DPC of this invention under different operating conditions.

[0033] Figure 10 This is a schematic diagram comparing the trajectory tracking RMSE of traditional MPC and the Nonlinear DPC of this invention under different operating conditions. Detailed Implementation

[0034] To enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art should fall within the protection scope of the present invention.

[0035] See Figure 1 The present invention discloses an adaptive dynamic evolution direct data-driven vehicle trajectory tracking control method, applied to a vehicle control system. This method mainly includes: Step S101: In each control cycle of the vehicle control system, the linear independence index of the data in the current buffer is calculated based on the real-time collected vehicle input and output data sequence, and the buffer data is dynamically updated based on the calculation results to obtain the historical data of the buffer. Step S102: Map the historical data in the buffer to a local vehicle coordinate system with the current vehicle centroid as the origin and the vehicle's heading direction as the X-axis; Step S103: Based on the local vehicle coordinate system, construct a predictive control optimization model that includes virtual setpoints and double regularization, and transform it into a quadratic programming problem through algebraic reconstruction; Step S104: In each control cycle of the vehicle control system, solve the quadratic programming problem online to obtain the optimal control sequence in the local vehicle coordinate system, and extract the first control quantity of the optimal control sequence as a control command to act on the steering and power actuators of the vehicle control system.

[0036] Optionally, the method further includes: collecting the latest status response data of the vehicle after executing the control command; using the latest status response data as a new vehicle input / output data sequence to update the historical data in the buffer for calculation of the next control cycle.

[0037] Optionally, the step of calculating the linear independence index of the data in the current buffer and dynamically updating the buffer data according to the calculation result includes: calculating the minimum singular value of the Hankel matrix composed of the data in the current buffer as the linear independence index; comparing the minimum singular value with a preset threshold, and determining whether the data in the current buffer meets the continuous stimulus condition according to the comparison result; if the continuous stimulus condition is met, then the first update strategy is executed; if the continuous stimulus condition is not met, then the second update strategy is executed.

[0038] Optionally, the first update strategy is to update the buffer using a first-in-first-out strategy; the second update strategy is to activate an information compensation mechanism; wherein the information compensation mechanism is to refuse to remove historical data frames with high excitation characteristics in the buffer and only replace the data frames that contribute the least to the data richness; or to superimpose a jitter excitation signal that meets the amplitude limit on the current control output.

[0039] Optionally, determining whether the data in the current buffer meets the continuous excitation condition based on the comparison result specifically includes: before updating the data in each control cycle, assuming that the buffer is updated using a first-in-first-out strategy, pre-calculating the minimum singular value of the updated Hankel matrix; if the pre-calculated minimum singular value is greater than a preset threshold, it is determined that the continuous excitation condition is met; if the pre-calculated minimum singular value is not greater than the preset threshold, it is determined that the continuous excitation condition is not met.

[0040] Optionally, the preset threshold is calibrated through offline simulation, specifically including: obtaining the distribution range of singular values ​​of historical data of the vehicle under straight-line and steering conditions; combining the distribution range of singular values ​​of historical data and the covariance intensity estimation of sensor measurement noise, setting a minimum boundary value that allows the Hankel matrix to maintain linear independence after noise interference is removed as the preset threshold.

[0041] Optionally, the objective function of the predictive control optimization model It adopts a quadratic form structure, consisting of a trajectory tracking error term, a control input term, and a double regularization term:

[0042] in, For the current time step, To predict the number of steps, To predict the length of the time domain; and In time Predicted future The input and output trajectories of the step; and These are the online optimized virtual input setpoints and virtual output setpoints, respectively. Set a point for the global objective; The weight vector when constructing a predictive control optimization model based on data; Relaxation variables introduced to handle data noise and local linearization errors; This is the weight matrix for the control quantity cost term, corresponding to the penalty for the predicted control quantity deviating from the virtual input setpoint; This is the weight matrix for the output cost term, corresponding to the penalty for the predicted output deviating from the virtual output setpoint; This is the weight matrix for the virtual setpoint penalty term, corresponding to the penalty for the virtual output setpoint deviating from the global target setpoint; and These are regularization parameters, used to apply to the weight vector. and slack variables The norm is used for regularization constraints to reduce the impact of noise and prevent slack variables from becoming too large.

[0043] Optionally, the dual regularization term includes: a first regularization term, which suppresses multiplication noise in historical data in the buffer and prevents overfitting by penalizing the L2 norm of the data combination weight vector; and a second regularization term, which compensates for sensor additive noise and local modeling errors by introducing an initial state relaxation variable.

[0044] Specifically, the solution of the present invention is further described with reference to the following examples: S1: Construct a historical data buffer based on an adaptive dynamic evolution mechanism. This step addresses the rank deficiency problem of the Hankel matrix under steady-state conditions through dynamic filtering in the time dimension. Specifically, this invention abandons the traditional first-in-first-out (FIFO) data update strategy and establishes a dynamic buffer with a real-time quality assessment mechanism. Within each control cycle, the vehicle's input and output data sequences are collected in real time, and the linear independence index of the data in the current buffer is calculated, preferably by calculating the minimum singular value of the Hankel matrix. If the index is higher than a preset threshold, a conventional "new in, old out" update is performed; if the index is lower than the threshold, a keyframe retention mechanism is triggered, locking historical data segments with high lateral excitation characteristics in the buffer to prevent their removal, or a small jitter excitation signal is superimposed on the control command to forcibly maintain the continuous excitation characteristics of the system data and prevent the controlled system from diverging.

[0045] S2: Perform local spatiotemporal coordinate reconstruction based on the current pose. This step eliminates nonlinear errors caused by global displacement through spatial coordinate mapping. Specifically, the historical data in the buffer selected in step S1 is mapped to a local vehicle coordinate system with the vehicle's centroid at the current time t as the origin and the vehicle's heading direction as the X-axis. Using coordinate translation and rotation transformation formulas, the global coordinates of historical trajectory points are transformed into local coordinates relative to the current vehicle body, and the relative heading angle is updated synchronously. On this basis, the final state of the historical data is required to be geometrically aligned with the measured initial state of the current vehicle, thereby transforming the nonlinear global trajectory motion into a locally linear affine system dynamic, ensuring that the data-driven prediction model always unfolds near the origin of the state space, thus improving the accuracy of linear approximation.

[0046] S3: Construct a predictive control optimization model incorporating a virtual setpoint and dual regularization. This step aims to construct a noise-tolerant quadratic programming (QP) problem and achieve robust control using locally linearized data. Specifically, this invention introduces a virtual setpoint into the optimization objective function, constructing a two-layer buffer between physical feasibility and the remote task objective. By minimizing the combined error between the predicted trajectory and the virtual setpoint, and between the virtual setpoint and the global reference path, system oscillations caused by forcibly tracking unreachable paths are avoided. Simultaneously, a dual regularization mechanism is implemented: the first regularization term penalizes the L2 norm of the data combination weight vector to suppress multiplicative noise in historical data and prevent overfitting; the second regularization term, combined with the introduced initial state relaxation variable, compensates for sensor additive noise and local modeling errors, ensuring the continued feasibility of the optimization problem in the rolling time domain.

[0047] S4: Execute rolling time-domain solution and inverse mapping command output. This step realizes real-time execution and iterative data update of closed-loop feedback control. Within each control cycle, the system solves the quadratic programming problem constructed in step S3 online to obtain the optimal control sequence in the local coordinate system. The system extracts only the first control variable in this sequence and applies it as an incremental command to the vehicle's underlying steering and power actuators, either according to the inverse transformation logic of the coordinate system or directly. After the command is executed, the system collects the latest dynamic response data of the vehicle in real time and feeds it back to step S1. Through continuous sampling, reconstruction, optimization, and execution loops, high-precision and robust real-time tracking control of the vehicle's target trajectory is achieved.

[0048] S1 includes: S11: Define the system state based on the kinematic model of the vehicle-mounted monorail bicycle, serving as the physical basis for data acquisition and processing. The relevant assumptions for the vehicle-mounted monorail bicycle model include: (1) The motion of the vehicle in the vertical direction is not considered, that is, the motion of the vehicle is assumed to be a two-dimensional plane (X, Y).

[0049] (2) Assuming that the left and right tires of the vehicle have the same steering angle and speed at any time, the motion of the two tires on the left and right sides of the wheel can be combined into one tire to describe the motion.

[0050] (3) Assume that the vehicle speed changes slowly and ignore the transfer of load between the front and rear axles.

[0051] (4) Assume that the vehicle body and suspension system are both rigid systems.

[0052] See Figure 2 The symbols and definitions in the vehicle monorail bicycle model are as follows: : Center point of the front wheel; : Rear wheel center point; Vehicle center of gravity; Front wheel steering angle; Rear wheel steering angle; : The distance from the center point of the front wheel to the center point of the vehicle's mass; : The distance from the center point of the rear wheel to the center point of the vehicle's mass; Vehicle wheelbase ; The speed of the vehicle's center of gravity; Slip angle: The angle between the direction of the vehicle's center of gravity velocity and the vehicle's longitudinal axis; The instantaneous center of rotation of the vehicle; The radius of the vehicle's trajectory; : Vehicle heading angle; Define the system state vector Control input quantity .

[0053] When the vehicle speed is very low (<5m / s), a continuous-time model of vehicle dynamics can be derived:

[0054] S12: Construct a two-point reference controller and data acquisition environment to meet continuous excitation requirements. The offline data acquisition part of the actual vehicle trajectory tracking control aims to collect data that contains all information about the vehicle model, thus meeting the continuous excitation requirements. For an unstable actual vehicle system, data generation is not easy; instability does not automatically guarantee continuous excitation, and damage to the unstable system during trajectory generation must be avoided. Therefore, when generating the initial I / O trajectory, the system needs to be pre-stabilized. For this purpose, a reference controller is used for trajectory tracking control to collect the required data from the vehicle model. Specifically, a lateral and longitudinal decoupling control method is used: longitudinally, a PID controller tracks the speed, and laterally, a pure tracking method is used, such as... Figure 3 As shown.

[0055] The longitudinal controller is a PID speed tracking controller.

[0056] in, For speed error, For PID gain coefficient, For the desired output acceleration, satisfying .

[0057] The lateral controller is a pure tracking method based on the vehicle's single-track kinematic model. The control variable of the pure tracking method is the front wheel steering angle. The expression is:

[0058] in, It refers to the vehicle's wheelbase. It is the angle between the aiming point and the vehicle body. , These are the coordinates of the center point of the rear axle of the vehicle. The coordinates of the aiming point. For the vehicle's heading angle, For the pre-aiming distance, , To determine the degree to which the aiming distance is positively correlated with speed, This is the minimum aiming distance.

[0059] To achieve continuous excitation, uniformly distributed random noise needs to be added to the output of the feedback controller, i.e., the input of the vehicle control system. The noise should be large enough to ensure continuous excitation, but small enough to avoid affecting system stability.

[0060] In a control example based on a vehicle's single-track kinematics model, the control period is 0.1s, and the control input includes the front wheel steering angle. longitudinal acceleration Increased random noise , Sampling time is The aforementioned feedback controller with lateral and longitudinal decoupling is used to control the vehicle to track a double-twisted trajectory, such as... Figure 4 The diagram shows the actual inputs acting on the system and the system's response, including the vehicle's actual position coordinates, heading angle, and velocity.

[0061] S13: Implement data adaptive dynamic evolution by introducing an "information gatekeeper" mechanism, such as... Figure 6 As shown. The data sequence length is [length missing]. Historical data buffer By using a pre-calculated singular value discrimination mechanism to dynamically manage data quality, the problem of data degradation under linear operating conditions can be solved.

[0062] (1) Buffer size definition: Set the length of the data sequence Its value must meet the requirements of the system's continuous excitation order. ,in For the input dimension, Let be the system order. The initial condition length, To predict the length of the time domain.

[0063] (2) Information pre-evaluation logic: Set the minimum threshold for the full rank of the Hankel matrix rows. At that moment Before updating the data, the system first performs pre-calculation: assuming a first-in-first-out (FIFO) update strategy is adopted, i.e., the oldest data is removed and the latest data is added, the minimum singular value of the Hankel matrix after the update is calculated. .

[0064] (3) Singular value threshold The selection logic is as follows: First, obtain the distribution range of singular values ​​of historical data of the vehicle under straight and turning conditions. Combined with the covariance intensity estimation of sensor measurement noise, set a minimum boundary value that allows the Hankel matrix to maintain linear independence after noise interference is removed. This threshold is calibrated through offline simulation to ensure that the information compensation mechanism can be triggered in time under insufficient excitation conditions.

[0065] Adaptive classification update strategy: Condition 1: Sufficient excitation: If the pre-calculation results meet the requirements... If the current information is sufficient, then a regular FIFO update is performed directly to maintain the local timeliness of the buffer.

[0066] Condition 2: Insufficient excitation: If the pre-calculation results meet the requirements... If the system then initiates "gatekeeper" intervention: it refuses to remove historical data frames with high excitation characteristics from the buffer, and only replaces the data frames in the buffer that contribute the least to richness; or, in the current control output... Superimposed with a satisfying Gaussian white noise is used to actively excite the system dynamics, ensuring that the data sequence always meets the continuous excitation conditions.

[0067] like Figure 5 As shown, this embodiment verifies the data richness management mechanism described in S1. Figure 5 The black dotted line represents the tracking effect when using only low-excitation (straight-line driving) historical data. It shows that the vehicle loses control and diverges when entering a curve because steering features cannot be extracted. The solid black line and dashed line represent the effect when using high-excitation (figure-eight and circular) historical data, respectively. The vehicle achieves high-precision tracking of the reference trajectory shown by the dashed line. This result intuitively demonstrates that the strategy of identifying and locking high-excitation data frames through singular value discrimination in S13 plays a decisive role in preventing rank deficiency in the Hankel matrix and ensuring the stability of closed-loop control.

[0068] See Figure 7 The S2 spatiotemporal coordinate reconstruction includes: S21: Local coordinate mapping and translation / rotation transformation based on the current vehicle pose. To eliminate nonlinear distortion caused by global position shift during large-scale vehicle movement and to align the historical trajectory geometrically with the current vehicle state, a buffer is used. All global state data is transformed to a local vehicle coordinate system with the current vehicle's centroid as the origin. Let the current time be... The vehicle's position in the global coordinate system is The heading angle is For any historical moment in the buffer global coordinates Its local coordinates in the current vehicle coordinate system The calculation formula is:

[0069] This transformation ensures that the data-driven prediction model always expands near the origin of the state space, satisfying the premise of the superposition principle of linear systems.

[0070] S22: State geometry alignment and relative heading angle update. Based on the completed spatial position transformation, the vehicle's state variables are further aligned to ensure the reconstructed data conforms to the dynamics of the local affine system. Keeping the input variables constant, the heading angle is converted to a relative heading angle. .

[0071] After the above transformations, the processed local historical output sequence is constructed. and the corresponding input sequence This requires that the final state of the historical data be perfectly aligned geometrically with the actual initial physical state of the current vehicle. Through spatial reconstruction, the nonlinear global trajectory motion is effectively transformed into a locally linear affine system dynamic representation, thus making the linear approximation more accurate.

[0072] S23: Formal construction of the local Hankel matrix based on the reconstructed data. Using the local historical input-output sequence processed in S22, the Hankel matrix required for online predictive control is constructed as follows:

[0073] The input vector is defined as the control quantity, and the output vector is defined as the state quantity.

[0074]

[0075] The matrix depth here is .

[0076] S24: Extraction of the initial condition sequence for the current control cycle. With the current initial state of the system fixed, extract the sequence of length [length missing] from the updated data in the buffer. The input-output sequence is used as the initial condition for the current control cycle:

[0077]

[0078] The initial condition sequence and In subsequent optimization problems, equality constraints will be established with the historical part of the Hankel matrix, thereby implicitly determining the current dynamic state of the system without the need for an explicit state observer.

[0079] S3 includes: S31: Construct a robust objective function that includes a virtual setpoint. Using the reconstructed local linear data and matrices from S2, establish a quadratic programming (QP) optimization problem whose objective function aims to balance tracking accuracy, control smoothness, and task feasibility.

[0080] Within each control cycle, the set of optimization variables is defined as follows: .in, For online optimization of virtual setpoints, These represent the predicted control input and output sequences, respectively. An objective function is constructed for online optimization. objective function It adopts a quadratic form structure, consisting of a trajectory tracking error term, a control input term, and a double regularization term:

[0081] in, For the current time step, To predict the number of steps, To predict the length of the time domain; and In time Predicted future The input and output trajectories of the step; and These are the online optimized virtual input setpoints and virtual output setpoints, respectively. Set a point for the global objective; The weight vector when constructing a predictive control optimization model based on data; Relaxation variables introduced to handle data noise and local linearization errors; This is the weight matrix for the control quantity cost term, corresponding to the penalty for the predicted control quantity deviating from the virtual input setpoint; This is the weight matrix for the output cost term, corresponding to the penalty for the predicted output deviating from the virtual output setpoint; This is the weight matrix for the virtual setpoint penalty term, corresponding to the penalty for the virtual output setpoint deviating from the global target setpoint; and These are regularization parameters, used to apply to the weight vector. and slack variables The norm is used for regularization constraints to reduce the impact of noise and prevent slack variables from becoming too large.

[0082] S32: Implement a two-layer buffer optimization mechanism based on virtual setpoints. By introducing virtual setpoints into the objective function, a buffer layer is constructed between physical feasibility and the remote mission objective to address environmental interference and unreachable path issues. The objective function does not require the predicted trajectory to directly approximate potentially unreachable global targets. Instead, we first optimize the virtual setpoints. This allows the system to find the optimal balance between "physical feasibility" and "mission objectives." A two-layer buffer structure is formed by minimizing the deviation between the predicted trajectory and the virtual setpoint, as well as the deviation between the virtual setpoint and the global path. This mechanism effectively avoids system oscillations or unsolvable optimization problems caused by drastic jumps in control input or forced tracking of unreachable paths when the autonomous vehicle deviates significantly from the reference path.

[0083] S33: Implement dual regularization for noise suppression and model compensation. Introduce penalty terms for different noise sources into the optimization model to improve the system's robustness in real-world noisy environments.

[0084] A first regularization constraint is applied to the weight vector to mitigate the impact of multiplication noise. During the optimization process, a first regularization penalty is applied to the norm of the linear combination weight vector. This includes restricting the parameter space and resisting multiplicative uncertainties; the former refers to the weight vector satisfying Willems' fundamental lemma. There may be an infinite number of solutions. Regularization can filter out the optimal solution with the smaller norm from the feasible solutions. The latter refers to the role of noise in the historical data as a factor in the prediction equation. The uncertainty of multiplication arises, which can be addressed through regularization. The magnitude of the amplitude can prevent the prediction model from becoming overly dependent on noisy historical data, weaken the propagation of historical data noise as multiplicative uncertainty in the prediction equation, prevent the model from overfitting, and improve the smoothness and accuracy of the prediction trajectory.

[0085] A second regularization relaxation is implemented to compensate for additive noise due to initial state bias. Relaxation variables are introduced. The initial state constraints are applied to the system, and a second regularization penalty term is imposed. Its detailed functions include: (1) Initial sequence alignment: slack variables Used to compensate for the initial measurement sequence acquired at the current moment. The algebraic deviation between the local dynamical subspace characterized by the historical data Hankel matrix and the data.

[0086] (2) Ensure the feasibility of the solution: Due to the existence of output measurement noise, forcing the predicted trajectory starting point to be exactly the same as the initial measured value often leads to an unsolvable optimization problem; by penalizing the cost function This allows the system to moderately relax initial conditions in the presence of additive noise, ensuring flexible alignment between the predicted trajectory starting point and the actual vehicle state in noisy environments, thus enhancing algorithm stability.

[0087] S34: Establish a complete system of linear equality and inequality constraints. Integrate the components constructed in the previous steps to form a complete set of constraints for the optimization problem.

[0088] (1) Construct enhanced dynamic initial trajectory equality constraints with relaxation factors. The relaxation variables... Integrate this into the system's initial state constraint equations to establish a mathematical relationship between the predicted trajectory and the measured trajectory:

[0089] in, These are the parts of the input and output Hankel matrices used to characterize the historical dynamics of the system, respectively. Past data collected at the present moment Actual input / output measurement sequence. The constraints ensure the weight vector... While reconstructing future predicted trajectories, it is possible to use slack variables. The flexible compensation ensures that the starting point of the predicted trajectory remains consistent with the current measured state, which is noisy, in geometric space.

[0090] (2) Constructing affine consistency equality constraints for the weight vector. In the optimization process of predictive control, a linear combination of historical trajectory data is used to characterize the future behavior of the system. To ensure that this combination has affine properties mathematically, a constraint is introduced for the linear combination weight vector. Affine consistency constraints:

[0091] in, Weight vector The One portion, Let be the column number of the Hankel matrix. This constraint is expressed as a hard constraint and added to the equality constraint matrix of the quadratic programming problem. middle.

[0092] (3) Construct physical limiting constraints for the actuators. For the predictive control sequence... Apply hard constraints to the vehicle's physical actuators. For example, in S12, set the front wheel steering angle constraint. rad, longitudinal acceleration constraint This is to ensure that the output commands are within the vehicle's physical limits.

[0093] See Figure 8 S4 includes: S41: Matrix Reconstruction and Online Efficient Solution of the Quadratic Programming Problem. For the nonlinear predictive control optimization model with a double-layer buffer objective and double regularization constraints constructed in step S3, it is transformed into a standard quadratic programming form through algebraic reconstruction and solved online. First, matrix reconstruction is performed, converting the optimization variables... The stacked vectors are used to form a standard optimization vector, and the coefficient matrix of the quadratic term and the gradient vector of the linear term are extracted from the objective function. Next, online numerical solutions are performed. Within each control cycle, efficient quadratic programming solvers such as qpOASES or quadprog are used to calculate the optimal control sequence in the current local coordinate system, while satisfying the physical amplitude constraint described in step S34. .

[0094] S42: First-order control command extraction and inverse mapping execution in the local coordinate system. Following the rolling time-domain principle of predictive control, the calculation results in the local coordinate system are transformed into actual commands recognizable by the vehicle actuators. Only the control component at the first sampling time is extracted from the optimal control sequence obtained by the solution. Since step S2 performs a coordinate transformation based on the vehicle's pose on the input data, it is necessary to restore the local control commands to global execution commands according to the inverse transformation logic of the coordinate system; or, depending on actual engineering needs, the obtained local control components can be directly applied as control increments to the vehicle's underlying steering motor and power drive controller. This method ensures that the vehicle command output can match the current motion trajectory in real time.

[0095] S43: Real-time system status feedback acquisition and dynamic closed-loop iterative update. After executing the current control command, the system acquires the latest dynamic response of the vehicle through sensors, completing the rolling iteration of the entire control system.

[0096] (1) Response data acquisition: At the end of the current control cycle, the latest vehicle status observation values ​​are collected in real time through on-board sensors. .

[0097] (2) Closed-loop rolling update: The newly generated input and output data are updated accordingly. Feedback is sent to step S1. The system again invokes the "information gatekeeper" mechanism in S13 to maintain the buffer, and then executes the space reconstruction in S2 and the optimization calculation in S3 in sequence.

[0098] (3) Iterative loop: Through this closed-loop mechanism of "online sampling - spatiotemporal reconstruction - rolling solution - feedback update", the autonomous vehicle can achieve high-precision and robust real-time tracking of the target reference trajectory.

[0099] Combining steps S1 to S4 above, Figure 8 A pseudocode diagram of the nonlinear data-driven predictive control algorithm described in this invention is provided. Specifically, the algorithm flow mainly consists of two stages: offline data acquisition and online computation and solution. In the offline stage, the main goal is to construct a historical dataset that meets the requirements of continuous excitation. The system calculates the tracking error based on the set reference trajectory points and reference speed and applies a reference controller. Simultaneously, random noise disturbances are superimposed on the control input and applied to the vehicle model. This process is repeated until initial input-output data of sufficient length is acquired for subsequent Hankel matrix construction. In the online stage, the system acquires the current vehicle pose at the beginning of each control cycle and constructs and dynamically updates the Hankel matrix in the local coordinate system based on historical data. After extracting the current and past initial measurement sequences, local space reconstruction and target coordinate transformation are performed. Subsequently, a quadratic programming optimization problem with double regularization is solved online, and the first control variable of the optimal control sequence is extracted and applied as the actual input. The above online process is executed over time, thereby achieving high-precision and robust tracking of the target trajectory.

[0100] See Figure 9 , Figure 10S5: Simulation experiment verification and comparative analysis.

[0101] To verify the effectiveness of the method of this invention, a high-fidelity vehicle test environment was constructed on the CarSim and MATLAB / Simulink co-simulation platform. The experiment selected the classic linear model predictive control as the benchmark algorithm and conducted tests under the same vehicle physical parameters and controller constraints.

[0102] The experiment was designed with two representative, high-difficulty scenarios to comprehensively evaluate the algorithm's performance: Scenario 1: Double Lane Change and Obstacle Avoidance. The vehicle must perform two consecutive lane changes at high speed to avoid obstacles. This scenario primarily tests the controller's stability and overshoot resistance under rapid dynamic response.

[0103] Condition 2: U-shaped bend: The vehicle needs to pass through a U-shaped bend with a radius of 40m. This condition mainly examines the trajectory tracking accuracy of the controller under strong nonlinear geometric distortion.

[0104] like Figure 9 , Figure 10 The simulation results are compared and analyzed as follows: (1) In the double lane change scenario: Traditional MPC, based on a linearized model, cannot accurately predict the nonlinear vehicle dynamics during high-speed lane changes, resulting in significant overshoot and phase lag during the return-to-center phase, with an RMSE error of 0.2877m. In contrast, the Nonlinear DPC of this invention benefits from the adaptive processing of nonlinearity by local spatiotemporal reconstruction. The method of this invention tracks more closely at the peak of the lane change, with no significant overshoot, and the RMSE error is reduced to 0.2043m. Compared with traditional MPC, the tracking accuracy is improved by approximately 29%.

[0105] (2) In U-shaped bend conditions: In high-curvature bends, the prediction bias of the linear model of traditional MPC accumulates with the increase of the sideslip angle, causing the vehicle trajectory to deviate significantly towards the inside of the bend, resulting in a large lateral error, with an RMSE error of 0.3256m. However, the method of this invention effectively compensates for model mismatch through a double-layer regularization mechanism, ensuring that the vehicle trajectory always closely follows the reference path, with an RMSE error of only 0.2179m. Compared with traditional MPC, the tracking accuracy in high-curvature conditions is improved by about 33%, significantly solving the problem of easy divergence of existing technologies under extreme conditions.

[0106] In summary, the simulation experiments strongly demonstrate that the present invention has significant technical advantages over traditional MPC in solving the problems of "nonlinear geometric distortion" and "dynamic response lag".

[0107] Compared with the prior art, the present invention has the following beneficial effects: (1) This invention effectively solves the problem of geometric distortion in extreme conditions such as sharp turns and U-turns for autonomous vehicles, significantly improving driving safety. This invention maps the strongly nonlinear trajectory in the global coordinate system to the local vehicle coordinate system by performing local spatiotemporal coordinate reconstruction based on the current pose. This spatial dimension geometric alignment technology ensures that the data-driven model always unfolds near the origin of the state space, thereby greatly improving the prediction accuracy and path compliance of the vehicle in complex scenarios such as curves and U-turns at intersections, and effectively avoiding the risk of the vehicle running off the path due to model linear distortion.

[0108] (2) This invention overcomes the potential data degradation problem in steady-state cruise conditions of autonomous driving by adaptively and dynamically evolving historical data. This invention abandons the rigid data update mode in traditional data-driven methods and establishes a dynamic evolution mechanism that can perceive data incentive characteristics in real time. In "low-incentive" scenarios such as long-distance straight-line driving, this mechanism can spontaneously lock "high-value" historical data with rich dynamic characteristics, ensuring that the Hankel matrix always meets the continuous incentive conditions, greatly improving the reliability of the system under all operating conditions.

[0109] (3) This invention balances robustness in high-noise environments with ride comfort, achieving "human-like" smooth trajectory tracking. This invention constructs an optimization model that includes a virtual setpoint and dual regularization. The dual-layer buffer mechanism prevents the vehicle from rigidly correcting itself when faced with sensor disturbances or unreachable target paths, instead finding the optimal balance point within the range of physical feasibility, effectively eliminating actuator jitter. Combined with dual regularization terms targeting multiplicative and additive noise, this solution not only protects the hardware lifespan of the vehicle's steering and powertrain systems but also significantly reduces passenger motion sickness, providing a smoother driving experience closer to human driving habits.

[0110] (4) This invention improves real-time computational efficiency in high-speed autonomous driving scenarios and enhances the system's emergency response capability. Although this invention deals with a complex nonlinear tracking problem, it reduces the original problem to a standard convex quadratic programming (QP) problem with extremely high computational efficiency through local spatiotemporal reconstruction. This enables the algorithm to achieve millisecond-level rolling time-domain solutions on a vehicle-mounted platform with limited computing power, ensuring that the vehicle can make optimal control decisions as soon as it encounters sudden obstacles or drastic changes in road conditions, thus guaranteeing the determinism of real-time closed-loop control.

[0111] Another aspect of the present invention provides an electronic device, which includes: a processor, a memory, a communication bus, and a communication interface.

[0112] in: The processor, memory, and communication interface communicate with each other via a communication bus.

[0113] A communication interface is used to communicate with other electronic devices or servers.

[0114] The processor is used to execute programs, specifically the steps of any of the adaptive dynamic evolution direct data-driven vehicle trajectory tracking control methods described in the above embodiments.

[0115] Specifically, the program may include program code, which includes computer operation instructions.

[0116] The processor may be a central processing unit (CPU), an application-specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application. The one or more processors included in the smart device may be processors of the same type, such as one or more CPUs; or they may be processors of different types, such as one or more CPUs and one or more ASICs.

[0117] Memory is used to store programs. Memory may include high-speed RAM, and may also include non-volatile memory, such as at least one disk drive.

[0118] Specifically, the program can be used to cause the processor to execute the steps of any of the adaptive dynamic evolution direct data driven vehicle trajectory tracking control methods described in the embodiments. The specific implementation of each step in the program can be found in the corresponding descriptions of the steps and units executed in any of the aforementioned adaptive dynamic evolution direct data driven vehicle trajectory tracking control methods, and will not be repeated here. Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the devices and modules described above can be referred to the corresponding process descriptions in the foregoing method embodiments.

[0119] An exemplary embodiment of this application also provides a non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to cause a computer to perform the methods of various embodiments of this application.

[0120] The methods described above according to embodiments of the present invention can be implemented in hardware, firmware, or as software or computer code that can be stored in a recording medium (such as a CD-ROM, RAM, floppy disk, hard disk, or magneto-optical disk), or as computer code originally stored on a remote recording medium or a non-transitory machine-readable medium and subsequently stored on a local recording medium, downloaded via a network. Thus, the methods described herein can be processed by software stored on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as an ASIC or FPGA). It is understood that the computer, processor, microprocessor controller, or programmable hardware includes storage components (e.g., RAM, ROM, flash memory, etc.) capable of storing or receiving software or computer code, which, when accessed and executed by the computer, processor, or hardware, implements the methods described herein. Furthermore, when a general-purpose computer accesses code used to implement the methods shown herein, the execution of the code transforms the general-purpose computer into a dedicated computer for executing the methods shown herein.

[0121] Specific embodiments of the present invention have now been described. Other embodiments are within the scope of the appended claims. In some cases, the actions described in the claims can be performed in a different order and still achieve the desired result. Furthermore, the processes depicted in the drawings do not necessarily require a specific or sequential order to achieve the desired result.

[0122] It should be noted that all directional indications (such as up, down, left, right, back, etc.) in the embodiments of the present invention are only used to explain the relative positional relationship between the components in a certain order (as shown in the figure). If the specific order changes, the directional indication will also change accordingly.

[0123] In the description of this invention, the terms "first" and "second" are used only for convenience in describing different components or names, and should not be construed as indicating or implying a sequential relationship, relative importance, or implicitly specifying the number of technical features indicated. Thus, a feature defined with "first" and "second" may explicitly or implicitly include at least one of that feature.

[0124] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.

[0125] It should be noted that although specific embodiments of the present invention have been described in detail with reference to the accompanying drawings, this should not be construed as limiting the scope of protection of the present invention. Various modifications and variations that can be made by those skilled in the art without inventive effort within the scope described in the claims still fall within the scope of protection of the present invention.

[0126] The examples of the embodiments of the present invention are intended to concisely illustrate the technical features of the embodiments of the present invention, so that those skilled in the art can intuitively understand the technical features of the embodiments of the present invention, and are not intended to be an improper limitation of the embodiments of the present invention.

[0127] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An adaptive, dynamically evolving direct data-driven vehicle trajectory tracking control method, characterized in that, The method is applied to a vehicle control system and includes: In each control cycle of the vehicle control system, the linear independence index of the data in the current buffer is calculated based on the real-time collected vehicle input and output data sequence, and the buffer data is dynamically updated based on the calculation results to obtain the historical data of the buffer. The historical data in the buffer is mapped to a local vehicle coordinate system with the current vehicle centroid as the origin and the vehicle's heading direction as the X-axis; Based on the local vehicle coordinate system, a predictive control optimization model including virtual setpoints and double regularization is constructed, and it is transformed into a quadratic programming problem through algebraic reconstruction. In each control cycle of the vehicle control system, the quadratic programming problem is solved online to obtain the optimal control sequence in the local vehicle coordinate system. The first control quantity of the optimal control sequence is extracted as a control command and applied to the steering and power actuators of the vehicle control system.

2. The method according to claim 1, characterized in that, The method further includes: Collect the latest status response data of the vehicle after executing the control command; The latest status response data is used as a new vehicle input / output data sequence to update the historical data in the buffer for calculation in the next control cycle.

3. The method according to claim 1, characterized in that, The calculation of the linear independence index of the data in the current buffer, and the dynamic updating of the buffer data based on the calculation result, includes: The minimum singular value of the Hankel matrix, which is composed of the data in the current buffer, is calculated as the linear independence index. The minimum singular value is compared with a preset threshold, and the comparison result is used to determine whether the data in the current buffer meets the continuous excitation condition. If the conditions for continued incentive are met, the first update strategy will be executed; If the conditions for continued incentive are not met, the second update strategy will be executed.

4. The method according to claim 3, characterized in that, The first update strategy is to update the buffer using a first-in, first-out (FIFO) strategy; the second update strategy is to activate an information compensation mechanism. The information compensation mechanism is as follows: refusing to remove historical data frames with high excitation characteristics in the buffer and only replacing the data frames that contribute the least to the data richness; or superimposing a jitter excitation signal that meets the amplitude limit on the current control output.

5. The method according to claim 3, characterized in that, The step of determining whether the data in the current buffer meets the continuous excitation condition based on the comparison result specifically includes: Before updating the data in each control cycle, it is assumed that the buffer is updated using a first-in-first-out strategy, and the minimum singular value of the updated Hankel matrix is ​​pre-calculated. If the pre-calculated minimum singular value is greater than the preset threshold, then the continuous excitation condition is determined to be met. If the pre-calculated minimum singular value is not greater than the preset threshold, then the continuous excitation condition is not met.

6. The method according to claim 5, characterized in that, The preset threshold is calibrated through offline simulation, specifically including: Obtain the distribution range of singular values ​​in historical data of the vehicle under straight-line and steering conditions; Based on the distribution range of singular values ​​in the historical data and the covariance intensity estimation of sensor measurement noise, a minimum boundary value is set as the preset threshold so that the Hankel matrix still maintains linear independence after noise interference is removed.

7. The method according to claim 1, characterized in that, The objective function of the predictive control optimization model It adopts a quadratic form structure, consisting of a trajectory tracking error term, a control input term, and a double regularization term: in, For the current time step, To predict the number of steps, To predict the length of the time domain; and In time Predicted future The input and output trajectories of the step; and These are the online optimized virtual input setpoints and virtual output setpoints, respectively. Set a point for the global objective; The weight vector when constructing a predictive control optimization model based on data; Relaxation variables introduced to handle data noise and local linearization errors; This is the weight matrix for the control quantity cost term, corresponding to the penalty for the predicted control quantity deviating from the virtual input setpoint; This is the weight matrix for the output cost term, corresponding to the penalty for the predicted output deviating from the virtual output setpoint; This is the weight matrix for the virtual setpoint penalty term, corresponding to the penalty for the virtual output setpoint deviating from the global target setpoint; and These are regularization parameters, used to apply to the weight vector. and slack variables The norm is used for regularization constraints to reduce the impact of noise and prevent slack variables from becoming too large.

8. The method according to claim 7, characterized in that, The double regularization term includes: The first regularization term suppresses multiplicative noise in the historical data in the buffer and prevents overfitting by penalizing the L2 norm of the combined weight vector of the data. The second regularization term, through the introduction of an initial state relaxation variable, compensates for sensor additive noise and local modeling errors.

9. An electronic device, characterized in that, include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements the steps of the method as described in any one of claims 1-8.

10. A computer storage medium, characterized in that, The computer storage medium stores a computer program, which, when executed by a processor, implements the steps of the method as described in any one of claims 1-8.

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