Model predictive control method based on online adjustment of constraints of model error

Abstract

The application discloses a model predictive control method based on online adjustment of model error constraints, and the method comprises the following steps: constructing a nonlinear bicycle model, performing linearization processing, initializing model error, calculating accumulated error in a prediction period considering feedback action according to error boundary, and modifying input and output constraints of the model error; then, the model predictive control problem is solved through a nominal system model under the constraints, and the system model error used for iteration is obtained through online updating, and the model predictive control is realized through cyclic updating of the error; the application adjusts state and input boundary constraints according to the observation data and the model estimation of the model mismatch degree while driving the prediction state through online data, adjusts the state and input boundary constraints online according to the model error, guarantees the safe operation of the system during the model updating of the prediction control, improves the reliability, realizes more accurate model mismatch boundary constraints, and is beneficial to improving the performance of the closed-loop system.

Description

Technical Field

[0001] This invention relates to a technology in the field of model predictive control, specifically a model predictive control method based on online adjustment constraints of model error. Background Technology

[0002] Model predictive control (MPC) is capable of handling multivariable systems and constraints. In practical applications, unavoidable factors such as disturbance noise and system uncertainties always exist, leading to unavoidable modeling errors and thus affecting performance. Existing Tube-based MPC techniques separate the deterministic and uncertain parts of the control system, using uncertainty to calculate and tighten constraints. Uncertainty is no longer considered in the system model of the nominal system MPC optimization problem, reducing the complexity of the optimization problem. However, existing Tube-based MPC works, to ensure system safety, suffer from constraints imposed by initial uncertainty estimation, resulting in a small feasible space and exhibiting strong conservatism. Summary of the Invention

[0003] To address the aforementioned shortcomings of existing technologies, as well as the modeling errors caused by interference noise and system uncertainties introduced into the controller, this invention proposes a model predictive control method based on online adjustment constraints of model error. This method utilizes online data to drive the prediction of the state while simultaneously adjusting the state and input boundary constraints based on observed data and model estimation of model mismatch. By adjusting the state and input boundary constraints online according to model error, the method ensures safe system operation during predictive control model updates, improves reliability, and achieves more accurate model mismatch boundary constraints, thereby enhancing the performance of the closed-loop system.

[0004] This invention is achieved through the following technical solution:

[0005] This invention relates to a model predictive control method based on online adjustment constraints of model error. The method involves constructing a nonlinear bicycle model and linearizing it, then initializing the model error and calculating the cumulative error within the prediction period considering feedback, based on the error boundary. The input and output constraints of the model error are then modified. Under these constraints, the model predictive control problem is solved using a nominal system model, and the system model error is updated online for iteration. Model predictive control is then achieved by iteratively updating this error.

[0006] The nonlinear bicycle model is as follows: Where: state vector The values ​​are: vehicle speed on the horizontal axis, speed on the vertical axis, heading angular velocity, yaw angle, lateral deviation of the vehicle relative to the desired path, and distance along the desired path in the s direction. Let u be the derivative of the state vector, and let u = [β, δ].T Front and rear wheel brake throttle ratio β f =β r =β, δ is the steering angle, m is the vehicle mass, I z For the moment of inertia, l f l is the distance from the gear to the front tire. r C is the distance from the wheel hub to the rear tire. f For the front tire steering stiffness, C r For rear tire steering stiffness, F zf F zr These represent the lateral forces acting on the front and rear tires, respectively, and μ is the coefficient of friction.

[0007] The model error ε={|e i |≤δ i (0), i = 1, 2, ..., n y}, δ i (0) is the initial upper bound of the error. Based on the actual physical process and safety constraints, the input and output state constraint sets are defined. u LB u LU These are the upper and lower bounds of the input constraints, y LB y LU To output the upper and lower bounds of the constraints. For a dimension of n u input space, For a dimension of n y The output space.

[0008] The input / output constraints include: Where: ε′(l), l=1,2,...,P is the cumulative error within the prediction period after considering the feedback effect, calculated based on the error boundary. This represents set operations. These are the updated sets of input and output state constraints, respectively.

[0009] The nominal system model refers to a predictive control model that does not consider uncertainties, specifically: Where: k is the current sampling time, P is the total predictive control step size, l is the l-th prediction step, L is the predictive control objective function, x is the system state, u is the system output, A and B are the coefficient matrices of the system state equation, y is the system observation, H is the gain of the state observer, and C is the system observation coefficient matrix. These are the input and output constraint sets, This is the set of terminal state constraints.

[0010] The aforementioned solution to the model predictive control problem specifically involves: calculating the optimal control law u.* (1:P-1|k), and the control action u(k)=u * (k|k)+K(x(k|k)-x(k|k-1)) is applied to the actual vehicle system; the system model error ε={|e} is obtained online through statistical historical error or set element identification method. i |≤δ i (k)i=1,2,...,n y}

[0011] This invention relates to a system for implementing the above-described method, comprising: an initialization constraint unit, a model predictive control (MRC) solving unit, a data collection unit, and a constraint update unit. The initialization constraint unit defines input and output state constraint set information based on actual physical processes and safety constraints to perform initial error estimation, thereby obtaining initial input and output state constraint sets. The MRC solving unit solves the nominal model predictive control problem based on the linearized model and the unit input and output state constraint set information to obtain the optimal output. The data collection unit applies the optimal output to the actual system and obtains new error information through observation. The constraint update unit updates the input and output state constraint sets based on the new error information to obtain the input and output state constraint sets for the optimization problem at the next time step. Technical effect

[0012] This invention addresses model uncertainty by adjusting model error constraints online based on the model error. Compared to existing technologies, this invention addresses systems with model mismatch uncertainty, large initial estimation errors leading to limited feasible space. By adjusting error constraints online, it reduces the system conservatism caused by model errors, thus decreasing the total distance increment caused by obstacle avoidance during vehicle obstacle avoidance. Attached Figure Description

[0013] Figure 1 This is a bicycle model diagram of the present invention;

[0014] Figure 2 This is a flowchart of the online process of the present invention;

[0015] Figure 3 This is a comparison diagram of the system's operating trajectory when the present invention controls the system using other methods. Detailed Implementation

[0016] like Figure 1-2 As shown, this embodiment provides a model predictive control method based on online model error adjustment constraints, including:

[0017] S1, Construct a nonlinear bicycle model and perform linearization;

[0018] The nonlinear bicycle model is as follows: Where: state vector The values ​​are: vehicle speed on the horizontal axis, speed on the vertical axis, heading angular velocity, yaw angle, lateral deviation of the vehicle relative to the desired path, and distance along the desired path in the s direction. Let u be the derivative of the state vector, and let u = [β, δ]. T Front and rear wheel brake throttle ratio β f =β r =β, δ is the steering angle, m is the vehicle mass, I z For the moment of inertia, l f l is the distance from the gear to the front tire. r C is the distance from the wheel hub to the rear tire. f For the front tire steering stiffness, C r For rear tire steering stiffness, F zf F zr These represent the lateral forces acting on the front and rear tires, respectively, and μ is the coefficient of friction.

[0019] The linearization process refers to linearizing the derivative increment of the state vector. Where Δξ is the increment of the state vector and Δu is the input increment.

[0020] S2, Construct the initial model error ε={|e i |≤δ i (0), i = 1, 2, ..., n y}, e i For the system model error, δ i (0) represents the upper bound of the initial error, n y For the output dimension, define the input and output state constraint sets based on actual physical processes and safety limitations. Where: u LB u LU These are the upper and lower bounds of the input constraints, y LB y LU To output the upper and lower bounds of the constraints. For a dimension of n u input space, For a dimension of n y The output space.

[0021] S3, calculate the cumulative error ε′(l) within the prediction period considering feedback based on the error boundary, l=1,2,...,P, and then modify the input and output constraints. Where: ε′(l), l=1,2,...,P is the cumulative error within the prediction period after considering the feedback effect, calculated based on the error boundary. This represents set operations. These are the updated sets of input and output state constraints, respectively.

[0022] S4. Using the vehicle linear model obtained in step S1, and the constraints obtained in steps S2 and S3, construct a nominal system model to solve the model predictive control problem and calculate the optimal control law u. * (1:P-1|k), and control u(k)=u * When (k|k)+K(x(k|k)-x(k|k-1)) is applied to a real vehicle system, for a state-space equation optimization problem: Where: k is the current sampling time, P is the total predictive control step size, l is the l-th prediction step, L is the predictive control objective function, x is the system state, u is the system output, A and B are the coefficient matrices of the system state equation, y is the system observation, H is the gain of the state observer, and C is the system observation coefficient matrix. These are the input and output constraint sets, This is the set of terminal state constraints.

[0023] S5, by statistically analyzing historical errors, obtain the system model error ε={|e i |≤δ i (k), i = 1, 2, ..., n y}, where: e i For the system model error, δ i (k) represents the upper bound of the system model error after online update, h y For output dimensions.

[0024] The operation process for statistical historical error is as follows: the deviation from the model prediction value is recorded through online observation.

[0025] S6, in the new control cycle, return to step S3 to obtain the new error boundary and repeat the operation, finally realizing model predictive control.

[0026] Through specific practical experiments, this method was tested using a vehicle system to reach the target location while simultaneously avoiding obstacles. The vehicle system was simplified to a bicycle model, with the two front wheels and two rear wheels each considered as a single wheel. The system dynamics were linearized. The system trajectory diagram of this embodiment when controlling the system using other methods is shown below. Figure 2As shown in the figure, the vehicle will touch the edge of the obstacle in the nonlinear MPC (NMPC) control method. The closest distance between the vehicle and the obstacle in the Tube-based MPC is 0.3m, while the closest distance between the vehicle and the obstacle in this invention is 0.1m. This invention can complete the obstacle avoidance task and adjust the error constraint online. Compared with the Tube-based MPC, it can adapt the system model online and reduce the system conservatism.

[0027] Compared with existing technologies, this method can successfully complete obstacle avoidance tasks while reducing the vehicle's obstacle avoidance distance, which is more conducive to the safe operation of the system and improves reliability. Adjusting the state and input boundary constraints online based on model error helps reduce conservatism caused by excessive initial estimation errors.

[0028] The above-described specific implementations can be partially adjusted by those skilled in the art in different ways without departing from the principles and purpose of the present invention. The scope of protection of the present invention is defined by the claims and is not limited to the above-described specific implementations. All implementation schemes within the scope of the claims are bound by the present invention.

Claims

1. A model predictive control method based on online adjustment constraints for model error, characterized in that, After constructing and linearizing a nonlinear bicycle model, the model error is initialized, and the cumulative error considering feedback within the prediction period is calculated based on the error boundary. The input and output constraints of the model error are then modified. Under these constraints, the model predictive control problem is solved using a nominal system model, and the system model error used for iteration is updated online. Model predictive control is achieved by iteratively updating this error. The nonlinear bicycle model is as follows: , , , , , , where: state vector The values ​​are: vehicle speed on the horizontal axis, speed on the vertical axis, heading angular velocity, yaw angle, lateral deviation of the vehicle relative to the desired path, and distance along the desired path in the s direction. The derivative of the state vector, input Front and rear wheel brake throttle ratio , For steering angle, For vehicle quality, For rotational inertia, This is the distance from the gear to the front tire. This is the distance from the wheel hub to the rear tire. For front tire steering stiffness, For rear tire steering stiffness, , These represent the lateral forces acting on the front and rear tires, respectively. is the coefficient of friction.

2. The model predictive control method based on online model error adjustment constraints according to claim 1, characterized in that, The model error mentioned , As an initial upper bound for the error, define the input and output state constraint sets based on actual physical processes and safety limitations. , , , These are the upper and lower bounds of the input constraints, respectively. , To output the upper and lower bounds of the constraints, For dimension input space, For dimension The output space.

3. The model predictive control method based on online model error adjustment constraints according to claim 1, characterized in that, The input / output constraints include: , To calculate the cumulative error within the prediction period, taking into account feedback effects, based on the error boundary, Represents set operations, , These are the updated sets of input and output state constraints, respectively.

4. The model predictive control method based on online model error adjustment constraints according to claim 1, characterized in that, The nominal system model refers to a predictive control model that does not consider uncertainties, specifically: ,in: At the current sampling time, The total predictive control step size, For the first Prediction step, To predict the control objective function, For system status, For system output, , It is the coefficient matrix of the system state equations. For system observation, For the gain of the state observer, The system observation coefficient matrix, , These are the input and output constraint sets, This is the set of terminal state constraints.

5. The model predictive control method based on online model error adjustment constraints according to claim 1, characterized in that, The aforementioned solution to the model predictive control problem specifically involves: calculating the optimal control law. and will control It applies to actual vehicle systems; The system model error is obtained online by statistical historical error or by set element identification method. .

6. The model predictive control method based on online model error adjustment constraints according to any one of claims 1-5, characterized in that, specifically... include: S1, Construct a nonlinear bicycle model and perform linearization; The linearization process refers to linearizing the derivative increment of the state vector. ,in: The increment of the state vector, Input increment; S2, Constructing the initial model error , For system model error, This is the upper bound of the initial error. For the output dimension; define the input and output state constraint sets based on actual physical processes and safety limitations. , ,in: , These are the upper and lower bounds of the input constraints, respectively. , To output the upper and lower bounds of the constraints; For dimension input space, For dimension The output space; S3, Calculate the cumulative error within the prediction period, taking into account feedback, based on the error boundary. This leads to the modification of input and output constraints. , ,in: To calculate the cumulative error within the prediction period, taking into account feedback effects, based on the error boundary, Represents set operations; , These are the updated sets of input and output state constraints, respectively. S4. Using the linear vehicle model obtained in step S1, and based on the constraints obtained in steps S2 and S3, construct a nominal system model to solve the model predictive control problem and calculate the optimal control law. and will control When applied to a real vehicle system, for a state-space equation optimization problem: ,in: At the current sampling time, The total predictive control step size, For the first Prediction step, To predict the control objective function, For system status, For system output, , It is the coefficient matrix of the system state equations. For system observation, For the gain of the state observer, The system observation coefficient matrix, , These are the input and output constraint sets, For the terminal state constraint set; S5 obtains the system model error by statistically analyzing historical errors. ,in: For system model error, This is the upper bound of the error of the system model after online updates. For output dimensions; The operation process for the statistical historical error is as follows: Record the deviation from the model prediction value through online observation; S6, in the new control cycle, return to step S3 to obtain the new error boundary and repeat the operation, finally realizing model predictive control.

7. A system for implementing the model predictive control method based on online model error adjustment constraints as described in any one of claims 1-6, characterized in that, include: The system comprises an initialization constraint unit, a model predictive control (MRC) solution unit, a data collection unit, and a constraint update unit. Specifically: the initialization constraint unit defines input and output state constraint sets based on actual physical processes and safety limitations, performs initial error estimation, and estimates the initial input and output state constraint sets. The model predictive control solution unit solves the nominal model predictive control problem based on the linearized model and the unit's input and output state constraint sets, obtaining the optimal output. The data collection unit applies the optimal output to the actual system and obtains new error information through observation. The constraint update unit updates the input and output state constraint sets based on the new error information, obtaining the input and output state constraint sets for the optimization problem at the next time step.

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