A method and system for self-tuning motion control parameters of electric vehicles

Abstract

This invention discloses a method and system for self-tuning motion control parameters of electric vehicles, belonging to the field of electric vehicle stability motion control technology. The method includes: establishing a vehicle dynamics model; designing a nonlinear model predictive controller; calculating the gradient of the state trajectory and control sequence with respect to the hyperparameters based on the differentiable Pontryagin extremum principle, and automatically adjusting the hyperparameters online using the gradient descent method to optimize vehicle control performance. The method automatically adjusts the hyperparameters of the vehicle control algorithm online, thereby further improving the longitudinal motion stability of the vehicle.

Description

Technical Field

[0001] This invention relates to the field of electric vehicle stability motion control technology, and more specifically to a method and system for self-tuning electric vehicle motion control parameters. Background Technology

[0002] In extreme road conditions such as icy and snowy conditions, dangerous driving maneuvers including sudden braking, rapid acceleration, and sharp steering can lead to tire lateral force saturation, thereby compromising vehicle stability. These critical safety hazards urgently require the development of advanced active control systems. Torque vectoring control (TVC) systems alleviate these challenges to some extent by optimizing the torque distribution to each wheel to generate additional yaw moment, thereby improving vehicle handling under harsh driving conditions.

[0003] However, TVC systems still face two core challenges: 1. To achieve better control performance, a high-order nonlinear vehicle model is required. Therefore, to obtain the optimal control action, a complex nonlinear optimization problem needs to be solved. Due to the computational limitations of the onboard controller, a specialized solver needs to be developed to obtain the solution within a limited time. 2. Extensive expert knowledge is required to correctly adjust the control parameters of the TVC system. Traditional manual calibration methods based on engineering expertise are both time-consuming and insufficient for adapting to dynamic operating conditions. Furthermore, the parameters optimized through simulation are often difficult to transfer to actual vehicles.

[0004] Current methods for vehicle stability control rely on manual adjustment of control parameters, and different parameters need to be adapted for different operating conditions, making it difficult to comprehensively cover diverse driving needs. For example, patent CN116279409A proposes a cooperative control method for a four-wheel independent drive and steering electric vehicle to improve vehicle driving stability. This method considers the solution complexity of nonlinear optimization problems and proposes a fast solution algorithm. However, this method requires manually specifying the controller's weight parameters, which necessitates extensive simulation or experimental debugging, incurring significant manpower and material costs. Patent CN117706939A proposes a control parameter adjustment method based on Kalman filtering; however, its specific implementation shows that parameter adjustment requires a long convergence process, making online automatic tuning impossible.

[0005] Therefore, how to provide a method and system for self-tuning motion control parameters of electric vehicles is a problem that urgently needs to be solved by those skilled in the art. Summary of the Invention

[0006] In view of this, the present invention provides a method and system for self-tuning motion control parameters of electric vehicles, which can automatically adjust the hyperparameters of the vehicle control algorithm online to further improve the lateral longitudinal motion stability of the vehicle.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A method for self-tuning motion control parameters of an electric vehicle includes:

[0009] Step 1: Establish a vehicle dynamics model, including a two-degree-of-freedom vehicle model and a nonlinear tire model, and generate a reference yaw rate and a reference center-of-gravity sideslip angle;

[0010] Step 2: Design a nonlinear model predictive controller. The nonlinear model predictive controller calculates the additional yaw moment by solving an optimization problem based on the vehicle dynamics model and reference quantities. The objective function of the optimization problem includes hyperparameters to be tuned.

[0011] Step 3: Based on the differentiable Pontryagin extremum principle, calculate the gradient of the state trajectory and control sequence with respect to the hyperparameters, and use the gradient descent method to automatically adjust the hyperparameters online to optimize vehicle control performance.

[0012] Furthermore, the state variables of the two-degree-of-freedom vehicle model are the yaw rate γ and the sideslip angle β, and the control variable is the additional yaw moment M.

[0013] The vehicle dynamics equations are expressed as follows:

[0014]

[0015] in Vehicle status. This indicates the yaw rate of the vehicle. The sideslip angle is the angle of the centroid. and These represent the lateral forces of the front and rear wheels, respectively. and These represent the distances from the front and rear axles to the vehicle's center of gravity, respectively. It is the moment of inertia of the vehicle rotating about its center of mass. It's about vehicle quality. The vehicle's longitudinal speed is the control variable, and the additional yaw torque is the control variable. .

[0016] Furthermore, in step 1, a nonlinear brush tire model is used to calculate the lateral forces of the front and rear wheels:

[0017]

[0018] in, For tire lateral stiffness, Indicates tire lateral stiffness (front wheel is) The rear wheel is ), It is the road adhesion coefficient. This indicates the normal vertical load on the tire.

[0019] Furthermore, the process of generating the reference yaw rate and the reference centroid sideslip angle in step 1 includes:

[0020] Based on a two-degree-of-freedom linear model, reference quantities are generated using transfer functions.

[0021]

[0022]

[0023]

[0024]

[0025]

[0026]

[0027] .

[0028] in, For vehicle quality, The sideslip angle is the angle of the centroid. For longitudinal vehicle speed, For the front wheel steering angle, For the front wheel lateral stiffness, For rear wheel lateral stiffness, This refers to the front axle wheelbase. This refers to the rear axle wheelbase. The yaw rate is angular velocity. for Reference yaw rate within the domain, for The steering wheel angle of the domain, It is a time constant. for Domain change symbol, For the vehicle's inherent frequency, The damping coefficient is... Wheelbase As a stability factor, This is the yaw rate gain.

[0029] Furthermore, the optimization problem of the nonlinear model predictive controller in step 2 is formulated as follows:

[0030]

[0031] in, Indicates the prediction time domain, These are the predicted state sequence and the optimized control sequence at the current time t, respectively. To simplify the parameter tuning process, and Set as a diagonal matrix. Given control dimensions. , Fix and adjust automatically The diagonal elements.

[0032] The constraints are ( ):

[0033]

[0034]

[0035] in To control the input constraints, the objective function formula is:

[0036]

[0037] in In the objective function and the state variables The corresponding penalty term indicates tracking the desired yaw rate and reducing the sideslip angle.

[0038] Furthermore, the hyperparameter tuning in step 3 is achieved by solving the outer optimization problem of a two-layer optimization problem, which can be expressed as:

[0039]

[0040] The constraint is a nonlinear model predictive control optimization problem;

[0041] in, , This is an index function.

[0042] Furthermore, the index function L Defined as:

[0043]

[0044] in, and These represent the lengths of past data collected online and the predicted future data, respectively. This is the regularization factor.

[0045] Furthermore, the differentiable Pontryagin extremum principle includes the following equations:

[0046]

[0047]

[0048]

[0049]

[0050] in, These are costate variables.

[0051] An electric vehicle motion control parameter self-tuning system, comprising:

[0052] The modeling module establishes a vehicle dynamics model, including a two-degree-of-freedom vehicle model and a nonlinear tire model, and generates a reference yaw rate and a reference center-of-gravity sideslip angle.

[0053] The first processing module designs a nonlinear model predictive controller. The nonlinear model predictive controller calculates the additional yaw moment by solving an optimization problem based on the vehicle dynamics model and reference quantities. The objective function of the optimization problem includes hyperparameters to be tuned.

[0054] The second processing module, based on the differentiable Pontryagin extremum principle, calculates the gradient of the state trajectory and control sequence with respect to the hyperparameters, and uses the gradient descent method to automatically adjust the hyperparameters online to optimize vehicle control performance.

[0055] As can be seen from the above technical solution, compared with the prior art, this invention discloses a method and system for self-tuning motion control parameters of electric vehicles, and discloses an online automatic parameter adjustment TVC strategy to improve the dynamic performance of the vehicle. The method includes establishing a nonlinear vehicle model and designing a model predictive controller (MPC), which calculates the optimal yaw moment by tracking reference yaw rate and sideslip angle. The resulting nonlinear programming problem is solved using the Pontryagin minimum principle (PMP). More importantly, this invention develops a novel differentiable PMP for calculating the gradient of the state trajectory and control sequence with respect to the MPC weight parameters, thereby achieving gradient-based online parameter adaptation. Hardware-in-the-loop experiments conducted under the standardized dual lane change (DLC) condition demonstrate that, compared with the manually adjusted TVC strategy, the proposed self-tuning method significantly improves vehicle handling and stability. Attached Figure Description

[0056] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0057] Figure 1 This is a schematic diagram of the method flow provided by the present invention;

[0058] Figure 2 The overall architecture of the hyperparameter tuning strategy provided by this invention;

[0059] Figure 3 This is a schematic diagram of a two-degree-of-freedom model provided by the present invention;

[0060] Figure 4 A comparison chart of vehicle longitudinal speed and steering wheel angle during the DLC test;

[0061] Figure 5 A comparison chart of yaw rate tracking results and sideslip angle from the DLC test;

[0062] Figure 6 The weight hyperparameter adjustment curve for DLC testing. Detailed Implementation

[0063] The technical solutions of the embodiments of the present invention will be clearly and completely 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 without creative effort are within the scope of protection of the present invention.

[0064] Example 1:

[0065] See Figure 1 This invention discloses a method for self-tuning motion control parameters of an electric vehicle, comprising:

[0066] Step 1: Establish a vehicle dynamics model, including a two-degree-of-freedom vehicle model and a nonlinear tire model, and generate a reference yaw rate and a reference center-of-gravity sideslip angle;

[0067] Step 2: Design a nonlinear model predictive controller. The nonlinear model predictive controller calculates the additional yaw moment by solving an optimization problem based on the vehicle dynamics model and reference quantities. The objective function of the optimization problem includes hyperparameters to be tuned.

[0068] Step 3: Based on the differentiable Pontryagin extremum principle, calculate the gradient of the state trajectory and control sequence with respect to the hyperparameters, and use the gradient descent method to automatically adjust the hyperparameters online to optimize vehicle control performance.

[0069] Specifically, PMP is used to solve the quadratic programming optimization problem inherent in nonlinear MPC. Furthermore, a differentiable PMP is introduced to compute the gradients of the state trajectory and control sequence with respect to the weight hyperparameters in the MPC objective function. An indicator function is defined, and gradient descent is used to automatically optimize the hyperparameters to improve control performance. Finally, experiments conducted on the HIL platform validate the method of this invention.

[0070] Figure 2 The block diagram of the proposed control structure is described. This invention proposes an online automatic parameter adjustment torque vector control (TVC) strategy to improve vehicle dynamic performance. The method involves establishing a nonlinear vehicle model and designing a model predictive controller (MPC) that calculates the optimal yaw moment by tracking reference yaw rate and sideslip angle. The resulting nonlinear programming problem is solved using the Pontryagin minimum principle (PMP), and a novel differentiable PMP is developed to compute the state trajectory and control the input gradient relative to the MPC weight parameters, thereby achieving gradient-based parameter adaptation. The main design process is described below:

[0071] See Figure 3 The two-degree-of-freedom model is one of the most commonly used simplified models in vehicle dynamics. It only considers the lateral and yaw motions of the vehicle's center of mass in the horizontal plane, thus having two degrees of freedom: Lateral degree of freedom: the motion of the vehicle's center of mass in the yaw direction; Yaw degree of freedom: the yaw motion of the vehicle about its center of mass. The vehicle's longitudinal velocity is considered a known or constant input and is not considered a degree of freedom. Each tire generates a slip angle when cornering and a slip ratio when driving, resulting in lateral and longitudinal forces on all four wheels.

[0072] Step 1: Model Building

[0073] 1) Establishment of a two-degree-of-freedom model for the vehicle:

[0074] The present invention first establishes a two-degree-of-freedom model of the vehicle, which takes into account the lateral motion and yaw motion of the vehicle.

[0075] (1)

[0076] in Vehicle status. This indicates the yaw rate of the vehicle. The sideslip angle is the angle of the centroid. and These represent the lateral forces of the front and rear wheels, respectively. and These represent the distances from the front and rear axles to the vehicle's center of gravity, respectively. It is the moment of inertia of the vehicle rotating about its center of mass. It's about vehicle quality. The vehicle's longitudinal speed is the control variable, and the additional yaw torque is the control variable. .

[0077] 2) Tire model:

[0078] A nonlinear brush tire model is used to calculate the lateral force on the wheel, thereby describing the tire-ground relationship of the vehicle, as shown below:

[0079] (2)

[0080] in Indicates tire lateral stiffness (front wheel is) The rear wheel is ), It is the road adhesion coefficient. Indicates the normal vertical load of the tire (front axle is) The rear axle is The tire slip angle is calculated as follows:

[0081] (3)

[0082] in and These are the slip angles of the front and rear wheels, respectively. This refers to the steering angle of the front wheels.

[0083] 3) Tracking and reference:

[0084] To ensure vehicle stability, appropriate reference center of gravity sideslip angle and reference yaw rate need to be generated based on the front wheel steering angle input by the driver, according to the vehicle's two-degree-of-freedom model:

[0085] (4)

[0086] The following reference values ​​can be generated:

[0087] (5)

[0088] in For vehicle quality, The sideslip angle is the angle of the centroid. For longitudinal vehicle speed, This refers to the steering angle of the front wheels.

[0089]

[0090]

[0091]

[0092]

[0093]

[0094] (6)

[0095] Step 2: Controller Design:

[0096] This step focuses on the design of a nonlinear model predictive controller (NMPC) to enhance vehicle lateral stability. The controller calculates the additional yaw moment based on the vehicle state and the desired yaw rate. Subsequently, the control motion generation module converts this torque into actuator commands for the hub motor. To facilitate controller design, the system's state-space model is first discretized into a first-order Euler form and then applied to the prediction equations in the computer system.

[0097] (7)

[0098] in For the discrete time of the computer system.

[0099] Parameters need to be adjusted The NMPC optimization problem is summarized as follows:

[0100] Optimization issue 1:

[0101] (8)

[0102] in, Indicates the prediction time domain, These are the predicted state sequence and the optimized control sequence at the current time, respectively. The constraints are ( ):

[0103] (9)

[0104] (10)

[0105] in To control the input constraints, the objective function formula is:

[0106] (11)

[0107] in In the objective function and the state variables The corresponding penalty term represents tracking the desired yaw rate and reducing the sideslip angle. Furthermore, the control input... The regularization term is used to limit the additional yaw torque to avoid controlling oscillations. Solving the above optimization problem yields the yaw torque. Finally, the torque is evenly distributed to the four hub motors.

[0108] Specifically, determining the objective function weights is challenging in Model Predictive Control (MPC) optimization problems. To address this significant challenge, this invention addresses the issue by assigning weights... and Parameterization Furthermore, online automatic adjustment is achieved by solving the bi-level optimization problem in the next section. To simplify the parameter adjustment process, and Set as a diagonal matrix. Given control dimensions. , Fix and adjust automatically The diagonal elements.

[0109] Step 3: Online automatic tuning method for hyperparameters:

[0110] 1) Description of the bi-level optimization problem:

[0111] This invention introduces a differentiable PMP (DPMP) method for automatically adjusting the hyperparameters from the previous section. The DPMP method can efficiently compute the state gradient and input trajectory gradient with respect to the weight parameters, thereby optimizing hyperparameters through gradient descent techniques.

[0112] Optimization issue 2:

[0113] (12)

[0114] Constraints: Optimization problem 1;

[0115] in , For index functions. If known about If the gradient is known, then gradient descent can be directly applied to update the parameters. :

[0116] (13)

[0117] in For learning rate, The following can be calculated:

[0118] (14)

[0119] In the gradient calculation process (14), the main difficulty lies in the gradient of the state trajectory and the control sequence relative to the parameters. The calculation of DPMP proposed in this invention can efficiently solve the above problems.

[0120] Choose the index function in optimization problem 2. for:

[0121] (15)

[0122] in and These represent the lengths of past data collected online and the predicted future data, respectively. Let be the regularization factor. Then we can obtain...

[0123] (16)

[0124] 2) PMP-based optimization problem-solving algorithms:

[0125] Problem 1 involves nonlinear programming (NLP) computation. Solving this problem using traditional techniques such as the interior-point method requires significant computational resources, posing a considerable challenge for real-time control systems. Furthermore, solving bilevel optimization problem 2, which uses optimization problem 1 as a constraint, is even more difficult. To alleviate the computational burden, applying Programming Per Minute Model (PMP) is key to solving both problems.

[0126] Based on the system model (7) and objective function (11) of optimization problem 1, the Hamiltonian function is defined as follows: ):

[0127] (17)

[0128] in This represents the Lagrange multiplier associated with the dynamic constraints, also known as the costate variable. According to the PMP principle, there exists a sequence of costate variables. and an optimal trajectory And it meets the following conditions:

[0129] (18)

[0130] (19)

[0131] (20)

[0132] (twenty one)

[0133] The four equations above are respectively called the dynamic equations, costate equations, input equations, and boundary conditions of the PMP. Efficient numerical algorithms already exist for solving this system of equations. However, the purpose of this invention is not only to solve problem 1, but more importantly, to handle the bi-level optimization problem 2 in real time.

[0134] 3) Differentiable PMP:

[0135] To calculate the state trajectory Regarding the gradient of the weight parameters, this invention derives the gradient of the parameters. Differentiable PMP equations.

[0136] (twenty two)

[0137] (twenty three)

[0138] (twenty four)

[0139] (25)

[0140] In the above system of equations, the complexity stems from the product of the second derivative of the system model and the gradient of the state or input trajectory with respect to the parameters. However, based on the vehicle model (1), (2), and (3), it can be derived that... and Then, numerical methods can be used to solve the system of equations (22)(23)(24)(25).

[0141] To facilitate the representation of the system of equations (22)(23)(24)(25) in matrix form, subsequent symbols are introduced.

[0142] (26)

[0143] (27)

[0144] (28)

[0145] (29)

[0146] Expanding formula (23) yields:

[0147] (30)

[0148] (31)

[0149] Expanding formula (24) yields

[0150] (32)

[0151] Expanding formula (25) yields

[0152] (33)

[0153] (34)

[0154] The solutions to the nonlinear system of equations (18)(19)(20)(21) can be obtained using numerical methods such as the Nelder-Mead algorithm. In each iteration, equations (22)(23)(24)(25) are solved simultaneously. Once the system of equations (18)(19)(20)(21) converges and an optimal sequence is found... Then the required gradient This will also be determined at the same time, thus enabling the solution of the bi-level optimization problem 2.

[0155] Example 2:

[0156] Embodiment 2 of this invention uses a driver-in-the-loop simulator for verification. Detailed simulator information can be found in patent "CN113219944B". This experimental platform integrates a full-view driving simulator with a 180° projection screen (for visual immersion) and a six-degree-of-freedom motion platform (for providing realistic vehicle dynamics feedback). The system architecture includes three industrial computers (IPCs): IPC1 runs the vehicle dynamics model and transmits the motion state to the HIL platform; IPC2 executes the SCANeR software for visual rendering; and IPC3 implements the proposed control algorithm. A monitoring laptop is used for system monitoring and controller calibration. All components communicate via a Controller Area Network (CAN) bus (for control signal transmission) and via User Data Protocol (UDP) (for monitoring data).

[0157] Simulation experiments for verification and comparison:

[0158] The initial parameter value is set to , and The prediction time domain is... , and For comparative analysis, we use PMP to implement NMPC to solve NLP problem 1. The proposed method is called Hyperparameter Tuning PMP (HTPMP).

[0159] The effectiveness of the proposed method in improving vehicle handling stability was evaluated through a dual lane change (DLC) test conducted on a low-adhesion road surface. The driver followed a predefined standard DLC trajectory at a speed of approximately 75 km / h. Figure 4 This demonstrates a comparison of vehicle longitudinal speed and steering wheel angle during the DLC test. When the controller was off, the DLC test could not be completed even at speeds below 70 km / h. In contrast, both HTPMP and PMP successfully assisted the driver in completing the DLC operation at approximately 75 km / h. Notably, HTPMP required a smaller steering wheel angle, further reducing the driver's workload.

[0160] Figure 5 The yaw rate and sideslip angle responses of three control algorithms were compared. With the controller off, the vehicle failed to track the target yaw rate and lost stability after 6 seconds, while HTPMP and PMP maintained stability throughout the DLC test. However, PMP exhibited a larger yaw rate tracking error and sideslip angle than HTPMP, reflecting its poorer handling and stability performance. This performance gap stems from the online adaptive capability of the proposed method's weight parameters. Figure 6 As shown, HTPMP quickly adjusts during DLC ​​testing. and , among which This value is particularly effective for minimizing yaw rate tracking error.

[0161] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0162] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An automatic tuning method for hyperparameters of electric vehicle motion control based on the differentiable Pontryagin extremum principle, characterized in that, include: Step 1: Establish a vehicle dynamics model, including a two-degree-of-freedom vehicle model and a nonlinear tire model, and generate a reference yaw rate and a reference center-of-gravity sideslip angle; Step 2: Design a nonlinear model predictive controller. The nonlinear model predictive controller calculates the additional yaw moment by solving an optimization problem based on the vehicle dynamics model and reference quantities. The objective function of the optimization problem includes hyperparameters to be tuned. Step 3: Based on the principle of differentiable Pontryagin extrema, calculate the gradient of the state trajectory and control sequence with respect to the hyperparameters, and use the gradient descent method to automatically adjust the hyperparameters online to optimize vehicle control performance; In step 3, the hyperparameter tuning is achieved by solving the outer optimization problem of a two-layer optimization problem, which can be expressed as follows: The constraint is a nonlinear model predictive control optimization problem; in, , For index functions; The differentiable Pontryagin extremum principle includes the following equations: in, These are costate variables.

2. The automatic tuning method for hyperparameters of electric vehicle motion control based on the differentiable Pontryagin extremum principle according to claim 1, characterized in that, The state variables of the two-degree-of-freedom vehicle model are the yaw rate γ and the sideslip angle β, and the control variable is the additional yaw moment M. The vehicle dynamics equations are expressed as follows: in Vehicle status. This indicates the yaw rate of the vehicle. The sideslip angle is the angle of the centroid. and These represent the lateral forces of the front and rear wheels, respectively. and These represent the distances from the front and rear axles to the vehicle's center of gravity, respectively. It is the moment of inertia of the vehicle rotating about its center of mass. It's about vehicle quality. The vehicle's longitudinal speed is the control variable, and the additional yaw torque is the control variable. .

3. The automatic tuning method for hyperparameters of electric vehicle motion control based on the differentiable Pontryagin extremum principle according to claim 1, characterized in that, In step 1, a nonlinear brush tire model is used to calculate the lateral forces of the front and rear wheels: in, For tire lateral stiffness, Indicates tire lateral stiffness. It is the road adhesion coefficient. This indicates the normal vertical load on the tire.

4. The automatic tuning method for hyperparameters of electric vehicle motion control based on the differentiable Pontryagin extremum principle according to claim 1, characterized in that, The process of generating the reference yaw rate and the reference centroid sideslip angle in step 1 includes: Based on a two-degree-of-freedom linear model, reference quantities are generated using transfer functions. in, For vehicle quality, The sideslip angle is the angle of the centroid. For longitudinal vehicle speed, For the front wheel steering angle, For the front wheel lateral stiffness, For rear wheel lateral stiffness, This refers to the front axle wheelbase. This refers to the rear axle wheelbase. The yaw rate is angular velocity. for Reference yaw rate within the domain, for The steering wheel angle of the domain, It is a time constant. for Domain change symbol, For the vehicle's inherent frequency, The damping coefficient is... Wheelbase As a stability factor, This is the yaw rate gain.

5. The automatic tuning method for hyperparameters of electric vehicle motion control based on the differentiable Pontryagin extremum principle according to claim 1, characterized in that, The optimization problem of the nonlinear model predictive controller in step 2 is expressed as follows: in, Indicates the prediction time domain, These are the predicted state sequence and the optimized control input sequence at the current moment, respectively; among them, to simplify the parameter tuning process, and Set as a diagonal matrix, given control dimension , Fix and adjust automatically The diagonal elements; The constraints are ( ): in To control the input constraints, the objective function formula is: in In the objective function and the state variables The corresponding penalty term indicates tracking the desired yaw rate and reducing the sideslip angle.

6. The automatic tuning method for hyperparameters of electric vehicle motion control based on the differentiable Pontryagin extremum principle according to claim 1, characterized in that, The index function L Defined as: in, and These represent the lengths of past data collected online and the predicted future data, respectively. This is the regularization factor.

7. An automatic tuning system for hyperparameters of electric vehicle motion control based on the principle of differentiable Pontryagin's extrema, utilizing the automatic tuning method for hyperparameters of electric vehicle motion control based on any one of claims 1-6, characterized in that, include: The modeling module establishes a vehicle dynamics model, including a two-degree-of-freedom vehicle model and a nonlinear tire model, and generates a reference yaw rate and a reference center-of-gravity sideslip angle. The first processing module designs a nonlinear model predictive controller. The nonlinear model predictive controller calculates the additional yaw moment by solving an optimization problem based on the vehicle dynamics model and reference quantities. The objective function of the optimization problem includes hyperparameters to be tuned. The second processing module, based on the differentiable Pontryagin extremum principle, calculates the gradient of the state trajectory and control sequence with respect to the hyperparameters, and uses the gradient descent method to automatically adjust the hyperparameters online to optimize vehicle control performance.

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