Self-adaptive dynamic programming-based robust tracking control method and system for soil cabin pressure of soil pressure balance shield tunneling machine

Abstract

The invention discloses an earth pressure balance shield machine earth cabin pressure robust tracking control method and system based on adaptive dynamic programming, and the method comprises the following steps: collecting historical operation data of an earth cabin pressure system of an earth pressure balance shield machine, and carrying out the preprocessing of the historical operation data, and obtaining the preprocessed data; performing dynamic modeling on the soil cabin pressure system by using the preprocessed data, constructing an RBF-ARX model, and optimizing the RBF-ARX model; the optimized RBF-ARX model is reconstructed, and a state space model is obtained; then constructing a comprehensive controller comprising a steady-state controller and a disturbance feedback controller; and converting the state space model into an equivalent nominal system through a utility function, then constructing an optimality equation of dynamic programming, learning a control strategy through an adaptive dynamic programming method, and obtaining approximate optimal control input of the nominal system.

Description

Technical Field

[0001] This invention belongs to the field of tunnel engineering construction control technology, and in particular relates to a robust tracking control method and system for earth pressure balance shield machine earth chamber pressure based on adaptive dynamic programming. Background Technology

[0002] In earth pressure balance (EPB) tunnel boring machine (TBM) construction, precise and stable control of earth chamber pressure is crucial to preventing surface subsidence. Existing control technologies rely on accurate mathematical models. However, the earth chamber pressure system of the TBM is strongly coupled with multiple factors such as complex geology and tunneling speed, making its nonlinear dynamics difficult to model accurately. Model mismatch leads to a decline in control performance. On the other hand, existing robust control methods based on adaptive dynamic programming are mainly geared towards continuous-time systems, typically assuming that the system state is measurable or dependent on a state observer. When applied to discrete-time (DT) systems with practical embedded implementations, they struggle to effectively handle completely unknown dynamic uncertainties and external bounded disturbances (such as groundwater pressure fluctuations), resulting in insufficient robustness and increased tracking errors. Summary of the Invention

[0003] To address the problems of existing technologies, this invention proposes a robust tracking control method for earth chamber pressure in discrete-time nonlinear systems based on adaptive winter programming. The core of this method lies in abandoning the reliance on precise mechanistic models and employing a data-driven model dynamic identification system based on radial basis function networks (RBF-ARX). Furthermore, it innovatively constructs a comprehensive structure including a steady-state controller and a disturbance feedback controller. By defining a modified utility function, the robust tracking problem is transformed into the optimal control problem of the nominal system. Finally, the optimal control strategy is learned online using an adaptive dynamic programming (ADP) method within the discrete-time Hamiltonian-Jacobi-Bellman (DT HJB) equation framework.

[0004] The technical solution of this invention is implemented as follows:

[0005] A robust tracking control method for earth pressure balance shield tunneling machine earth chamber pressure based on adaptive dynamic programming includes the following steps:

[0006] S1. Collect historical operating data of the earth pressure balance shield machine's earth chamber pressure system, preprocess the historical operating data, and obtain the preprocessed data.

[0007] S2. Use the preprocessed data to dynamically model the soil chamber pressure system, construct the RBF-ARX model, and optimize the RBF-ARX model.

[0008] S3. Reconstruct the optimized RBF-ARX model to obtain the state-space model; then construct a comprehensive controller that includes a steady-state controller and a disturbance feedback controller; transform the state-space model into an equivalent nominal system through a utility function; then construct the optimality equation of dynamic programming; learn the control strategy through an adaptive dynamic programming method to obtain the approximate optimal control input of the nominal system.

[0009] Furthermore, in S1, the historical operating data includes earth pressure, screw conveyor speed, propulsion speed, total thrust, and foam flow rate;

[0010] The historical operating data is preprocessed, specifically by interpolating missing values ​​at a sampling period of 1 second to obtain preprocessed data.

[0011] Furthermore, in S2, the network approximation state dependence coefficients of the Gaussian radial basis function are used to construct the RBF-ARX model; the linear and nonlinear parameters are alternately updated to optimize the RBF-ARX model.

[0012] Linear parameters are optimized using regularized least squares, while nonlinear parameters are optimized using gradient-based optimization algorithms.

[0013] Furthermore, for the earth pressure system of the earth pressure balance shield machine, the RBF-ARX model is used to describe its dynamic characteristics, namely:

[0014]

[0015] Where k represents discrete time, y represents earth pressure output, u represents the input vector consisting of screw conveyor speed, propulsion speed, and total thrust, v represents the measurable disturbance variable in foam flow rate, and n y Indicates the order of the output, n u Indicates the order of the input, n v The order of the perturbation is represented by α0(s(k)), where w represents the uncertain perturbation including modeling error.

[0016] The state dependence coefficients, which vary with the system operating point s(k), are represented by a Gaussian radial basis function vector, and s(k) represents the state variables related to the input and output.

[0017] Furthermore, in step S3, the optimized RBF-ARX model is reconstructed to obtain a state-space model, specifically including: defining the output bias:

[0018] Δy(k+i)=y(k+i)-y r,k+i (i = 1, 0, -1, -2, ...);

[0019] Where Δy(k+i) represents the output deviation, y r,k+i This represents the expected output at time k+i;

[0020] Define the input increment:

[0021] Δu(k+j)=u(k+j)-u(k+j-1)(j=0,-1,-2,…);

[0022] Where Δu(k+j) represents the input increment;

[0023] Construct a one-step forward prediction output bias model:

[0024]

[0025] Where, k n =max{n y ,n u}, y r,k+i Let α represent the expected output of the system at time k+i. 0,k , and Let α0(s(k)) represent the state dependence coefficients in the RBF-ARX model. and

[0026] Define the state vector:

[0027]

[0028] Where Δx(k+1) represents the state vector,

[0029]

[0030] Construct a state-space model based on the state vector:

[0031]

[0032] in,

[0033] Furthermore, in step S3, a comprehensive controller comprising a steady-state controller and a disturbance feedback controller is constructed. Specifically, this is achieved by setting the desired trajectory Δx of the state-space model. d (k) is in the form of:

[0034]

[0035] Where, Δu d (k) is the desired control input to the system, Δx d (k) represents the desired trajectory of the state-space model, Δyd (k) represents the desired output deviation. It is known at time k;

[0036] The stable controller Δu is obtained d The formula for (k) is:

[0037]

[0038] Among them, (CB) k ) -1 Indicates CB k The false rebellion.

[0039] Furthermore, based on the state-space model and the desired trajectory, the error system can be represented as:

[0040]

[0041] Where z(k)=Δx(k)-Δx d (k), δu(k)=Δu(k)-Δu d (k),

[0042] The nominal system corresponding to the error system is defined as follows:

[0043]

[0044] The corresponding utility function is defined as:

[0045]

[0046] Among them, l(z,δu)=U(z,δu)+μ(z), μ(z)≥0, Let Q1 > 0 and R1 > 0 be the basic utility function, and let Q1 > 0 and R1 > 0 be the weight matrices.

[0047] The modification term of the utility function is defined as:

[0048]

[0049] Where, λ max (·) represents the largest eigenvalue of the matrix. It represents V * The Hessian matrix of (z(k)), λ f It is the upper bound of ||d||, that is,

[0050] Furthermore, based on the utility function, the optimality equation for dynamic programming is constructed, namely the DT HJB equation, which is:

[0051] V(z)=μ(z(k))+U(z(k),δu(k))+V(A k z(k)+B k δu(k));

[0052] Let V * (z) is the optimal value of V(z). According to the Bellman optimality principle, the optimal value function V * The difference equation satisfied by (z) is:

[0053] V * (z)=min{μ(z(k))+U(z(k),δu(k))+V * (A k z(k)+B k δu(k))};

[0054] According to optimal control theory, the optimal control law is:

[0055]

[0056] Optimal feedback control law δu * The specific formula for calculating (k) is:

[0057]

[0058] Where z(k+1)=A k z(k)+B k δu(k), Represents the gradient vector.

[0059] The optimality equation is further obtained as follows:

[0060] V * (z(k))=μ(z(k))+U(z(k),δu * (k))+V * (A k z(k)+B k δu * (k)).

[0061] Furthermore, the control strategy δu in the DT HJB equations is learned using an adaptive dynamic programming method. * (k) means that performance evaluation and control strategy updates are achieved by alternating between the evaluation network and the action network;

[0062] Let V in the optimality equation * (z(k)) is represented as:

[0063]

[0064] The number of neurons in the hidden layer is N. c , This represents the unknown optimal weight.

[0065] Represents a bounded activation function vector;

[0066] make After the i-th iteration The estimate of V is then * The estimate is expressed as:

[0067]

[0068] Evaluation of the approximation error of the network Defined as:

[0069]

[0070] in, The optimal feedback control law δu after the i-th iteration * The estimated value of (k);

[0071] The weights of the network are evaluated by minimizing the residuals. Training with the square of:

[0072]

[0073] The weight update rule for the evaluation network based on the gradient descent algorithm is as follows:

[0074]

[0075] Where, γ c To evaluate the learning rate of the network,

[0076] Optimal feedback control law δu * (k) is approximated by an action network:

[0077]

[0078] The number of neurons in the hidden layer is N. a , Represents the unknown ideal weight.

[0079] Represents a bounded activation function vector;

[0080] make After the i-th iteration The estimate of the optimal feedback control law δu is then obtained. * The estimate of (z(k)) can be expressed as:

[0081]

[0082] The weights of the action network are trained using an objective function.

[0083]

[0084] in,

[0085]

[0086] The weights of the action network are trained based on the objective function. Based on the gradient descent rule, the weight update formula for the action network is obtained as follows:

[0087]

[0088] Where, γ a >0 represents the learning rate of the action network.

[0089] The robust tracking control system for earth pressure balance shield tunneling machine soil chamber pressure based on adaptive dynamic programming is characterized by applying the robust tracking control method for earth pressure balance shield tunneling machine soil chamber pressure based on adaptive dynamic programming as described above.

[0090] Compared with the prior art, the present invention achieves the following beneficial effects:

[0091] This invention provides a robust tracking control method and system for earth pressure balance shield tunneling machine earth chamber pressure based on adaptive dynamic programming. It is applicable to DT nonlinear systems with unknown and uncertain disturbances, such as the earth pressure system of an earth pressure balance shield tunneling machine. This method achieves dynamic identification of the unknown system through a data-driven RBF-ARX model, requiring no prior knowledge of the underlying mechanisms. By constructing a comprehensive control structure including a steady-state controller and a disturbance feedback controller, and combining a modified utility function and the DT HJB equations, unbiased tracking of earth pressure under bounded disturbances is achieved.

[0092] The significant advantages of this method are: it only uses measurable input / output data, without the need for state observers or precise models; its robust controller can effectively compensate for all unknown bounded uncertainties (including constant disturbances), ensuring that the soil chamber pressure tracks the expected value quickly and without deviation under complex disturbances, thereby improving the safety and efficiency of shield tunneling.

[0093] The method presented in this invention reconstructs the system state using only measurable system input / output data, without requiring a state observer, which differs from most existing works that rely on state observers or measurable system states.

[0094] The robust controller provided by this invention includes a steady-state controller and a disturbance feedback controller based on the ADP method, which can allow the realization of all unknown bounded uncertainties, including the case of constant unknown disturbances.

[0095] The robust controller constructed in this invention can accommodate all unknown bounded uncertainties, including constant unknown disturbances. When the tunnel boring machine's soil chamber system is subjected to external bounded disturbances (such as sinusoidal disturbances or square wave disturbances), its pressure can quickly converge to the desired value. Attached Figure Description

[0096] Figure 1 This is a flowchart of a robust tracking control method for earth pressure balance shield machine earth chamber pressure based on adaptive dynamic programming, provided in an embodiment of the present invention. Detailed Implementation

[0097] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0098] Example

[0099] like Figure 1 A robust tracking control method for earth pressure balance shield tunneling machine earth chamber pressure based on adaptive dynamic programming includes the following steps:

[0100] S1. Collect historical operating data of the earth pressure balance shield machine's earth chamber pressure system, preprocess the historical operating data, and obtain the preprocessed data.

[0101] S2. Use the preprocessed data to dynamically model the soil chamber pressure system, construct the RBF-ARX model, and optimize the RBF-ARX model.

[0102] S3. Reconstruct the optimized RBF-ARX model to obtain the state-space model; then construct a comprehensive controller that includes a steady-state controller and a disturbance feedback controller; transform the state-space model into an equivalent nominal system through a utility function; then construct the optimality equation of dynamic programming; learn the control strategy through an adaptive dynamic programming method to obtain the approximate optimal control input of the nominal system.

[0103] The English abbreviations and their corresponding meanings involved in this invention are as follows:

[0104] SCRS: Screw Conveyor Rotational Speed

[0105] AS: Advance Speed

[0106] TTF: Total Thrust Force

[0107] RBF-ARX: Radial Basis Function-AutoRegressive with eXogenous Input

[0108] DT HJB: Discrete-Time Hamilton-Jacobi-Bellman Equations

[0109] ADP: Adaptive Dynamic Programming

[0110] EPB: Earth Pressure Balance

[0111] CT: Continuous-Time

[0112] DT: Discrete-Time

[0113] Specifically, the model is reconstructed into a state-space model of the reference trajectory deviation, thus transforming the robust tracking problem into a robust regulation problem. A comprehensive controller, including a steady-state controller and a disturbance feedback controller, is constructed. By selecting an appropriate utility function, the robust regulation problem is transformed into the optimal control problem of the equivalent nominal system. For the optimal control problem, the optimality equation of dynamic programming, namely the discrete-time Hamilton-Jacobi-Bellman (DT HJB) equation, is constructed. The control strategy is learned through adaptive dynamic programming (ADP) to obtain the approximate optimal control input of the nominal system.

[0114] In S1, the historical operating data includes earth pressure (EP), screw conveyor speed (SCRS), propulsion speed (AS), total thrust (TTF), and foam flow rate (FFR);

[0115] The historical operating data is preprocessed, specifically by interpolating missing values ​​at a sampling period of 1 second to obtain preprocessed data.

[0116] The missing values ​​are interpolated at a sampling period of 1 second. First, a linear function passing through the known missing data points is constructed based on the historical data points before and after the missing data. Then, the value of the unknown points is calculated through the linear function to obtain the preprocessed data.

[0117] Specifically, historical operational data also includes data on non-excavation states such as segment assembly and routine maintenance.

[0118] In S2, the network approximation state dependence coefficients of the Gaussian radial basis function are used to construct the RBF-ARX model; the linear and nonlinear parameters are alternately updated to optimize the RBF-ARX model.

[0119] Linear parameters are optimized using regularized least squares (LSM) to address overfitting and improve generalization ability by imposing constraints on the model parameters. Nonlinear parameters are solved using gradient-based optimization algorithms, such as the Levenberg-Marquardt algorithm.

[0120] For the earth pressure balance shield machine's earth pressure system, the RBF-ARX model is used to describe its dynamic characteristics, namely:

[0121] Where k represents discrete time, y represents earth pressure output, u represents the input vector consisting of screw conveyor speed, propulsion speed, and total thrust, v represents the measurable disturbance variable in foam flow rate, and n y Indicates the order of the output, n u Indicates the order of the input, n v The order of the perturbation is represented by α0(s(k)), where w represents the uncertain perturbation including modeling error.

[0122] The state dependence coefficients, which vary with the system operating point s(k), are represented by a Gaussian radial basis function vector, and s(k) represents the state variables related to the input and output.

[0123] In step S3, the optimized RBF-ARX model is reconstructed to obtain a state-space model, specifically including: defining the output bias:

[0124] Δy(k+i)=y(k+i)-y r,k+i (i = 1, 0, -1, -2, ...);

[0125] Where Δy(k+i) represents the output deviation, y r,k+i This represents the expected output at time k+i;

[0126] Define the input increment:

[0127] Δu(k+j)=u(k+j)-u(k+j-1)(j=0,-1,-2,…);

[0128] Where Δu(k+j) represents the input increment;

[0129] Construct a one-step forward prediction output bias model:

[0130]

[0131] Where, k n =max{n y ,n u}, y r,k+i Let α represent the expected output of the system at time k+i. 0,k , and Let α0(s(k)) represent the state dependence coefficients in the RBF-ARX model. and

[0132] Define the state vector:

[0133]

[0134] Where Δx(k+1) represents the state vector,

[0135]

[0136] Construct a state-space model based on the state vector:

[0137]

[0138] in,

[0139] In step S3, a comprehensive controller comprising a steady-state controller and a disturbance feedback controller is constructed. Specifically, the desired trajectory Δx of the state-space model is defined. d (k) is in the form of:

[0140]

[0141] Where, Δu d (k) is the desired control input to the system, Δx d (k) represents the desired trajectory of the state-space model, Δy d (k) represents the desired output deviation. It is known at time k;

[0142] The stable controller Δu is obtained d The formula for (k) is:

[0143]

[0144] Among them, (CB) k ) -1 Indicates CB k The false rebellion.

[0145] Based on the state-space model and the desired trajectory, the error system is represented as:

[0146]

[0147] Where z(k)=Δx(k)-Δx d (k), δu(k)=Δu(k)-Δu d (k),

[0148] The nominal system corresponding to the error system is defined as follows:

[0149]

[0150] The corresponding utility function is defined as:

[0151]

[0152] Among them, l(z,δu)=U(z,δu)+μ(z), μ(z)≥0, Let Q1 > 0 and R1 > 0 be the basic utility function, and let Q1 > 0 and R1 > 0 be the weight matrices.

[0153] The modification term of the utility function is defined as:

[0154]

[0155] Where, λ max (·) represents the largest eigenvalue of the matrix. It represents V * The Hessian matrix of (z(k)), λ f It is the upper bound of ||d||, that is,

[0156] For a nominal system with a modified utility function, if μ(z(k)) is defined as follows, then according to Lyapunov stability theory, the optimal control policy δu * (k) can ensure the asymptotic stability of the error system.

[0157] Based on the utility function, construct the optimality equation for the dynamic programming problem, namely the DT HJB equation, which is:

[0158] V(z)=μ(z(k))+U(z(k),δu(k))+V(A k z(k)+B k δu(k));

[0159] Let V * (z) is the optimal value of V(z). According to the Bellman optimality principle, the optimal value function V * The difference equation satisfied by (z) is:

[0160] V * (z)=min{μ(z(k))+U(z(k),δu(k))+V * (A k z(k)+B k δu(k))};

[0161] According to optimal control theory, the optimal control law is:

[0162]

[0163] Optimal feedback control law δu * The specific calculation formula for (k) (corresponding to the disturbance feedback controller) is as follows:

[0164]

[0165] Where z(k+1)=A k z(k)+B k δu(k), Represents the gradient vector.

[0166] The optimality equation is further obtained as follows:

[0167] V * (z(k))=μ(z(k))+U(z(k),δu * (k))+V * (A k z(k)+B k δu * (k));

[0168] The control strategy δu in the DT HJB equations is learned using an adaptive dynamic programming method. * (k) means that performance evaluation and control strategy updates are achieved by alternating between the evaluation network and the action network;

[0169] Let V in the optimality equation * (z(k)) is represented as:

[0170]

[0171] The number of neurons in the hidden layer is N. c ,

[0172] This represents the unknown optimal weight.

[0173] Represents a bounded activation function vector;

[0174] make After the i-th iteration The estimate of V is then * The estimate is expressed as:

[0175]

[0176] Evaluation of the approximation error of the network Defined as:

[0177]

[0178] in, The optimal feedback control law δu after the i-th iteration * The estimated value of (k);

[0179] The weights of the network are evaluated by minimizing the residuals. Training with the square of:

[0180]

[0181] The weight update rule for the evaluation network based on the gradient descent algorithm is as follows:

[0182]

[0183] Where, γ c To evaluate the learning rate of the network,

[0184] Optimal feedback control law δu * (k) is approximated by an action network:

[0185]

[0186] The number of neurons in the hidden layer is N. a , Represents the unknown ideal weight.

[0187] Represents a bounded activation function vector;

[0188] make After the i-th iteration The estimate of the optimal feedback control law δu is then obtained. * The estimate of (z(k)) can be expressed as:

[0189]

[0190] The weights of the action network are trained using an objective function.

[0191]

[0192] in,

[0193]

[0194] The weights of the action network are trained based on the objective function. Based on the gradient descent rule, the weight update formula for the action network is obtained as follows:

[0195]

[0196] Where, γ a >0 is the learning rate of the action network.

[0197] The online control and parameter iterative optimization process designed in this invention is divided into two stages: offline and online. In the offline stage, historical data is used to estimate model parameters, determine the model order, and complete initialization (iteration count, network weights, etc.), constructing an initial state based on historical input and output data. In the online stage, a cyclical iteration is initiated, using the estimated model parameters and state variables to calculate the correlation matrix and control input. The control input is applied to the actual system to obtain the output. Then, the evaluation network and action network are trained and their parameters are updated. Simultaneously, the collected input-output sequences and state variables are continuously updated. The process stops when the number of iterations reaches its maximum and the parameter convergence condition is met (parameter change is less than a threshold). Finally, relevant approximate values ​​are recorded, achieving online optimization control and parameter adjustment of the system.

[0198] The robust tracking control system for earth pressure balance shield tunneling machine soil chamber pressure based on adaptive dynamic programming is characterized by applying the robust tracking control method for earth pressure balance shield tunneling machine soil chamber pressure based on adaptive dynamic programming as described above.

[0199] Based on the disclosure and teachings of the foregoing specification, those skilled in the art can make changes and modifications to the above embodiments. Therefore, the present invention is not limited to the specific embodiments disclosed and described above, and some modifications and changes to the present invention should also fall within the protection scope of the claims of the present invention. Furthermore, although some specific terms are used in this specification, these terms are only for convenience of explanation and do not constitute any limitation on the present invention.

Claims

1. A robust tracking control method for earth pressure balance shield machine earth chamber pressure based on adaptive dynamic programming, characterized in that, Includes the following steps: S1. Collect historical operating data of the earth pressure balance shield machine's earth chamber pressure system, preprocess the historical operating data, and obtain the preprocessed data. S2. Use the preprocessed data to dynamically model the soil chamber pressure system, construct the RBF-ARX model, and optimize the RBF-ARX model. S3. Reconstruct the optimized RBF-ARX model to obtain the state-space model; then construct a comprehensive controller that includes a steady-state controller and a disturbance feedback controller; transform the state-space model into an equivalent nominal system through a utility function; then construct the optimality equation of dynamic programming; learn the control strategy through an adaptive dynamic programming method to obtain the approximate optimal control input of the nominal system.

2. The robust tracking control method for earth pressure balance shield machine earth chamber pressure based on adaptive dynamic programming according to claim 1, characterized in that, In S1, the historical operating data includes earth pressure, screw conveyor speed, propulsion speed, total thrust, and foam flow rate; The historical operating data is preprocessed, specifically by interpolating missing values ​​at a sampling period of 1 second to obtain preprocessed data.

3. The robust tracking control method for earth pressure balance shield machine earth chamber pressure based on adaptive dynamic programming according to claim 2, characterized in that, In S2, the network approximation state dependence coefficients of the Gaussian radial basis function are used to construct the RBF-ARX model; the linear and nonlinear parameters are alternately updated to optimize the RBF-ARX model. Linear parameters are optimized using regularized least squares, while nonlinear parameters are optimized using gradient-based optimization algorithms.

4. The robust tracking control method for earth pressure balance shield machine earth chamber pressure based on adaptive dynamic programming according to claim 3, characterized in that, For the earth pressure balance shield machine's earth pressure system, the RBF-ARX model is used to describe its dynamic characteristics, namely: Where k represents discrete time, y represents earth pressure output, u represents the input vector consisting of screw conveyor speed, propulsion speed, and total thrust, v represents the measurable disturbance variable in foam flow rate, and n y Indicates the order of the output, n u Indicates the order of the input, n v The order of the perturbation is represented by α0(s(k)), where w represents the uncertain perturbation including modeling error. The state dependence coefficients, which vary with the system operating point s(k), are represented by a Gaussian radial basis function vector, and s(k) represents the state variables related to the input and output.

5. The robust tracking control method for earth pressure balance shield machine earth chamber pressure based on adaptive dynamic programming according to claim 4, characterized in that, In step S3, the optimized RBF-ARX model is reconstructed to obtain a state-space model, specifically including: defining the output bias: Ay(k + i) = y(k + i) - y(k + i - 1) r,k+i (i = 1, 0, -1, -2,...); where Δy(k+i) represents the output deviation, y r,k+i represents the expected output at the k+i time; Define the input increment: Δu(k+j)=u(k+j)-u(k+j-1)(j=0,-1,-2,…); Where Δu(k+j) represents the input increment; Construct a one-step forward prediction output bias model: Where, k n =max{n y ,n u }, y r,k+i Let α represent the expected output of the system at time k+i. 0,k , and Let α0(s(k)) represent the state dependence coefficients in the RBF-ARX model. and Define the state vector: Where Δx(k+1) represents the state vector, Construct a state-space model based on the state vector: in, 6. The robust tracking control method for earth pressure balance shield machine earth chamber pressure based on adaptive dynamic programming according to claim 5, characterized in that, In the S3, a comprehensive controller containing a steady-state controller and a disturbance feedback controller is constructed, and the specific method is to set the desired trajectory Δx of the state space model d (k) is in the form of: Where, Δu d (k) is the desired control input to the system, Δx d (k) represents the desired trajectory of the state-space model, Δy d (k) represents the desired output deviation. It is known at time k; The stable controller Δu d The formula for (k) is: Among them, (CB) k ) -1 Indicates CB k The false rebellion.

7. The robust tracking control method for earth pressure balance shield machine earth chamber pressure based on adaptive dynamic programming according to claim 6, characterized in that, Based on the state-space model and the desired trajectory, the error system is represented as: Where, z(k)=Δx(k)-Δx d (k), δu(k)=Δu(k)-Δu d (k), The nominal system corresponding to the error system is defined as follows: The corresponding utility function is defined as: Among them, l(z,δu)=U(z,δu)+μ(z), μ(z)≥0, Let Q1 > 0 and R1 > 0 be the basic utility function, and let Q1 > 0 and R1 > 0 be the weight matrices. The modification term of the utility function is defined as: Where, λ max (·) represents the largest eigenvalue of the matrix, V * (z(k)) is the optimal value function, ▽V * (z(k)) represents V * The first derivative of (z(k)), δu * (k) is the optimal value of δu(k). It represents V * The Hessian matrix of (z(k)), λ f It is the upper bound of ||d||, that is, 8. The robust tracking control method for earth pressure balance shield machine earth chamber pressure based on adaptive dynamic programming according to claim 7, characterized in that, Based on the utility function, construct the optimality equation for the dynamic programming problem, namely the DT HJB equation, which is: V(z)=μ(z(k))+U(z(k),δu(k))+V(A k z(k)+B k δu(k)); Let V * (z) is the optimal value of V(z). According to the Bellman optimality principle, the optimal value function V * The difference equation satisfied by (z) is: V * (z)=min{μ(z(k))+U(z(k),δu(k))+V * (AND k z(k)+B k δu(k))}; According to optimal control theory, the optimal control law is: Optimal feedback control law δu * The specific formula for calculating (k) is: Where z(k+1)=A k z(k)+B k δu(k), Represents the gradient vector. The optimality equation is further obtained as follows: V * (z(k))=μ(z(k))+U(z(k),δu * (k))+V * (AND k z(k)+B k δu * (k))。 9. The robust tracking control method for earth pressure balance shield machine earth chamber pressure based on adaptive dynamic programming according to claim 8, characterized in that, The control strategy δu in the DT HJB equations is learned using an adaptive dynamic programming method. * (k) means that performance evaluation and control strategy updates are achieved by alternating between the evaluation network and the action network; Let V in the optimality equation * (z(k)) is represented as: The number of neurons in the hidden layer is N. c , This represents the unknown optimal weight. Represents a bounded activation function vector; make After the i-th iteration The estimate of V is then * The estimate is expressed as: Evaluation of the approximation error of the network Defined as: in, The optimal feedback control law δu after the i-th iteration * The estimated value of (k); The weights of the network are evaluated by minimizing the residuals. Training with the square of: The weight update rule for the evaluation network based on the gradient descent algorithm is as follows: Where, γ c To evaluate the learning rate of the network, Optimal feedback control law δu * (k) is approximated by an action network: The number of neurons in the hidden layer is N. a , Represents the unknown ideal weight. Represents a bounded activation function vector; make After the i-th iteration The estimate of the optimal feedback control law δu is then obtained. * The estimate of (z(k)) can be expressed as: The weights of the action network are trained using an objective function. in, The weights of the action network are trained based on the objective function. Based on the gradient descent rule, the weight update formula for the action network is obtained as follows: Where, γ a >0 represents the learning rate of the action network.

10. A robust tracking control system for earth pressure balance shield machine earth chamber pressure based on adaptive dynamic programming, characterized in that, The robust tracking control method for earth pressure balance shield machine earth chamber pressure based on adaptive dynamic programming, as described in any one of claims 1 to 9, was applied.

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